# API¶

Top level user functions:

 add(x1, x2, /[, out, where, casting, order, …]) This docstring was copied from numpy.add. all(a[, axis, keepdims, split_every, out]) Test whether all array elements along a given axis evaluate to True. allclose(arr1, arr2[, rtol, atol, equal_nan]) Returns True if two arrays are element-wise equal within a tolerance. angle(x[, deg]) Return the angle of the complex argument. any(a[, axis, keepdims, split_every, out]) Test whether any array element along a given axis evaluates to True. append(arr, values[, axis]) Append values to the end of an array. apply_along_axis(func1d, axis, arr, *args[, …]) Apply a function to 1-D slices along the given axis. apply_over_axes(func, a, axes) Apply a function repeatedly over multiple axes. arange(*args, **kwargs) Return evenly spaced values from start to stop with step size step. arccos(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.arccos. arccosh(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.arccosh. arcsin(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.arcsin. arcsinh(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.arcsinh. arctan(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.arctan. arctan2(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.arctan2. arctanh(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.arctanh. argmax(x[, axis, split_every, out]) Return the maximum of an array or maximum along an axis. argmin(x[, axis, split_every, out]) Return the minimum of an array or minimum along an axis. argtopk(a, k[, axis, split_every]) Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. argwhere(a) Find the indices of array elements that are non-zero, grouped by element. around(x[, decimals]) Evenly round to the given number of decimals. array(object[, dtype, copy, order, subok, …]) This docstring was copied from numpy.array. asanyarray(a) Convert the input to a dask array. asarray(a, **kwargs) Convert the input to a dask array. atleast_1d(*arys) Convert inputs to arrays with at least one dimension. atleast_2d(*arys) View inputs as arrays with at least two dimensions. atleast_3d(*arys) View inputs as arrays with at least three dimensions. average(a[, axis, weights, returned]) Compute the weighted average along the specified axis. bincount(x[, weights, minlength]) This docstring was copied from numpy.bincount. bitwise_and(x1, x2, /[, out, where, …]) This docstring was copied from numpy.bitwise_and. bitwise_not(x, /[, out, where, casting, …]) This docstring was copied from numpy.invert. bitwise_or(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.bitwise_or. bitwise_xor(x1, x2, /[, out, where, …]) This docstring was copied from numpy.bitwise_xor. block(arrays[, allow_unknown_chunksizes]) Assemble an nd-array from nested lists of blocks. blockwise(func, out_ind, *args[, name, …]) Tensor operation: Generalized inner and outer products broadcast_arrays(*args, **kwargs) Broadcast any number of arrays against each other. broadcast_to(x, shape[, chunks, meta]) Broadcast an array to a new shape. cbrt(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.cbrt. coarsen(reduction, x, axes[, trim_excess]) Coarsen array by applying reduction to fixed size neighborhoods ceil(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.ceil. choose(a, choices) Construct an array from an index array and a set of arrays to choose from. clip(*args, **kwargs) Clip (limit) the values in an array. compress(condition, a[, axis]) Return selected slices of an array along given axis. concatenate(seq[, axis, …]) Concatenate arrays along an existing axis conj(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.conjugate. copysign(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.copysign. corrcoef(x[, y, rowvar]) Return Pearson product-moment correlation coefficients. cos(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.cos. cosh(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.cosh. count_nonzero(a[, axis]) Counts the number of non-zero values in the array a. cov(m[, y, rowvar, bias, ddof]) Estimate a covariance matrix, given data and weights. cumprod(x[, axis, dtype, out, method]) Return the cumulative product of elements along a given axis. cumsum(x[, axis, dtype, out, method]) Return the cumulative sum of the elements along a given axis. deg2rad(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.deg2rad. degrees(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.degrees. diag(v) Extract a diagonal or construct a diagonal array. diagonal(a[, offset, axis1, axis2]) Return specified diagonals. diff(a[, n, axis]) Calculate the n-th discrete difference along the given axis. divmod(x1, x2[, out1, out2], / [[, out, …]) This docstring was copied from numpy.divmod. digitize(a, bins[, right]) Return the indices of the bins to which each value in input array belongs. dot(a, b[, out]) This docstring was copied from numpy.dot. dstack(tup[, allow_unknown_chunksizes]) Stack arrays in sequence depth wise (along third axis). ediff1d(ary[, to_end, to_begin]) The differences between consecutive elements of an array. einsum(subscripts, *operands[, out, dtype, …]) This docstring was copied from numpy.einsum. empty(*args, **kwargs) Blocked variant of empty empty_like(a[, dtype, order, chunks, name, …]) Return a new array with the same shape and type as a given array. equal(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.equal. exp(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.exp. exp2(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.exp2. expm1(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.expm1. eye(N[, chunks, M, k, dtype]) Return a 2-D Array with ones on the diagonal and zeros elsewhere. fabs(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.fabs. fix(*args, **kwargs) Round to nearest integer towards zero. flatnonzero(a) Return indices that are non-zero in the flattened version of a. flip(m, axis) Reverse element order along axis. flipud(m) Flip array in the up/down direction. fliplr(m) Flip array in the left/right direction. float_power(x1, x2, /[, out, where, …]) This docstring was copied from numpy.float_power. floor(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.floor. floor_divide(x1, x2, /[, out, where, …]) This docstring was copied from numpy.floor_divide. fmax(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.fmax. fmin(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.fmin. fmod(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.fmod. frexp(x[, out1, out2], / [[, out, where, …]) This docstring was copied from numpy.frexp. fromfunction(func[, chunks, shape, dtype]) Construct an array by executing a function over each coordinate. frompyfunc(func, nin, nout, *[, identity]) This docstring was copied from numpy.frompyfunc. full(shape, fill_value, *args, **kwargs) Blocked variant of full full_like(a, fill_value[, order, dtype, …]) Return a full array with the same shape and type as a given array. gradient(f, *varargs, **kwargs) Return the gradient of an N-dimensional array. greater(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.greater. greater_equal(x1, x2, /[, out, where, …]) This docstring was copied from numpy.greater_equal. histogram(a[, bins, range, normed, weights, …]) Blocked variant of numpy.histogram(). histogramdd(sample, bins[, range, normed, …]) Blocked variant of numpy.histogramdd(). hstack(tup[, allow_unknown_chunksizes]) Stack arrays in sequence horizontally (column wise). hypot(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.hypot. imag(*args, **kwargs) Return the imaginary part of the complex argument. indices(dimensions[, dtype, chunks]) Implements NumPy’s indices for Dask Arrays. insert(arr, obj, values, axis) Insert values along the given axis before the given indices. invert(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.invert. isclose(arr1, arr2[, rtol, atol, equal_nan]) Returns a boolean array where two arrays are element-wise equal within a tolerance. iscomplex(*args, **kwargs) Returns a bool array, where True if input element is complex. isfinite(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.isfinite. isin(element, test_elements[, …]) Calculates element in test_elements, broadcasting over element only. isinf(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.isinf. isneginf This docstring was copied from numpy.equal. isnan(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.isnan. isnull(values) pandas.isnull for dask arrays isposinf This docstring was copied from numpy.equal. isreal(*args, **kwargs) Returns a bool array, where True if input element is real. ldexp(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.ldexp. less(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.less. linspace(start, stop[, num, endpoint, …]) Return num evenly spaced values over the closed interval [start, stop]. log(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.log. log10(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.log10. log1p(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.log1p. log2(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.log2. logaddexp(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.logaddexp. logaddexp2(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.logaddexp2. logical_and(x1, x2, /[, out, where, …]) This docstring was copied from numpy.logical_and. logical_not(x, /[, out, where, casting, …]) This docstring was copied from numpy.logical_not. logical_or(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.logical_or. logical_xor(x1, x2, /[, out, where, …]) This docstring was copied from numpy.logical_xor. map_overlap(func, *args[, depth, boundary, …]) Map a function over blocks of arrays with some overlap map_blocks(func, *args[, name, token, …]) Map a function across all blocks of a dask array. matmul(x1, x2, /[, out, casting, order, …]) This docstring was copied from numpy.matmul. max(a[, axis, keepdims, split_every, out]) Return the maximum of an array or maximum along an axis. maximum(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.maximum. mean(a[, axis, dtype, keepdims, …]) Compute the arithmetic mean along the specified axis. median(a[, axis, keepdims, out]) Compute the median along the specified axis. meshgrid(*xi, **kwargs) Return coordinate matrices from coordinate vectors. min(a[, axis, keepdims, split_every, out]) Return the minimum of an array or minimum along an axis. minimum(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.minimum. mod(x1, x2, /[, out, where, casting, order, …]) This docstring was copied from numpy.remainder. modf(x[, out1, out2], / [[, out, where, …]) This docstring was copied from numpy.modf. moment(a, order[, axis, dtype, keepdims, …]) moveaxis(a, source, destination) Move axes of an array to new positions. multiply(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.multiply. nanargmax(x[, axis, split_every, out]) Return the maximum of an array or maximum along an axis, ignoring any NaNs. nanargmin(x[, axis, split_every, out]) Return minimum of an array or minimum along an axis, ignoring any NaNs. nancumprod(x, axis[, dtype, out, method]) Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. nancumsum(x, axis[, dtype, out, method]) Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. nanmax(a[, axis, keepdims, split_every, out]) Return the maximum of an array or maximum along an axis, ignoring any NaNs. nanmean(a[, axis, dtype, keepdims, …]) Compute the arithmetic mean along the specified axis, ignoring NaNs. nanmedian(a[, axis, keepdims, out]) Compute the median along the specified axis, while ignoring NaNs. nanmin(a[, axis, keepdims, split_every, out]) Return minimum of an array or minimum along an axis, ignoring any NaNs. nanprod(a[, axis, dtype, keepdims, …]) Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones. nanstd(a[, axis, dtype, keepdims, ddof, …]) Compute the standard deviation along the specified axis, while ignoring NaNs. nansum(a[, axis, dtype, keepdims, …]) Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. nanvar(a[, axis, dtype, keepdims, ddof, …]) Compute the variance along the specified axis, while ignoring NaNs. nan_to_num(*args, **kwargs) Replace NaN with zero and infinity with large finite numbers (default behaviour) or with the numbers defined by the user using the nan, posinf and/or neginf keywords. negative(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.negative. nextafter(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.nextafter. nonzero(a) Return the indices of the elements that are non-zero. not_equal(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.not_equal. notnull(values) pandas.notnull for dask arrays ones(*args, **kwargs) Blocked variant of ones ones_like(a[, dtype, order, chunks, name, shape]) Return an array of ones with the same shape and type as a given array. outer(a, b) Compute the outer product of two vectors. pad(array, pad_width[, mode]) Pad an array. percentile(a, q[, interpolation, method]) Approximate percentile of 1-D array PerformanceWarning A warning given when bad chunking may cause poor performance piecewise(x, condlist, funclist, *args, **kw) Evaluate a piecewise-defined function. power(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.power. prod(a[, axis, dtype, keepdims, …]) Return the product of array elements over a given axis. ptp(a[, axis]) Range of values (maximum - minimum) along an axis. rad2deg(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.rad2deg. radians(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.radians. ravel(array_like) Return a contiguous flattened array. real(*args, **kwargs) Return the real part of the complex argument. reciprocal(x, /[, out, where, casting, …]) This docstring was copied from numpy.reciprocal. rechunk(x[, chunks, threshold, …]) Convert blocks in dask array x for new chunks. reduction(x, chunk, aggregate[, axis, …]) General version of reductions register_chunk_type(type) Register the given type as a valid chunk and downcast array type remainder(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.remainder. repeat(a, repeats[, axis]) Repeat elements of an array. reshape(x, shape[, merge_chunks]) Reshape array to new shape result_type(*arrays_and_dtypes) This docstring was copied from numpy.result_type. rint(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.rint. roll(array, shift[, axis]) Roll array elements along a given axis. rollaxis(a, axis[, start]) rot90(m[, k, axes]) Rotate an array by 90 degrees in the plane specified by axes. round(a[, decimals]) Round an array to the given number of decimals. sign(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.sign. signbit(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.signbit. sin(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.sin. sinc(*args, **kwargs) Return the normalized sinc function. sinh(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.sinh. sqrt(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.sqrt. square(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.square. squeeze(a[, axis]) Remove axes of length one from a. stack(seq[, axis, allow_unknown_chunksizes]) Stack arrays along a new axis std(a[, axis, dtype, keepdims, ddof, …]) Compute the standard deviation along the specified axis. subtract(x1, x2, /[, out, where, casting, …]) This docstring was copied from numpy.subtract. sum(a[, axis, dtype, keepdims, split_every, out]) Sum of array elements over a given axis. take(a, indices[, axis]) Take elements from an array along an axis. tan(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.tan. tanh(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.tanh. tensordot(lhs, rhs[, axes]) Compute tensor dot product along specified axes. tile(A, reps) Construct an array by repeating A the number of times given by reps. topk(a, k[, axis, split_every]) Extract the k largest elements from a on the given axis, and return them sorted from largest to smallest. trace(a[, offset, axis1, axis2, dtype]) Return the sum along diagonals of the array. transpose(a[, axes]) Reverse or permute the axes of an array; returns the modified array. true_divide(x1, x2, /[, out, where, …]) This docstring was copied from numpy.true_divide. tril(m[, k]) Lower triangle of an array. triu(m[, k]) Upper triangle of an array. trunc(x, /[, out, where, casting, order, …]) This docstring was copied from numpy.trunc. unify_chunks(*args, **kwargs) Unify chunks across a sequence of arrays unique(ar[, return_index, return_inverse, …]) Find the unique elements of an array. unravel_index(indices, shape[, order]) This docstring was copied from numpy.unravel_index. var(a[, axis, dtype, keepdims, ddof, …]) Compute the variance along the specified axis. vdot(a, b) This docstring was copied from numpy.vdot. vstack(tup[, allow_unknown_chunksizes]) Stack arrays in sequence vertically (row wise). where(condition, [x, y]) This docstring was copied from numpy.where. zeros(*args, **kwargs) Blocked variant of zeros zeros_like(a[, dtype, order, chunks, name, …]) Return an array of zeros with the same shape and type as a given array.

## Fast Fourier Transforms¶

 fft.fft_wrap(fft_func[, kind, dtype]) Wrap 1D, 2D, and ND real and complex FFT functions fft.fft(a[, n, axis]) Wrapping of numpy.fft.fft fft.fft2(a[, s, axes]) Wrapping of numpy.fft.fft2 fft.fftn(a[, s, axes]) Wrapping of numpy.fft.fftn fft.ifft(a[, n, axis]) Wrapping of numpy.fft.ifft fft.ifft2(a[, s, axes]) Wrapping of numpy.fft.ifft2 fft.ifftn(a[, s, axes]) Wrapping of numpy.fft.ifftn fft.rfft(a[, n, axis]) Wrapping of numpy.fft.rfft fft.rfft2(a[, s, axes]) Wrapping of numpy.fft.rfft2 fft.rfftn(a[, s, axes]) Wrapping of numpy.fft.rfftn fft.irfft(a[, n, axis]) Wrapping of numpy.fft.irfft fft.irfft2(a[, s, axes]) Wrapping of numpy.fft.irfft2 fft.irfftn(a[, s, axes]) Wrapping of numpy.fft.irfftn fft.hfft(a[, n, axis]) Wrapping of numpy.fft.hfft fft.ihfft(a[, n, axis]) Wrapping of numpy.fft.ihfft fft.fftfreq(n[, d, chunks]) Return the Discrete Fourier Transform sample frequencies. fft.rfftfreq(n[, d, chunks]) Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). fft.fftshift(x[, axes]) Shift the zero-frequency component to the center of the spectrum. fft.ifftshift(x[, axes]) The inverse of fftshift.

## Linear Algebra¶

 linalg.cholesky(a[, lower]) Returns the Cholesky decomposition, $$A = L L^*$$ or $$A = U^* U$$ of a Hermitian positive-definite matrix A. linalg.inv(a) Compute the inverse of a matrix with LU decomposition and forward / backward substitutions. linalg.lstsq(a, b) Return the least-squares solution to a linear matrix equation using QR decomposition. linalg.lu(a) Compute the lu decomposition of a matrix. linalg.norm(x[, ord, axis, keepdims]) Matrix or vector norm. linalg.qr(a) Compute the qr factorization of a matrix. linalg.solve(a, b[, sym_pos]) Solve the equation a x = b for x. linalg.solve_triangular(a, b[, lower]) Solve the equation a x = b for x, assuming a is a triangular matrix. linalg.svd(a[, coerce_signs]) Compute the singular value decomposition of a matrix. linalg.svd_compressed(a, k[, iterator, …]) Randomly compressed rank-k thin Singular Value Decomposition. linalg.sfqr(data[, name]) Direct Short-and-Fat QR linalg.tsqr(data[, compute_svd, …]) Direct Tall-and-Skinny QR algorithm

 ma.average(a[, axis, weights, returned]) Return the weighted average of array over the given axis. ma.filled(a[, fill_value]) Return input as an array with masked data replaced by a fill value. ma.fix_invalid(a[, fill_value]) Return input with invalid data masked and replaced by a fill value. ma.getdata(a) Return the data of a masked array as an ndarray. ma.getmaskarray(a) Return the mask of a masked array, or full boolean array of False. ma.masked_array(data[, mask, fill_value]) An array class with possibly masked values. ma.masked_equal(a, value) Mask an array where equal to a given value. ma.masked_greater(x, value[, copy]) Mask an array where greater than a given value. ma.masked_greater_equal(x, value[, copy]) Mask an array where greater than or equal to a given value. ma.masked_inside(x, v1, v2) Mask an array inside a given interval. ma.masked_invalid(a) Mask an array where invalid values occur (NaNs or infs). ma.masked_less(x, value[, copy]) Mask an array where less than a given value. ma.masked_less_equal(x, value[, copy]) Mask an array where less than or equal to a given value. ma.masked_not_equal(x, value[, copy]) Mask an array where not equal to a given value. ma.masked_outside(x, v1, v2) Mask an array outside a given interval. ma.masked_values(x, value[, rtol, atol, shrink]) Mask using floating point equality. ma.masked_where(condition, a) Mask an array where a condition is met. ma.set_fill_value(a, fill_value) Set the filling value of a, if a is a masked array.

## Random¶

 random.beta Draw samples from a Beta distribution. random.binomial Draw samples from a binomial distribution. random.chisquare Draw samples from a chi-square distribution. random.choice Generates a random sample from a given 1-D array random.exponential Draw samples from an exponential distribution. random.f Draw samples from an F distribution. random.gamma Draw samples from a Gamma distribution. random.geometric Draw samples from the geometric distribution. random.gumbel Draw samples from a Gumbel distribution. random.hypergeometric Draw samples from a Hypergeometric distribution. random.laplace Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). random.logistic Draw samples from a logistic distribution. random.lognormal Draw samples from a log-normal distribution. random.logseries Draw samples from a logarithmic series distribution. random.negative_binomial Draw samples from a negative binomial distribution. random.noncentral_chisquare Draw samples from a noncentral chi-square distribution. random.noncentral_f Draw samples from the noncentral F distribution. random.normal Draw random samples from a normal (Gaussian) distribution. random.pareto Draw samples from a Pareto II or Lomax distribution with specified shape. random.permutation Randomly permute a sequence, or return a permuted range. random.poisson Draw samples from a Poisson distribution. random.power Draws samples in [0, 1] from a power distribution with positive exponent a - 1. random.randint Return random integers from low (inclusive) to high (exclusive). random.random Return random floats in the half-open interval [0.0, 1.0). random.random_sample Return random floats in the half-open interval [0.0, 1.0). random.rayleigh Draw samples from a Rayleigh distribution. random.standard_cauchy Draw samples from a standard Cauchy distribution with mode = 0. random.standard_exponential Draw samples from the standard exponential distribution. random.standard_gamma Draw samples from a standard Gamma distribution. random.standard_normal Draw samples from a standard Normal distribution (mean=0, stdev=1). random.standard_t Draw samples from a standard Student’s t distribution with df degrees of freedom. random.triangular Draw samples from the triangular distribution over the interval [left, right]. random.uniform Draw samples from a uniform distribution. random.vonmises Draw samples from a von Mises distribution. random.wald Draw samples from a Wald, or inverse Gaussian, distribution. random.weibull Draw samples from a Weibull distribution. random.zipf Standard distributions

## Stats¶

 stats.ttest_ind(a, b[, axis, equal_var]) Calculate the T-test for the means of two independent samples of scores. stats.ttest_1samp(a, popmean[, axis, nan_policy]) Calculate the T-test for the mean of ONE group of scores. stats.ttest_rel(a, b[, axis, nan_policy]) Calculate the t-test on TWO RELATED samples of scores, a and b. stats.chisquare(f_obs[, f_exp, ddof, axis]) Calculate a one-way chi-square test. stats.power_divergence(f_obs[, f_exp, ddof, …]) Cressie-Read power divergence statistic and goodness of fit test. stats.skew(a[, axis, bias, nan_policy]) Compute the sample skewness of a data set. stats.skewtest(a[, axis, nan_policy]) Test whether the skew is different from the normal distribution. stats.kurtosis(a[, axis, fisher, bias, …]) Compute the kurtosis (Fisher or Pearson) of a dataset. stats.kurtosistest(a[, axis, nan_policy]) Test whether a dataset has normal kurtosis. stats.normaltest(a[, axis, nan_policy]) Test whether a sample differs from a normal distribution. stats.f_oneway(*args) Perform one-way ANOVA. stats.moment(a[, moment, axis, nan_policy]) Calculate the nth moment about the mean for a sample.

## Image Support¶

 image.imread(filename[, imread, preprocess]) Read a stack of images into a dask array

## Slightly Overlapping Computations¶

 overlap.overlap(x, depth, boundary) Share boundaries between neighboring blocks overlap.map_overlap(func, *args[, depth, …]) Map a function over blocks of arrays with some overlap lib.stride_tricks.sliding_window_view(x, …) Create a sliding window view into the array with the given window shape. overlap.trim_internal(x, axes[, boundary]) Trim sides from each block overlap.trim_overlap(x, depth[, boundary]) Trim sides from each block.

## Create and Store Arrays¶

 from_array(x[, chunks, name, lock, asarray, …]) Create dask array from something that looks like an array. from_delayed(value, shape[, dtype, meta, name]) Create a dask array from a dask delayed value from_npy_stack(dirname[, mmap_mode]) Load dask array from stack of npy files from_zarr(url[, component, storage_options, …]) Load array from the zarr storage format from_tiledb(uri[, attribute, chunks, …]) Load array from the TileDB storage format store(sources, targets[, lock, regions, …]) Store dask arrays in array-like objects, overwrite data in target to_hdf5(filename, *args, **kwargs) Store arrays in HDF5 file to_zarr(arr, url[, component, …]) Save array to the zarr storage format to_npy_stack(dirname, x[, axis]) Write dask array to a stack of .npy files to_tiledb(darray, uri[, compute, …]) Save array to the TileDB storage format

## Generalized Ufuncs¶

 apply_gufunc(func, signature, *args, **kwargs) Apply a generalized ufunc or similar python function to arrays. as_gufunc([signature]) Decorator for dask.array.gufunc. gufunc(pyfunc, **kwargs) Binds pyfunc into dask.array.apply_gufunc when called.

## Internal functions¶

 blockwise(func, out_ind, *args[, name, …]) Tensor operation: Generalized inner and outer products normalize_chunks(chunks[, shape, limit, …]) Normalize chunks to tuple of tuples

## Other functions¶

dask.array.add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.add.

Some inconsistencies with the Dask version may exist.

Parameters: x1, x2 : array_like The arrays to be added. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. add : ndarray or scalar The sum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

Notes

Equivalent to x1 + x2 in terms of array broadcasting.

Examples

>>> np.add(1.0, 4.0)  # doctest: +SKIP
5.0
>>> x1 = np.arange(9.0).reshape((3, 3))  # doctest: +SKIP
>>> x2 = np.arange(3.0)  # doctest: +SKIP
>>> np.add(x1, x2)  # doctest: +SKIP
array([[  0.,   2.,   4.],
[  3.,   5.,   7.],
[  6.,   8.,  10.]])


The + operator can be used as a shorthand for np.add on ndarrays.

>>> x1 = np.arange(9.0).reshape((3, 3))  # doctest: +SKIP
>>> x2 = np.arange(3.0)  # doctest: +SKIP
>>> x1 + x2  # doctest: +SKIP
array([[ 0.,  2.,  4.],
[ 3.,  5.,  7.],
[ 6.,  8., 10.]])

dask.array.all(a, axis=None, keepdims=False, split_every=None, out=None)[source]

Test whether all array elements along a given axis evaluate to True.

This docstring was copied from numpy.all.

Some inconsistencies with the Dask version may exist.

Parameters: a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical AND reduction is performed. The default (axis=None) is to perform a logical AND over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis. New in version 1.7.0. If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if dtype(out) is float, the result will consist of 0.0’s and 1.0’s). See Output type determination for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the all method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised. where : array_like of bool, optional (Not supported in Dask) Elements to include in checking for all True values. See ~numpy.ufunc.reduce for details. New in version 1.20.0. all : ndarray, bool A new boolean or array is returned unless out is specified, in which case a reference to out is returned.

ndarray.all
equivalent method
any
Test whether any element along a given axis evaluates to True.

Notes

Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero.

Examples

>>> np.all([[True,False],[True,True]])  # doctest: +SKIP
False

>>> np.all([[True,False],[True,True]], axis=0)  # doctest: +SKIP
array([ True, False])

>>> np.all([-1, 4, 5])  # doctest: +SKIP
True

>>> np.all([1.0, np.nan])  # doctest: +SKIP
True

>>> np.all([[True, True], [False, True]], where=[[True], [False]])  # doctest: +SKIP
True

>>> o=np.array(False)  # doctest: +SKIP
>>> z=np.all([-1, 4, 5], out=o)  # doctest: +SKIP
>>> id(z), id(o), z  # doctest: +SKIP
(28293632, 28293632, array(True)) # may vary

dask.array.allclose(arr1, arr2, rtol=1e-05, atol=1e-08, equal_nan=False)[source]

Returns True if two arrays are element-wise equal within a tolerance.

This docstring was copied from numpy.allclose.

Some inconsistencies with the Dask version may exist.

The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.

NaNs are treated as equal if they are in the same place and if equal_nan=True. Infs are treated as equal if they are in the same place and of the same sign in both arrays.

Parameters: a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array. New in version 1.10.0. allclose : bool Returns True if the two arrays are equal within the given tolerance; False otherwise.

Notes

If the following equation is element-wise True, then allclose returns True.

absolute(a - b) <= (atol + rtol * absolute(b))

The above equation is not symmetric in a and b, so that allclose(a, b) might be different from allclose(b, a) in some rare cases.

The comparison of a and b uses standard broadcasting, which means that a and b need not have the same shape in order for allclose(a, b) to evaluate to True. The same is true for equal but not array_equal.

allclose is not defined for non-numeric data types.

Examples

>>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])  # doctest: +SKIP
False
>>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])  # doctest: +SKIP
True
>>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])  # doctest: +SKIP
False
>>> np.allclose([1.0, np.nan], [1.0, np.nan])  # doctest: +SKIP
False
>>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)  # doctest: +SKIP
True

dask.array.angle(x, deg=0)[source]

Return the angle of the complex argument.

This docstring was copied from numpy.angle.

Some inconsistencies with the Dask version may exist.

Parameters: z : array_like (Not supported in Dask) A complex number or sequence of complex numbers. deg : bool, optional Return angle in degrees if True, radians if False (default). angle : ndarray or scalar The counterclockwise angle from the positive real axis on the complex plane in the range (-pi, pi], with dtype as numpy.float64. Changed in version 1.16.0: This function works on subclasses of ndarray like ma.array.

arctan2
absolute

Notes

Although the angle of the complex number 0 is undefined, numpy.angle(0) returns the value 0.

Examples

>>> np.angle([1.0, 1.0j, 1+1j])               # in radians  # doctest: +SKIP
array([ 0.        ,  1.57079633,  0.78539816]) # may vary
>>> np.angle(1+1j, deg=True)                  # in degrees  # doctest: +SKIP
45.0

dask.array.any(a, axis=None, keepdims=False, split_every=None, out=None)[source]

Test whether any array element along a given axis evaluates to True.

This docstring was copied from numpy.any.

Some inconsistencies with the Dask version may exist.

Returns single boolean unless axis is not None

Parameters: a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical OR reduction is performed. The default (axis=None) is to perform a logical OR over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis. New in version 1.7.0. If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of a). See Output type determination for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the any method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised. where : array_like of bool, optional (Not supported in Dask) Elements to include in checking for any True values. See ~numpy.ufunc.reduce for details. New in version 1.20.0. any : bool or ndarray A new boolean or ndarray is returned unless out is specified, in which case a reference to out is returned.

ndarray.any
equivalent method
all
Test whether all elements along a given axis evaluate to True.

Notes

Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero.

Examples

>>> np.any([[True, False], [True, True]])  # doctest: +SKIP
True

>>> np.any([[True, False], [False, False]], axis=0)  # doctest: +SKIP
array([ True, False])

>>> np.any([-1, 0, 5])  # doctest: +SKIP
True

>>> np.any(np.nan)  # doctest: +SKIP
True

>>> np.any([[True, False], [False, False]], where=[[False], [True]])  # doctest: +SKIP
False

>>> o=np.array(False)  # doctest: +SKIP
>>> z=np.any([-1, 4, 5], out=o)  # doctest: +SKIP
>>> z, o  # doctest: +SKIP
(array(True), array(True))
>>> # Check now that z is a reference to o
>>> z is o  # doctest: +SKIP
True
>>> id(z), id(o) # identity of z and o              # doctest: +SKIP
(191614240, 191614240)

dask.array.append(arr, values, axis=None)[source]

Append values to the end of an array.

This docstring was copied from numpy.append.

Some inconsistencies with the Dask version may exist.

Parameters: arr : array_like Values are appended to a copy of this array. values : array_like These values are appended to a copy of arr. It must be of the correct shape (the same shape as arr, excluding axis). If axis is not specified, values can be any shape and will be flattened before use. axis : int, optional The axis along which values are appended. If axis is not given, both arr and values are flattened before use. append : ndarray A copy of arr with values appended to axis. Note that append does not occur in-place: a new array is allocated and filled. If axis is None, out is a flattened array.

insert
Insert elements into an array.
delete
Delete elements from an array.

Examples

>>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]])  # doctest: +SKIP
array([1, 2, 3, ..., 7, 8, 9])


When axis is specified, values must have the correct shape.

>>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0)  # doctest: +SKIP
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
>>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0)  # doctest: +SKIP
Traceback (most recent call last):
...
ValueError: all the input arrays must have same number of dimensions, but
the array at index 0 has 2 dimension(s) and the array at index 1 has 1
dimension(s)

dask.array.apply_along_axis(func1d, axis, arr, *args, dtype=None, shape=None, **kwargs)[source]

Apply a function to 1-D slices along the given axis.

This docstring was copied from numpy.apply_along_axis.

Some inconsistencies with the Dask version may exist.

This is a blocked variant of numpy.apply_along_axis() implemented via dask.array.map_blocks()

Parameters: func1d : function (M,) -> (Nj…) This function should accept 1-D arrays. It is applied to 1-D slices of arr along the specified axis. axis : integer Axis along which arr is sliced. arr : ndarray (Ni…, M, Nk…) Input array. args : any Additional arguments to func1d. kwargs : any Additional named arguments to func1d. New in version 1.9.0. out : ndarray (Ni…, Nj…, Nk…) The output array. The shape of out is identical to the shape of arr, except along the axis dimension. This axis is removed, and replaced with new dimensions equal to the shape of the return value of func1d. So if func1d returns a scalar out will have one fewer dimensions than arr.

apply_over_axes
Apply a function repeatedly over multiple axes.

Notes

If either of dtype or shape are not provided, Dask attempts to determine them by calling func1d on a dummy array. This may produce incorrect values for dtype or shape, so we recommend providing them.

Execute func1d(a, *args, **kwargs) where func1d operates on 1-D arrays and a is a 1-D slice of arr along axis.

This is equivalent to (but faster than) the following use of ndindex and s_, which sets each of ii, jj, and kk to a tuple of indices:

Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
for kk in ndindex(Nk):
f = func1d(arr[ii + s_[:,] + kk])
Nj = f.shape
for jj in ndindex(Nj):
out[ii + jj + kk] = f[jj]


Equivalently, eliminating the inner loop, this can be expressed as:

Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
for kk in ndindex(Nk):
out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])


Examples

>>> def my_func(a):  # doctest: +SKIP
...     """Average first and last element of a 1-D array"""
...     return (a[0] + a[-1]) * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])  # doctest: +SKIP
>>> np.apply_along_axis(my_func, 0, b)  # doctest: +SKIP
array([4., 5., 6.])
>>> np.apply_along_axis(my_func, 1, b)  # doctest: +SKIP
array([2.,  5.,  8.])


For a function that returns a 1D array, the number of dimensions in outarr is the same as arr.

>>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])  # doctest: +SKIP
>>> np.apply_along_axis(sorted, 1, b)  # doctest: +SKIP
array([[1, 7, 8],
[3, 4, 9],
[2, 5, 6]])


For a function that returns a higher dimensional array, those dimensions are inserted in place of the axis dimension.

>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])  # doctest: +SKIP
>>> np.apply_along_axis(np.diag, -1, b)  # doctest: +SKIP
array([[[1, 0, 0],
[0, 2, 0],
[0, 0, 3]],
[[4, 0, 0],
[0, 5, 0],
[0, 0, 6]],
[[7, 0, 0],
[0, 8, 0],
[0, 0, 9]]])

dask.array.apply_over_axes(func, a, axes)[source]

Apply a function repeatedly over multiple axes.

This docstring was copied from numpy.apply_over_axes.

Some inconsistencies with the Dask version may exist.

func is called as res = func(a, axis), where axis is the first element of axes. The result res of the function call must have either the same dimensions as a or one less dimension. If res has one less dimension than a, a dimension is inserted before axis. The call to func is then repeated for each axis in axes, with res as the first argument.

Parameters: func : function This function must take two arguments, func(a, axis). a : array_like Input array. axes : array_like Axes over which func is applied; the elements must be integers. apply_over_axis : ndarray The output array. The number of dimensions is the same as a, but the shape can be different. This depends on whether func changes the shape of its output with respect to its input.

apply_along_axis
Apply a function to 1-D slices of an array along the given axis.

Notes

This function is equivalent to tuple axis arguments to reorderable ufuncs with keepdims=True. Tuple axis arguments to ufuncs have been available since version 1.7.0.

Examples

>>> a = np.arange(24).reshape(2,3,4)  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[[ 0,  1,  2,  3],
[ 4,  5,  6,  7],
[ 8,  9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])


Sum over axes 0 and 2. The result has same number of dimensions as the original array:

>>> np.apply_over_axes(np.sum, a, [0,2])  # doctest: +SKIP
array([[[ 60],
[ 92],
[124]]])


Tuple axis arguments to ufuncs are equivalent:

>>> np.sum(a, axis=(0,2), keepdims=True)  # doctest: +SKIP
array([[[ 60],
[ 92],
[124]]])

dask.array.arange(*args, **kwargs)[source]

Return evenly spaced values from start to stop with step size step.

The values are half-open [start, stop), so including start and excluding stop. This is basically the same as python’s range function but for dask arrays.

When using a non-integer step, such as 0.1, the results will often not be consistent. It is better to use linspace for these cases.

Parameters: start : int, optional The starting value of the sequence. The default is 0. stop : int The end of the interval, this value is excluded from the interval. step : int, optional The spacing between the values. The default is 1 when not specified. The last value of the sequence. chunks : int The number of samples on each block. Note that the last block will have fewer samples if len(array) % chunks != 0. dtype : numpy.dtype Output dtype. Omit to infer it from start, stop, step samples : dask array
dask.array.arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arccos.

Some inconsistencies with the Dask version may exist.

Trigonometric inverse cosine, element-wise.

The inverse of cos so that, if y = cos(x), then x = arccos(y).

Parameters: x : array_like x-coordinate on the unit circle. For real arguments, the domain is [-1, 1]. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. angle : ndarray The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi]. This is a scalar if x is a scalar.

cos, arctan, arcsin, emath.arccos

Notes

arccos is a multivalued function: for each x there are infinitely many numbers z such that cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi].

For real-valued input data types, arccos always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, arccos is a complex analytic function that has branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter.

The inverse cos is also known as acos or cos^-1.

References

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

Examples

We expect the arccos of 1 to be 0, and of -1 to be pi:

>>> np.arccos([1, -1])  # doctest: +SKIP
array([ 0.        ,  3.14159265])


Plot arccos:

>>> import matplotlib.pyplot as plt  # doctest: +SKIP
>>> x = np.linspace(-1, 1, num=100)  # doctest: +SKIP
>>> plt.plot(x, np.arccos(x))  # doctest: +SKIP
>>> plt.axis('tight')  # doctest: +SKIP
>>> plt.show()  # doctest: +SKIP

dask.array.arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arccosh.

Some inconsistencies with the Dask version may exist.

Inverse hyperbolic cosine, element-wise.

Parameters: x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. arccosh : ndarray Array of the same shape as x. This is a scalar if x is a scalar.

Notes

arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [-pi, pi] and the real part in [0, inf].

For real-valued input data types, arccosh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, arccosh is a complex analytical function that has a branch cut [-inf, 1] and is continuous from above on it.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arccosh

Examples

>>> np.arccosh([np.e, 10.0])  # doctest: +SKIP
array([ 1.65745445,  2.99322285])
>>> np.arccosh(1)  # doctest: +SKIP
0.0

dask.array.arcsin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arcsin.

Some inconsistencies with the Dask version may exist.

Inverse sine, element-wise.

Parameters: x : array_like y-coordinate on the unit circle. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. angle : ndarray The inverse sine of each element in x, in radians and in the closed interval [-pi/2, pi/2]. This is a scalar if x is a scalar.

Notes

arcsin is a multivalued function: for each x there are infinitely many numbers z such that $$sin(z) = x$$. The convention is to return the angle z whose real part lies in [-pi/2, pi/2].

For real-valued input data types, arcsin always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, arcsin is a complex analytic function that has, by convention, the branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter.

The inverse sine is also known as asin or sin^{-1}.

References

Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79ff. http://www.math.sfu.ca/~cbm/aands/

Examples

>>> np.arcsin(1)     # pi/2  # doctest: +SKIP
1.5707963267948966
>>> np.arcsin(-1)    # -pi/2  # doctest: +SKIP
-1.5707963267948966
>>> np.arcsin(0)  # doctest: +SKIP
0.0

dask.array.arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arcsinh.

Some inconsistencies with the Dask version may exist.

Inverse hyperbolic sine element-wise.

Parameters: x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Array of the same shape as x. This is a scalar if x is a scalar.

Notes

arcsinh is a multivalued function: for each x there are infinitely many numbers z such that sinh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2].

For real-valued input data types, arcsinh always returns real output. For each value that cannot be expressed as a real number or infinity, it returns nan and sets the invalid floating point error flag.

For complex-valued input, arccos is a complex analytical function that has branch cuts [1j, infj] and [-1j, -infj] and is continuous from the right on the former and from the left on the latter.

The inverse hyperbolic sine is also known as asinh or sinh^-1.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arcsinh

Examples

>>> np.arcsinh(np.array([np.e, 10.0]))  # doctest: +SKIP
array([ 1.72538256,  2.99822295])

dask.array.arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arctan.

Some inconsistencies with the Dask version may exist.

Trigonometric inverse tangent, element-wise.

The inverse of tan, so that if y = tan(x) then x = arctan(y).

Parameters: x : array_like out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Out has the same shape as x. Its real part is in [-pi/2, pi/2] (arctan(+/-inf) returns +/-pi/2). This is a scalar if x is a scalar.

arctan2
The “four quadrant” arctan of the angle formed by (x, y) and the positive x-axis.
angle
Argument of complex values.

Notes

arctan is a multi-valued function: for each x there are infinitely many numbers z such that tan(z) = x. The convention is to return the angle z whose real part lies in [-pi/2, pi/2].

For real-valued input data types, arctan always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, arctan is a complex analytic function that has [1j, infj] and [-1j, -infj] as branch cuts, and is continuous from the left on the former and from the right on the latter.

The inverse tangent is also known as atan or tan^{-1}.

References

Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

Examples

We expect the arctan of 0 to be 0, and of 1 to be pi/4:

>>> np.arctan([0, 1])  # doctest: +SKIP
array([ 0.        ,  0.78539816])

>>> np.pi/4  # doctest: +SKIP
0.78539816339744828


Plot arctan:

>>> import matplotlib.pyplot as plt  # doctest: +SKIP
>>> x = np.linspace(-10, 10)  # doctest: +SKIP
>>> plt.plot(x, np.arctan(x))  # doctest: +SKIP
>>> plt.axis('tight')  # doctest: +SKIP
>>> plt.show()  # doctest: +SKIP

dask.array.arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arctan2.

Some inconsistencies with the Dask version may exist.

Element-wise arc tangent of x1/x2 choosing the quadrant correctly.

The quadrant (i.e., branch) is chosen so that arctan2(x1, x2) is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2, x1). (Note the role reversal: the “y-coordinate” is the first function parameter, the “x-coordinate” is the second.) By IEEE convention, this function is defined for x2 = +/-0 and for either or both of x1 and x2 = +/-inf (see Notes for specific values).

This function is not defined for complex-valued arguments; for the so-called argument of complex values, use angle.

Parameters: x1 : array_like, real-valued y-coordinates. x2 : array_like, real-valued x-coordinates. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. angle : ndarray Array of angles in radians, in the range [-pi, pi]. This is a scalar if both x1 and x2 are scalars.

Notes

arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: [1]

x1 x2 arctan2(x1,x2)
+/- 0 +0 +/- 0
+/- 0 -0 +/- pi
> 0 +/-inf +0 / +pi
< 0 +/-inf -0 / -pi
+/-inf +inf +/- (pi/4)
+/-inf -inf +/- (3*pi/4)

Note that +0 and -0 are distinct floating point numbers, as are +inf and -inf.

References

 [1] ISO/IEC standard 9899:1999, “Programming language C.”

Examples

Consider four points in different quadrants:

>>> x = np.array([-1, +1, +1, -1])  # doctest: +SKIP
>>> y = np.array([-1, -1, +1, +1])  # doctest: +SKIP
>>> np.arctan2(y, x) * 180 / np.pi  # doctest: +SKIP
array([-135.,  -45.,   45.,  135.])


Note the order of the parameters. arctan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range [-pi, pi]:

>>> np.arctan2([1., -1.], [0., 0.])  # doctest: +SKIP
array([ 1.57079633, -1.57079633])
>>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])  # doctest: +SKIP
array([ 0.        ,  3.14159265,  0.78539816])

dask.array.arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.arctanh.

Some inconsistencies with the Dask version may exist.

Inverse hyperbolic tangent element-wise.

Parameters: x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Array of the same shape as x. This is a scalar if x is a scalar.

emath.arctanh

Notes

arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2].

For real-valued input data types, arctanh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, arctanh is a complex analytical function that has branch cuts [-1, -inf] and [1, inf] and is continuous from above on the former and from below on the latter.

The inverse hyperbolic tangent is also known as atanh or tanh^-1.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arctanh

Examples

>>> np.arctanh([0, -0.5])  # doctest: +SKIP
array([ 0.        , -0.54930614])

dask.array.argmax(x, axis=None, split_every=None, out=None)

Return the maximum of an array or maximum along an axis.

This docstring was copied from numpy.amax.

Some inconsistencies with the Dask version may exist.

Parameters: a : array_like (Not supported in Dask) Input data. axis : None or int or tuple of ints, optional Axis or axes along which to operate. By default, flattened input is used. New in version 1.7.0. If this is a tuple of ints, the maximum is selected over multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See Output type determination for more details. keepdims : bool, optional (Not supported in Dask) If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the amax method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised. initial : scalar, optional (Not supported in Dask) The minimum value of an output element. Must be present to allow computation on empty slice. See ~numpy.ufunc.reduce for details. New in version 1.15.0. where : array_like of bool, optional (Not supported in Dask) Elements to compare for the maximum. See ~numpy.ufunc.reduce for details. New in version 1.17.0. amax : ndarray or scalar Maximum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension a.ndim - 1.

amin
The minimum value of an array along a given axis, propagating any NaNs.
nanmax
The maximum value of an array along a given axis, ignoring any NaNs.
maximum
Element-wise maximum of two arrays, propagating any NaNs.
fmax
Element-wise maximum of two arrays, ignoring any NaNs.
argmax
Return the indices of the maximum values.
nanmin, minimum, fmin

Notes

NaN values are propagated, that is if at least one item is NaN, the corresponding max value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmax.

Don’t use amax for element-wise comparison of 2 arrays; when a.shape[0] is 2, maximum(a[0], a[1]) is faster than amax(a, axis=0).

Examples

>>> a = np.arange(4).reshape((2,2))  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[0, 1],
[2, 3]])
>>> np.amax(a)           # Maximum of the flattened array  # doctest: +SKIP
3
>>> np.amax(a, axis=0)   # Maxima along the first axis  # doctest: +SKIP
array([2, 3])
>>> np.amax(a, axis=1)   # Maxima along the second axis  # doctest: +SKIP
array([1, 3])
>>> np.amax(a, where=[False, True], initial=-1, axis=0)  # doctest: +SKIP
array([-1,  3])
>>> b = np.arange(5, dtype=float)  # doctest: +SKIP
>>> b[2] = np.NaN  # doctest: +SKIP
>>> np.amax(b)  # doctest: +SKIP
nan
>>> np.amax(b, where=~np.isnan(b), initial=-1)  # doctest: +SKIP
4.0
>>> np.nanmax(b)  # doctest: +SKIP
4.0


You can use an initial value to compute the maximum of an empty slice, or to initialize it to a different value:

>>> np.max([[-50], [10]], axis=-1, initial=0)  # doctest: +SKIP
array([ 0, 10])


Notice that the initial value is used as one of the elements for which the maximum is determined, unlike for the default argument Python’s max function, which is only used for empty iterables.

>>> np.max([5], initial=6)  # doctest: +SKIP
6
>>> max([5], default=6)  # doctest: +SKIP
5

dask.array.argmin(x, axis=None, split_every=None, out=None)

Return the minimum of an array or minimum along an axis.

This docstring was copied from numpy.amin.

Some inconsistencies with the Dask version may exist.

Parameters: a : array_like (Not supported in Dask) Input data. axis : None or int or tuple of ints, optional Axis or axes along which to operate. By default, flattened input is used. New in version 1.7.0. If this is a tuple of ints, the minimum is selected over multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See Output type determination for more details. keepdims : bool, optional (Not supported in Dask) If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the amin method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised. initial : scalar, optional (Not supported in Dask) The maximum value of an output element. Must be present to allow computation on empty slice. See ~numpy.ufunc.reduce for details. New in version 1.15.0. where : array_like of bool, optional (Not supported in Dask) Elements to compare for the minimum. See ~numpy.ufunc.reduce for details. New in version 1.17.0. amin : ndarray or scalar Minimum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension a.ndim - 1.

amax
The maximum value of an array along a given axis, propagating any NaNs.
nanmin
The minimum value of an array along a given axis, ignoring any NaNs.
minimum
Element-wise minimum of two arrays, propagating any NaNs.
fmin
Element-wise minimum of two arrays, ignoring any NaNs.
argmin
Return the indices of the minimum values.
nanmax, maximum, fmax

Notes

NaN values are propagated, that is if at least one item is NaN, the corresponding min value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmin.

Don’t use amin for element-wise comparison of 2 arrays; when a.shape[0] is 2, minimum(a[0], a[1]) is faster than amin(a, axis=0).

Examples

>>> a = np.arange(4).reshape((2,2))  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[0, 1],
[2, 3]])
>>> np.amin(a)           # Minimum of the flattened array  # doctest: +SKIP
0
>>> np.amin(a, axis=0)   # Minima along the first axis  # doctest: +SKIP
array([0, 1])
>>> np.amin(a, axis=1)   # Minima along the second axis  # doctest: +SKIP
array([0, 2])
>>> np.amin(a, where=[False, True], initial=10, axis=0)  # doctest: +SKIP
array([10,  1])

>>> b = np.arange(5, dtype=float)  # doctest: +SKIP
>>> b[2] = np.NaN  # doctest: +SKIP
>>> np.amin(b)  # doctest: +SKIP
nan
>>> np.amin(b, where=~np.isnan(b), initial=10)  # doctest: +SKIP
0.0
>>> np.nanmin(b)  # doctest: +SKIP
0.0

>>> np.min([[-50], [10]], axis=-1, initial=0)  # doctest: +SKIP
array([-50,   0])


Notice that the initial value is used as one of the elements for which the minimum is determined, unlike for the default argument Python’s max function, which is only used for empty iterables.

Notice that this isn’t the same as Python’s default argument.

>>> np.min([6], initial=5)  # doctest: +SKIP
5
>>> min([6], default=5)  # doctest: +SKIP
6

dask.array.argtopk(a, k, axis=-1, split_every=None)[source]

Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. If k is negative, extract the indices of the -k smallest elements instead, and return them sorted from smallest to largest.

This performs best when k is much smaller than the chunk size. All results will be returned in a single chunk along the given axis.

Parameters: x: Array Data being sorted k: int axis: int, optional split_every: int >=2, optional See topk(). The performance considerations for topk also apply here. Selection of np.intp indices of x with size abs(k) along the given axis.

Examples

>>> import dask.array as da
>>> x = np.array([5, 1, 3, 6])
>>> d = da.from_array(x, chunks=2)
>>> d.argtopk(2).compute()
array([3, 0])
>>> d.argtopk(-2).compute()
array([1, 2])

dask.array.argwhere(a)[source]

Find the indices of array elements that are non-zero, grouped by element.

This docstring was copied from numpy.argwhere.

Some inconsistencies with the Dask version may exist.

Parameters: a : array_like Input data. index_array : (N, a.ndim) ndarray Indices of elements that are non-zero. Indices are grouped by element. This array will have shape (N, a.ndim) where N is the number of non-zero items.

Notes

np.argwhere(a) is almost the same as np.transpose(np.nonzero(a)), but produces a result of the correct shape for a 0D array.

The output of argwhere is not suitable for indexing arrays. For this purpose use nonzero(a) instead.

Examples

>>> x = np.arange(6).reshape(2,3)  # doctest: +SKIP
>>> x  # doctest: +SKIP
array([[0, 1, 2],
[3, 4, 5]])
>>> np.argwhere(x>1)  # doctest: +SKIP
array([[0, 2],
[1, 0],
[1, 1],
[1, 2]])

dask.array.around(x, decimals=0)[source]

Evenly round to the given number of decimals.

This docstring was copied from numpy.around.

Some inconsistencies with the Dask version may exist.

Parameters: a : array_like (Not supported in Dask) Input data. decimals : int, optional Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point. out : ndarray, optional (Not supported in Dask) Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See Output type determination for more details. rounded_array : ndarray An array of the same type as a, containing the rounded values. Unless out was specified, a new array is created. A reference to the result is returned. The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float.

ndarray.round
equivalent method
ceil, fix, floor, rint, trunc

Notes

For values exactly halfway between rounded decimal values, NumPy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc.

np.around uses a fast but sometimes inexact algorithm to round floating-point datatypes. For positive decimals it is equivalent to np.true_divide(np.rint(a * 10**decimals), 10**decimals), which has error due to the inexact representation of decimal fractions in the IEEE floating point standard [1] and errors introduced when scaling by powers of ten. For instance, note the extra “1” in the following:

>>> np.round(56294995342131.5, 3)  # doctest: +SKIP
56294995342131.51


If your goal is to print such values with a fixed number of decimals, it is preferable to use numpy’s float printing routines to limit the number of printed decimals:

>>> np.format_float_positional(56294995342131.5, precision=3)  # doctest: +SKIP
'56294995342131.5'


The float printing routines use an accurate but much more computationally demanding algorithm to compute the number of digits after the decimal point.

Alternatively, Python’s builtin round function uses a more accurate but slower algorithm for 64-bit floating point values:

>>> round(56294995342131.5, 3)  # doctest: +SKIP
56294995342131.5
>>> np.round(16.055, 2), round(16.055, 2)  # equals 16.0549999999999997  # doctest: +SKIP
(16.06, 16.05)


References

 [1] “Lecture Notes on the Status of IEEE 754”, William Kahan, https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
 [2] “How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?”, William Kahan, https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf

Examples

>>> np.around([0.37, 1.64])  # doctest: +SKIP
array([0.,  2.])
>>> np.around([0.37, 1.64], decimals=1)  # doctest: +SKIP
array([0.4,  1.6])
>>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value  # doctest: +SKIP
array([0.,  2.,  2.,  4.,  4.])
>>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned  # doctest: +SKIP
array([ 1,  2,  3, 11])
>>> np.around([1,2,3,11], decimals=-1)  # doctest: +SKIP
array([ 0,  0,  0, 10])

dask.array.array(object, dtype=None, *, copy=True, order='K', subok=False, ndmin=0, like=None)[source]

This docstring was copied from numpy.array.

Some inconsistencies with the Dask version may exist.

Create an array.

Parameters:
object : array_like

An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence.

dtype : data-type, optional

The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence.

copy : bool, optional

If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (dtype, order, etc.).

order : {‘K’, ‘A’, ‘C’, ‘F’}, optional

Specify the memory layout of the array. If object is not an array, the newly created array will be in C order (row major) unless ‘F’ is specified, in which case it will be in Fortran order (column major). If object is an array the following holds.

order no copy copy=True
‘K’ unchanged F & C order preserved, otherwise most similar order
‘A’ unchanged F order if input is F and not C, otherwise C order
‘C’ C order C order
‘F’ F order F order

When copy=False and a copy is made for other reasons, the result is the same as if copy=True, with some exceptions for A, see the Notes section. The default order is ‘K’.

subok : bool, optional

If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default).

ndmin : int, optional

Specifies the minimum number of dimensions that the resulting array should have. Ones will be pre-pended to the shape as needed to meet this requirement.

like : array_like

Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as like supports the __array_function__ protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument.

Note

The like keyword is an experimental feature pending on acceptance of NEP 35.

New in version 1.20.0.

Returns:
out : ndarray

An array object satisfying the specified requirements.

empty_like
Return an empty array with shape and type of input.
ones_like
Return an array of ones with shape and type of input.
zeros_like
Return an array of zeros with shape and type of input.
full_like
Return a new array with shape of input filled with value.
empty
Return a new uninitialized array.
ones
Return a new array setting values to one.
zeros
Return a new array setting values to zero.
full
Return a new array of given shape filled with value.

Notes

When order is ‘A’ and object is an array in neither ‘C’ nor ‘F’ order, and a copy is forced by a change in dtype, then the order of the result is not necessarily ‘C’ as expected. This is likely a bug.

Examples

>>> np.array([1, 2, 3])  # doctest: +SKIP
array([1, 2, 3])


Upcasting:

>>> np.array([1, 2, 3.0])  # doctest: +SKIP
array([ 1.,  2.,  3.])


More than one dimension:

>>> np.array([[1, 2], [3, 4]])  # doctest: +SKIP
array([[1, 2],
[3, 4]])


Minimum dimensions 2:

>>> np.array([1, 2, 3], ndmin=2)  # doctest: +SKIP
array([[1, 2, 3]])


Type provided:

>>> np.array([1, 2, 3], dtype=complex)  # doctest: +SKIP
array([ 1.+0.j,  2.+0.j,  3.+0.j])


Data-type consisting of more than one element:

>>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')])  # doctest: +SKIP
>>> x['a']  # doctest: +SKIP
array([1, 3])


Creating an array from sub-classes:

>>> np.array(np.mat('1 2; 3 4'))  # doctest: +SKIP
array([[1, 2],
[3, 4]])

>>> np.array(np.mat('1 2; 3 4'), subok=True)  # doctest: +SKIP
matrix([[1, 2],
[3, 4]])

dask.array.asanyarray(a)[source]

Convert the input to a dask array.

Subclasses of np.ndarray will be passed through as chunks unchanged.

Parameters: a : array-like Input data, in any form that can be converted to a dask array. out : dask array Dask array interpretation of a.

Examples

>>> import dask.array as da
>>> import numpy as np
>>> x = np.arange(3)
>>> da.asanyarray(x)

>>> y = [[1, 2, 3], [4, 5, 6]]
>>> da.asanyarray(y)
dask.array<array, shape=(2, 3), dtype=int64, chunksize=(2, 3), chunktype=numpy.ndarray>

dask.array.asarray(a, **kwargs)[source]

Convert the input to a dask array.

Parameters: a : array-like Input data, in any form that can be converted to a dask array. out : dask array Dask array interpretation of a.

Examples

>>> import dask.array as da
>>> import numpy as np
>>> x = np.arange(3)
>>> da.asarray(x)

>>> y = [[1, 2, 3], [4, 5, 6]]
>>> da.asarray(y)
dask.array<array, shape=(2, 3), dtype=int64, chunksize=(2, 3), chunktype=numpy.ndarray>

dask.array.atleast_1d(*arys)[source]

Convert inputs to arrays with at least one dimension.

This docstring was copied from numpy.atleast_1d.

Some inconsistencies with the Dask version may exist.

Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved.

Parameters: arys1, arys2, … : array_like One or more input arrays. ret : ndarray An array, or list of arrays, each with a.ndim >= 1. Copies are made only if necessary.

Examples

>>> np.atleast_1d(1.0)  # doctest: +SKIP
array([1.])

>>> x = np.arange(9.0).reshape(3,3)  # doctest: +SKIP
>>> np.atleast_1d(x)  # doctest: +SKIP
array([[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]])
>>> np.atleast_1d(x) is x  # doctest: +SKIP
True

>>> np.atleast_1d(1, [3, 4])  # doctest: +SKIP
[array([1]), array([3, 4])]

dask.array.atleast_2d(*arys)[source]

View inputs as arrays with at least two dimensions.

This docstring was copied from numpy.atleast_2d.

Some inconsistencies with the Dask version may exist.

Parameters: arys1, arys2, … : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have two or more dimensions are preserved. res, res2, … : ndarray An array, or list of arrays, each with a.ndim >= 2. Copies are avoided where possible, and views with two or more dimensions are returned.

Examples

>>> np.atleast_2d(3.0)  # doctest: +SKIP
array([[3.]])

>>> x = np.arange(3.0)  # doctest: +SKIP
>>> np.atleast_2d(x)  # doctest: +SKIP
array([[0., 1., 2.]])
>>> np.atleast_2d(x).base is x  # doctest: +SKIP
True

>>> np.atleast_2d(1, [1, 2], [[1, 2]])  # doctest: +SKIP
[array([[1]]), array([[1, 2]]), array([[1, 2]])]

dask.array.atleast_3d(*arys)[source]

View inputs as arrays with at least three dimensions.

This docstring was copied from numpy.atleast_3d.

Some inconsistencies with the Dask version may exist.

Parameters: arys1, arys2, … : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have three or more dimensions are preserved. res1, res2, … : ndarray An array, or list of arrays, each with a.ndim >= 3. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1-D array of shape (N,) becomes a view of shape (1, N, 1), and a 2-D array of shape (M, N) becomes a view of shape (M, N, 1).

Examples

>>> np.atleast_3d(3.0)  # doctest: +SKIP
array([[[3.]]])

>>> x = np.arange(3.0)  # doctest: +SKIP
>>> np.atleast_3d(x).shape  # doctest: +SKIP
(1, 3, 1)

>>> x = np.arange(12.0).reshape(4,3)  # doctest: +SKIP
>>> np.atleast_3d(x).shape  # doctest: +SKIP
(4, 3, 1)
>>> np.atleast_3d(x).base is x.base  # x is a reshape, so not base itself  # doctest: +SKIP
True

>>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]):  # doctest: +SKIP
...     print(arr, arr.shape) # doctest: +SKIP
...
[[[1]
[2]]] (1, 2, 1)
[[[1]
[2]]] (1, 2, 1)
[[[1 2]]] (1, 1, 2)

dask.array.average(a, axis=None, weights=None, returned=False)[source]

Compute the weighted average along the specified axis.

This docstring was copied from numpy.average.

Some inconsistencies with the Dask version may exist.

Parameters: a : array_like Array containing data to be averaged. If a is not an array, a conversion is attempted. axis : None or int or tuple of ints, optional Axis or axes along which to average a. The default, axis=None, will average over all of the elements of the input array. If axis is negative it counts from the last to the first axis. New in version 1.7.0. If axis is a tuple of ints, averaging is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before. weights : array_like, optional An array of weights associated with the values in a. Each value in a contributes to the average according to its associated weight. The weights array can either be 1-D (in which case its length must be the size of a along the given axis) or of the same shape as a. If weights=None, then all data in a are assumed to have a weight equal to one. The 1-D calculation is: avg = sum(a * weights) / sum(weights)  The only constraint on weights is that sum(weights) must not be 0. returned : bool, optional Default is False. If True, the tuple (average, sum_of_weights) is returned, otherwise only the average is returned. If weights=None, sum_of_weights is equivalent to the number of elements over which the average is taken. retval, [sum_of_weights] : array_type or double Return the average along the specified axis. When returned is True, return a tuple with the average as the first element and the sum of the weights as the second element. sum_of_weights is of the same type as retval. The result dtype follows a genereal pattern. If weights is None, the result dtype will be that of a , or float64 if a is integral. Otherwise, if weights is not None and a is non- integral, the result type will be the type of lowest precision capable of representing values of both a and weights. If a happens to be integral, the previous rules still applies but the result dtype will at least be float64. ZeroDivisionError When all weights along axis are zero. See numpy.ma.average for a version robust to this type of error. TypeError When the length of 1D weights is not the same as the shape of a along axis.

mean
ma.average
average for masked arrays – useful if your data contains “missing” values
numpy.result_type
Returns the type that results from applying the numpy type promotion rules to the arguments.

Examples

>>> data = np.arange(1, 5)  # doctest: +SKIP
>>> data  # doctest: +SKIP
array([1, 2, 3, 4])
>>> np.average(data)  # doctest: +SKIP
2.5
>>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1))  # doctest: +SKIP
4.0

>>> data = np.arange(6).reshape((3,2))  # doctest: +SKIP
>>> data  # doctest: +SKIP
array([[0, 1],
[2, 3],
[4, 5]])
>>> np.average(data, axis=1, weights=[1./4, 3./4])  # doctest: +SKIP
array([0.75, 2.75, 4.75])
>>> np.average(data, weights=[1./4, 3./4])  # doctest: +SKIP
Traceback (most recent call last):
...
TypeError: Axis must be specified when shapes of a and weights differ.

>>> a = np.ones(5, dtype=np.float128)  # doctest: +SKIP
>>> w = np.ones(5, dtype=np.complex64)  # doctest: +SKIP
>>> avg = np.average(a, weights=w)  # doctest: +SKIP
>>> print(avg.dtype)  # doctest: +SKIP
complex256

dask.array.bincount(x, weights=None, minlength=0)[source]

This docstring was copied from numpy.bincount.

Some inconsistencies with the Dask version may exist.

Count number of occurrences of each value in array of non-negative ints.

The number of bins (of size 1) is one larger than the largest value in x. If minlength is specified, there will be at least this number of bins in the output array (though it will be longer if necessary, depending on the contents of x). Each bin gives the number of occurrences of its index value in x. If weights is specified the input array is weighted by it, i.e. if a value n is found at position i, out[n] += weight[i] instead of out[n] += 1.

Parameters: x : array_like, 1 dimension, nonnegative ints Input array. weights : array_like, optional Weights, array of the same shape as x. minlength : int, optional A minimum number of bins for the output array. New in version 1.6.0. out : ndarray of ints The result of binning the input array. The length of out is equal to np.amax(x)+1. ValueError If the input is not 1-dimensional, or contains elements with negative values, or if minlength is negative. TypeError If the type of the input is float or complex.

Examples

>>> np.bincount(np.arange(5))  # doctest: +SKIP
array([1, 1, 1, 1, 1])
>>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7]))  # doctest: +SKIP
array([1, 3, 1, 1, 0, 0, 0, 1])

>>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])  # doctest: +SKIP
>>> np.bincount(x).size == np.amax(x)+1  # doctest: +SKIP
True


The input array needs to be of integer dtype, otherwise a TypeError is raised:

>>> np.bincount(np.arange(5, dtype=float))  # doctest: +SKIP
Traceback (most recent call last):
...
TypeError: Cannot cast array data from dtype('float64') to dtype('int64')
according to the rule 'safe'


A possible use of bincount is to perform sums over variable-size chunks of an array, using the weights keyword.

>>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights  # doctest: +SKIP
>>> x = np.array([0, 1, 1, 2, 2, 2])  # doctest: +SKIP
>>> np.bincount(x,  weights=w)  # doctest: +SKIP
array([ 0.3,  0.7,  1.1])

dask.array.bitwise_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.bitwise_and.

Some inconsistencies with the Dask version may exist.

Compute the bit-wise AND of two arrays element-wise.

Computes the bit-wise AND of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator &.

Parameters: x1, x2 : array_like Only integer and boolean types are handled. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Result. This is a scalar if both x1 and x2 are scalars.

logical_and
bitwise_or
bitwise_xor
binary_repr
Return the binary representation of the input number as a string.

Examples

The number 13 is represented by 00001101. Likewise, 17 is represented by 00010001. The bit-wise AND of 13 and 17 is therefore 000000001, or 1:

>>> np.bitwise_and(13, 17)  # doctest: +SKIP
1

>>> np.bitwise_and(14, 13)  # doctest: +SKIP
12
>>> np.binary_repr(12)  # doctest: +SKIP
'1100'
>>> np.bitwise_and([14,3], 13)  # doctest: +SKIP
array([12,  1])

>>> np.bitwise_and([11,7], [4,25])  # doctest: +SKIP
array([0, 1])
>>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16]))  # doctest: +SKIP
array([ 2,  4, 16])
>>> np.bitwise_and([True, True], [False, True])  # doctest: +SKIP
array([False,  True])


The & operator can be used as a shorthand for np.bitwise_and on ndarrays.

>>> x1 = np.array([2, 5, 255])  # doctest: +SKIP
>>> x2 = np.array([3, 14, 16])  # doctest: +SKIP
>>> x1 & x2  # doctest: +SKIP
array([ 2,  4, 16])

dask.array.bitwise_not(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.invert.

Some inconsistencies with the Dask version may exist.

Compute bit-wise inversion, or bit-wise NOT, element-wise.

Computes the bit-wise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ~.

For signed integer inputs, the two’s complement is returned. In a two’s-complement system negative numbers are represented by the two’s complement of the absolute value. This is the most common method of representing signed integers on computers [1]. A N-bit two’s-complement system can represent every integer in the range $$-2^{N-1}$$ to $$+2^{N-1}-1$$.

Parameters: x : array_like Only integer and boolean types are handled. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Result. This is a scalar if x is a scalar.

bitwise_and, bitwise_or, bitwise_xor
logical_not
binary_repr
Return the binary representation of the input number as a string.

Notes

bitwise_not is an alias for invert:

>>> np.bitwise_not is np.invert  # doctest: +SKIP
True


References

 [1] Wikipedia, “Two’s complement”, https://en.wikipedia.org/wiki/Two’s_complement

Examples

We’ve seen that 13 is represented by 00001101. The invert or bit-wise NOT of 13 is then:

>>> x = np.invert(np.array(13, dtype=np.uint8))  # doctest: +SKIP
>>> x  # doctest: +SKIP
242
>>> np.binary_repr(x, width=8)  # doctest: +SKIP
'11110010'


The result depends on the bit-width:

>>> x = np.invert(np.array(13, dtype=np.uint16))  # doctest: +SKIP
>>> x  # doctest: +SKIP
65522
>>> np.binary_repr(x, width=16)  # doctest: +SKIP
'1111111111110010'


When using signed integer types the result is the two’s complement of the result for the unsigned type:

>>> np.invert(np.array([13], dtype=np.int8))  # doctest: +SKIP
array([-14], dtype=int8)
>>> np.binary_repr(-14, width=8)  # doctest: +SKIP
'11110010'


Booleans are accepted as well:

>>> np.invert(np.array([True, False]))  # doctest: +SKIP
array([False,  True])


The ~ operator can be used as a shorthand for np.invert on ndarrays.

>>> x1 = np.array([True, False])  # doctest: +SKIP
>>> ~x1  # doctest: +SKIP
array([False,  True])

dask.array.bitwise_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.bitwise_or.

Some inconsistencies with the Dask version may exist.

Compute the bit-wise OR of two arrays element-wise.

Computes the bit-wise OR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator |.

Parameters: x1, x2 : array_like Only integer and boolean types are handled. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Result. This is a scalar if both x1 and x2 are scalars.

logical_or
bitwise_and
bitwise_xor
binary_repr
Return the binary representation of the input number as a string.

Examples

The number 13 has the binaray representation 00001101. Likewise, 16 is represented by 00010000. The bit-wise OR of 13 and 16 is then 000111011, or 29:

>>> np.bitwise_or(13, 16)  # doctest: +SKIP
29
>>> np.binary_repr(29)  # doctest: +SKIP
'11101'

>>> np.bitwise_or(32, 2)  # doctest: +SKIP
34
>>> np.bitwise_or([33, 4], 1)  # doctest: +SKIP
array([33,  5])
>>> np.bitwise_or([33, 4], [1, 2])  # doctest: +SKIP
array([33,  6])

>>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4]))  # doctest: +SKIP
array([  6,   5, 255])
>>> np.array([2, 5, 255]) | np.array([4, 4, 4])  # doctest: +SKIP
array([  6,   5, 255])
>>> np.bitwise_or(np.array([2, 5, 255, 2147483647], dtype=np.int32),  # doctest: +SKIP
...               np.array([4, 4, 4, 2147483647], dtype=np.int32))
array([         6,          5,        255, 2147483647])
>>> np.bitwise_or([True, True], [False, True])  # doctest: +SKIP
array([ True,  True])


The | operator can be used as a shorthand for np.bitwise_or on ndarrays.

>>> x1 = np.array([2, 5, 255])  # doctest: +SKIP
>>> x2 = np.array([4, 4, 4])  # doctest: +SKIP
>>> x1 | x2  # doctest: +SKIP
array([  6,   5, 255])

dask.array.bitwise_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.bitwise_xor.

Some inconsistencies with the Dask version may exist.

Compute the bit-wise XOR of two arrays element-wise.

Computes the bit-wise XOR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ^.

Parameters: x1, x2 : array_like Only integer and boolean types are handled. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Result. This is a scalar if both x1 and x2 are scalars.

logical_xor
bitwise_and
bitwise_or
binary_repr
Return the binary representation of the input number as a string.

Examples

The number 13 is represented by 00001101. Likewise, 17 is represented by 00010001. The bit-wise XOR of 13 and 17 is therefore 00011100, or 28:

>>> np.bitwise_xor(13, 17)  # doctest: +SKIP
28
>>> np.binary_repr(28)  # doctest: +SKIP
'11100'

>>> np.bitwise_xor(31, 5)  # doctest: +SKIP
26
>>> np.bitwise_xor([31,3], 5)  # doctest: +SKIP
array([26,  6])

>>> np.bitwise_xor([31,3], [5,6])  # doctest: +SKIP
array([26,  5])
>>> np.bitwise_xor([True, True], [False, True])  # doctest: +SKIP
array([ True, False])


The ^ operator can be used as a shorthand for np.bitwise_xor on ndarrays.

>>> x1 = np.array([True, True])  # doctest: +SKIP
>>> x2 = np.array([False, True])  # doctest: +SKIP
>>> x1 ^ x2  # doctest: +SKIP
array([ True, False])

dask.array.block(arrays, allow_unknown_chunksizes=False)[source]

Assemble an nd-array from nested lists of blocks.

Blocks in the innermost lists are concatenated along the last dimension (-1), then these are concatenated along the second-last dimension (-2), and so on until the outermost list is reached

Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make block.ndim the same for all blocks. This is primarily useful for working with scalars, and means that code like block([v, 1]) is valid, where v.ndim == 1.

When the nested list is two levels deep, this allows block matrices to be constructed from their components.

Parameters: arrays : nested list of array_like or scalars (but not tuples) If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied). Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match. allow_unknown_chunksizes: bool Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results. block_array : ndarray The array assembled from the given blocks. The dimensionality of the output is equal to the greatest of: * the dimensionality of all the inputs * the depth to which the input list is nested ValueError If list depths are mismatched - for instance, [[a, b], c] is illegal, and should be spelt [[a, b], [c]] If lists are empty - for instance, [[a, b], []]

concatenate
Join a sequence of arrays together.
stack
Stack arrays in sequence along a new dimension.
hstack
Stack arrays in sequence horizontally (column wise).
vstack
Stack arrays in sequence vertically (row wise).
dstack
Stack arrays in sequence depth wise (along third dimension).
vsplit
Split array into a list of multiple sub-arrays vertically.

Notes

When called with only scalars, block is equivalent to an ndarray call. So block([[1, 2], [3, 4]]) is equivalent to array([[1, 2], [3, 4]]).

This function does not enforce that the blocks lie on a fixed grid. block([[a, b], [c, d]]) is not restricted to arrays of the form:

AAAbb
AAAbb
cccDD


But is also allowed to produce, for some a, b, c, d:

AAAbb
AAAbb
cDDDD


Since concatenation happens along the last axis first, block is _not_ capable of producing the following directly:

AAAbb
cccbb
cccDD


Matlab’s “square bracket stacking”, [A, B, ...; p, q, ...], is equivalent to block([[A, B, ...], [p, q, ...]]).

dask.array.blockwise(func, out_ind, *args, name=None, token=None, dtype=None, adjust_chunks=None, new_axes=None, align_arrays=True, concatenate=None, meta=None, **kwargs)[source]

Tensor operation: Generalized inner and outer products

A broad class of blocked algorithms and patterns can be specified with a concise multi-index notation. The blockwise function applies an in-memory function across multiple blocks of multiple inputs in a variety of ways. Many dask.array operations are special cases of blockwise including elementwise, broadcasting, reductions, tensordot, and transpose.

Parameters: func : callable Function to apply to individual tuples of blocks out_ind : iterable Block pattern of the output, something like ‘ijk’ or (1, 2, 3) *args : sequence of Array, index pairs Sequence like (x, ‘ij’, y, ‘jk’, z, ‘i’) **kwargs : dict Extra keyword arguments to pass to function dtype : np.dtype Datatype of resulting array. concatenate : bool, keyword only If true concatenate arrays along dummy indices, else provide lists adjust_chunks : dict Dictionary mapping index to function to be applied to chunk sizes new_axes : dict, keyword only New indexes and their dimension lengths

Examples

2D embarrassingly parallel operation from two arrays, x, and y.

>>> import operator, numpy as np, dask.array as da
>>> x = da.from_array([[1, 2],
...                    [3, 4]], chunks=(1, 2))
>>> y = da.from_array([[10, 20],
...                    [0, 0]])
>>> z = blockwise(operator.add, 'ij', x, 'ij', y, 'ij', dtype='f8')
>>> z.compute()
array([[11, 22],
[ 3,  4]])


Outer product multiplying a by b, two 1-d vectors

>>> a = da.from_array([0, 1, 2], chunks=1)
>>> b = da.from_array([10, 50, 100], chunks=1)
>>> z = blockwise(np.outer, 'ij', a, 'i', b, 'j', dtype='f8')
>>> z.compute()
array([[  0,   0,   0],
[ 10,  50, 100],
[ 20, 100, 200]])


z = x.T

>>> z = blockwise(np.transpose, 'ji', x, 'ij', dtype=x.dtype)
>>> z.compute()
array([[1, 3],
[2, 4]])


The transpose case above is illustrative because it does transposition both on each in-memory block by calling np.transpose and on the order of the blocks themselves, by switching the order of the index ij -> ji.

We can compose these same patterns with more variables and more complex in-memory functions

z = X + Y.T

>>> z = blockwise(lambda x, y: x + y.T, 'ij', x, 'ij', y, 'ji', dtype='f8')
>>> z.compute()
array([[11,  2],
[23,  4]])


Any index, like i missing from the output index is interpreted as a contraction (note that this differs from Einstein convention; repeated indices do not imply contraction.) In the case of a contraction the passed function should expect an iterable of blocks on any array that holds that index. To receive arrays concatenated along contracted dimensions instead pass concatenate=True.

Inner product multiplying a by b, two 1-d vectors

>>> def sequence_dot(a_blocks, b_blocks):
...     result = 0
...     for a, b in zip(a_blocks, b_blocks):
...         result += a.dot(b)
...     return result

>>> z = blockwise(sequence_dot, '', a, 'i', b, 'i', dtype='f8')
>>> z.compute()
250


Add new single-chunk dimensions with the new_axes= keyword, including the length of the new dimension. New dimensions will always be in a single chunk.

>>> def f(a):
...     return a[:, None] * np.ones((1, 5))

>>> z = blockwise(f, 'az', a, 'a', new_axes={'z': 5}, dtype=a.dtype)


New dimensions can also be multi-chunk by specifying a tuple of chunk sizes. This has limited utility as is (because the chunks are all the same), but the resulting graph can be modified to achieve more useful results (see da.map_blocks).

>>> z = blockwise(f, 'az', a, 'a', new_axes={'z': (5, 5)}, dtype=x.dtype)
>>> z.chunks
((1, 1, 1), (5, 5))


If the applied function changes the size of each chunk you can specify this with a adjust_chunks={...} dictionary holding a function for each index that modifies the dimension size in that index.

>>> def double(x):
...     return np.concatenate([x, x])

>>> y = blockwise(double, 'ij', x, 'ij',
...               adjust_chunks={'i': lambda n: 2 * n}, dtype=x.dtype)
>>> y.chunks
((2, 2), (2,))


Include literals by indexing with None

>>> z = blockwise(operator.add, 'ij', x, 'ij', 1234, None, dtype=x.dtype)
>>> z.compute()
array([[1235, 1236],
[1237, 1238]])

dask.array.broadcast_arrays(*args, **kwargs)[source]

Broadcast any number of arrays against each other.

This docstring was copied from numpy.broadcast_arrays.

Some inconsistencies with the Dask version may exist.

Parameters: *args : array_likes The arrays to broadcast. subok : bool, optional (Not supported in Dask) If True, then sub-classes will be passed-through, otherwise the returned arrays will be forced to be a base-class array (default). broadcasted : list of arrays These arrays are views on the original arrays. They are typically not contiguous. Furthermore, more than one element of a broadcasted array may refer to a single memory location. If you need to write to the arrays, make copies first. While you can set the writable flag True, writing to a single output value may end up changing more than one location in the output array. Deprecated since version 1.17: The output is currently marked so that if written to, a deprecation warning will be emitted. A future version will set the writable flag False so writing to it will raise an error.

broadcast
broadcast_to
broadcast_shapes

Examples

>>> x = np.array([[1,2,3]])  # doctest: +SKIP
>>> y = np.array([[4],[5]])  # doctest: +SKIP
>>> np.broadcast_arrays(x, y)  # doctest: +SKIP
[array([[1, 2, 3],
[1, 2, 3]]), array([[4, 4, 4],
[5, 5, 5]])]


Here is a useful idiom for getting contiguous copies instead of non-contiguous views.

>>> [np.array(a) for a in np.broadcast_arrays(x, y)]  # doctest: +SKIP
[array([[1, 2, 3],
[1, 2, 3]]), array([[4, 4, 4],
[5, 5, 5]])]

dask.array.broadcast_to(x, shape, chunks=None, meta=None)[source]

Broadcast an array to a new shape.

Parameters: x : array_like The array to broadcast. shape : tuple The shape of the desired array. chunks : tuple, optional If provided, then the result will use these chunks instead of the same chunks as the source array. Setting chunks explicitly as part of broadcast_to is more efficient than rechunking afterwards. Chunks are only allowed to differ from the original shape along dimensions that are new on the result or have size 1 the input array. meta : empty ndarray empty ndarray created with same NumPy backend, ndim and dtype as the Dask Array being created (overrides dtype) broadcast : dask array
dask.array.cbrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.cbrt.

Some inconsistencies with the Dask version may exist.

Return the cube-root of an array, element-wise.

New in version 1.10.0.

Parameters: x : array_like The values whose cube-roots are required. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray An array of the same shape as x, containing the cube cube-root of each element in x. If out was provided, y is a reference to it. This is a scalar if x is a scalar.

Examples

>>> np.cbrt([1,8,27])  # doctest: +SKIP
array([ 1.,  2.,  3.])

dask.array.coarsen(reduction, x, axes, trim_excess=False, **kwargs)[source]

Coarsen array by applying reduction to fixed size neighborhoods

Parameters: reduction: function Function like np.sum, np.mean, etc… x: np.ndarray Array to be coarsened axes: dict Mapping of axis to coarsening factor

Examples

>>> x = np.array([1, 2, 3, 4, 5, 6])
>>> coarsen(np.sum, x, {0: 2})          #doctest: +SKIP
array([ 3,  7, 11])
>>> coarsen(np.max, x, {0: 3})          #doctest: +SKIP
array([3, 6])


Provide dictionary of scale per dimension

>>> x = np.arange(24).reshape((4, 6))
>>> x
array([[ 0,  1,  2,  3,  4,  5],
[ 6,  7,  8,  9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23]])

>>> coarsen(np.min, x, {0: 2, 1: 3})    #doctest: +SKIP
array([[ 0,  3],
[12, 15]])


You must avoid excess elements explicitly

>>> x = np.array([1, 2, 3, 4, 5, 6, 7, 8])
>>> coarsen(np.min, x, {0: 3}, trim_excess=True)    #doctest: +SKIP
array([1, 4])

dask.array.ceil(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.ceil.

Some inconsistencies with the Dask version may exist.

Return the ceiling of the input, element-wise.

The ceil of the scalar x is the smallest integer i, such that i >= x. It is often denoted as $$\lceil x \rceil$$.

Parameters: x : array_like Input data. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or scalar The ceiling of each element in x, with float dtype. This is a scalar if x is a scalar.

Examples

>>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])  # doctest: +SKIP
>>> np.ceil(a)  # doctest: +SKIP
array([-1., -1., -0.,  1.,  2.,  2.,  2.])

dask.array.choose(a, choices)[source]

Construct an array from an index array and a set of arrays to choose from.

This docstring was copied from numpy.choose.

Some inconsistencies with the Dask version may exist.

First of all, if confused or uncertain, definitely look at the Examples - in its full generality, this function is less simple than it might seem from the following code description (below ndi = numpy.lib.index_tricks):

np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)]).

But this omits some subtleties. Here is a fully general summary:

Given an “index” array (a) of integers and a sequence of n arrays (choices), a and each choice array are first broadcast, as necessary, to arrays of a common shape; calling these Ba and Bchoices[i], i = 0,…,n-1 we have that, necessarily, Ba.shape == Bchoices[i].shape for each i. Then, a new array with shape Ba.shape is created as follows:

• if mode=raise (the default), then, first of all, each element of a (and thus Ba) must be in the range [0, n-1]; now, suppose that i (in that range) is the value at the (j0, j1, …, jm) position in Ba - then the value at the same position in the new array is the value in Bchoices[i] at that same position;
• if mode=wrap, values in a (and thus Ba) may be any (signed) integer; modular arithmetic is used to map integers outside the range [0, n-1] back into that range; and then the new array is constructed as above;
• if mode=clip, values in a (and thus Ba) may be any (signed) integer; negative integers are mapped to 0; values greater than n-1 are mapped to n-1; and then the new array is constructed as above.
Parameters: a : int array This array must contain integers in [0, n-1], where n is the number of choices, unless mode=wrap or mode=clip, in which cases any integers are permissible. choices : sequence of arrays Choice arrays. a and all of the choices must be broadcastable to the same shape. If choices is itself an array (not recommended), then its outermost dimension (i.e., the one corresponding to choices.shape[0]) is taken as defining the “sequence”. out : array, optional (Not supported in Dask) If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype. Note that out is always buffered if mode=’raise’; use other modes for better performance. mode : {‘raise’ (default), ‘wrap’, ‘clip’}, optional (Not supported in Dask) Specifies how indices outside [0, n-1] will be treated: ‘raise’ : an exception is raised ‘wrap’ : value becomes value mod n ‘clip’ : values < 0 are mapped to 0, values > n-1 are mapped to n-1 merged_array : array The merged result. ValueError: shape mismatch If a and each choice array are not all broadcastable to the same shape.

ndarray.choose
equivalent method
numpy.take_along_axis
Preferable if choices is an array

Notes

To reduce the chance of misinterpretation, even though the following “abuse” is nominally supported, choices should neither be, nor be thought of as, a single array, i.e., the outermost sequence-like container should be either a list or a tuple.

Examples

>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],  # doctest: +SKIP
...   [20, 21, 22, 23], [30, 31, 32, 33]]
>>> np.choose([2, 3, 1, 0], choices  # doctest: +SKIP
... # the first element of the result will be the first element of the
... # third (2+1) "array" in choices, namely, 20; the second element
... # will be the second element of the fourth (3+1) choice array, i.e.,
... # 31, etc.
... )
array([20, 31, 12,  3])
>>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)  # doctest: +SKIP
array([20, 31, 12,  3])
>>> # because there are 4 choice arrays
>>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)  # doctest: +SKIP
array([20,  1, 12,  3])
>>> # i.e., 0


A couple examples illustrating how choose broadcasts:

>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]  # doctest: +SKIP
>>> choices = [-10, 10]  # doctest: +SKIP
>>> np.choose(a, choices)  # doctest: +SKIP
array([[ 10, -10,  10],
[-10,  10, -10],
[ 10, -10,  10]])

>>> # With thanks to Anne Archibald
>>> a = np.array([0, 1]).reshape((2,1,1))  # doctest: +SKIP
>>> c1 = np.array([1, 2, 3]).reshape((1,3,1))  # doctest: +SKIP
>>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))  # doctest: +SKIP
>>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2  # doctest: +SKIP
array([[[ 1,  1,  1,  1,  1],
[ 2,  2,  2,  2,  2],
[ 3,  3,  3,  3,  3]],
[[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5]]])

dask.array.clip(*args, **kwargs)

Clip (limit) the values in an array.

This docstring was copied from numpy.clip.

Some inconsistencies with the Dask version may exist.

Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of [0, 1] is specified, values smaller than 0 become 0, and values larger than 1 become 1.

Equivalent to but faster than np.minimum(a_max, np.maximum(a, a_min)).

No check is performed to ensure a_min < a_max.

Parameters: a : array_like (Not supported in Dask) Array containing elements to clip. a_min, a_max : array_like or None Minimum and maximum value. If None, clipping is not performed on the corresponding edge. Only one of a_min and a_max may be None. Both are broadcast against a. out : ndarray, optional (Not supported in Dask) The results will be placed in this array. It may be the input array for in-place clipping. out must be of the right shape to hold the output. Its type is preserved. **kwargs For other keyword-only arguments, see the ufunc docs. New in version 1.17.0. clipped_array : ndarray An array with the elements of a, but where values < a_min are replaced with a_min, and those > a_max with a_max.

Examples

>>> a = np.arange(10)  # doctest: +SKIP
>>> np.clip(a, 1, 8)  # doctest: +SKIP
array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
>>> a  # doctest: +SKIP
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.clip(a, 3, 6, out=a)  # doctest: +SKIP
array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
>>> a = np.arange(10)  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)  # doctest: +SKIP
array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])

dask.array.compress(condition, a, axis=None)[source]

Return selected slices of an array along given axis.

This docstring was copied from numpy.compress.

Some inconsistencies with the Dask version may exist.

When working along a given axis, a slice along that axis is returned in output for each index where condition evaluates to True. When working on a 1-D array, compress is equivalent to extract.

Parameters: condition : 1-D array of bools Array that selects which entries to return. If len(condition) is less than the size of a along the given axis, then output is truncated to the length of the condition array. a : array_like Array from which to extract a part. axis : int, optional Axis along which to take slices. If None (default), work on the flattened array. out : ndarray, optional (Not supported in Dask) Output array. Its type is preserved and it must be of the right shape to hold the output. compressed_array : ndarray A copy of a without the slices along axis for which condition is false.

take, choose, diag, diagonal, select
ndarray.compress
Equivalent method in ndarray
extract
Equivalent method when working on 1-D arrays
Output type determination

Examples

>>> a = np.array([[1, 2], [3, 4], [5, 6]])  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[1, 2],
[3, 4],
[5, 6]])
>>> np.compress([0, 1], a, axis=0)  # doctest: +SKIP
array([[3, 4]])
>>> np.compress([False, True, True], a, axis=0)  # doctest: +SKIP
array([[3, 4],
[5, 6]])
>>> np.compress([False, True], a, axis=1)  # doctest: +SKIP
array([[2],
[4],
[6]])


Working on the flattened array does not return slices along an axis but selects elements.

>>> np.compress([False, True], a)  # doctest: +SKIP
array([2])

dask.array.concatenate(seq, axis=0, allow_unknown_chunksizes=False)[source]

Concatenate arrays along an existing axis

Given a sequence of dask Arrays form a new dask Array by stacking them along an existing dimension (axis=0 by default)

Parameters: seq: list of dask.arrays axis: int Dimension along which to align all of the arrays allow_unknown_chunksizes: bool Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.

Examples

Create slices

>>> import dask.array as da
>>> import numpy as np

>>> data = [da.from_array(np.ones((4, 4)), chunks=(2, 2))
...          for i in range(3)]

>>> x = da.concatenate(data, axis=0)
>>> x.shape
(12, 4)

>>> da.concatenate(data, axis=1).shape
(4, 12)


Result is a new dask Array

dask.array.conj(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.conjugate.

Some inconsistencies with the Dask version may exist.

Return the complex conjugate, element-wise.

The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.

Parameters: x : array_like Input value. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray The complex conjugate of x, with same dtype as y. This is a scalar if x is a scalar.

Notes

conj is an alias for conjugate:

>>> np.conj is np.conjugate  # doctest: +SKIP
True


Examples

>>> np.conjugate(1+2j)  # doctest: +SKIP
(1-2j)

>>> x = np.eye(2) + 1j * np.eye(2)  # doctest: +SKIP
>>> np.conjugate(x)  # doctest: +SKIP
array([[ 1.-1.j,  0.-0.j],
[ 0.-0.j,  1.-1.j]])

dask.array.copysign(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.copysign.

Some inconsistencies with the Dask version may exist.

Change the sign of x1 to that of x2, element-wise.

If x2 is a scalar, its sign will be copied to all elements of x1.

Parameters: x1 : array_like Values to change the sign of. x2 : array_like The sign of x2 is copied to x1. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar The values of x1 with the sign of x2. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.copysign(1.3, -1)  # doctest: +SKIP
-1.3
>>> 1/np.copysign(0, 1)  # doctest: +SKIP
inf
>>> 1/np.copysign(0, -1)  # doctest: +SKIP
-inf

>>> np.copysign([-1, 0, 1], -1.1)  # doctest: +SKIP
array([-1., -0., -1.])
>>> np.copysign([-1, 0, 1], np.arange(3)-1)  # doctest: +SKIP
array([-1.,  0.,  1.])

dask.array.corrcoef(x, y=None, rowvar=1)[source]

Return Pearson product-moment correlation coefficients.

This docstring was copied from numpy.corrcoef.

Some inconsistencies with the Dask version may exist.

Please refer to the documentation for cov for more detail. The relationship between the correlation coefficient matrix, R, and the covariance matrix, C, is

$R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }$

The values of R are between -1 and 1, inclusive.

Parameters: x : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of x represents a variable, and each column a single observation of all those variables. Also see rowvar below. y : array_like, optional An additional set of variables and observations. y has the same shape as x. rowvar : bool, optional If rowvar is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : _NoValue, optional (Not supported in Dask) Has no effect, do not use. Deprecated since version 1.10.0. ddof : _NoValue, optional (Not supported in Dask) Has no effect, do not use. Deprecated since version 1.10.0. dtype : data-type, optional (Not supported in Dask) Data-type of the result. By default, the return data-type will have at least numpy.float64 precision. New in version 1.20. R : ndarray The correlation coefficient matrix of the variables.

cov
Covariance matrix

Notes

Due to floating point rounding the resulting array may not be Hermitian, the diagonal elements may not be 1, and the elements may not satisfy the inequality abs(a) <= 1. The real and imaginary parts are clipped to the interval [-1, 1] in an attempt to improve on that situation but is not much help in the complex case.

This function accepts but discards arguments bias and ddof. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy.

Examples

In this example we generate two random arrays, xarr and yarr, and compute the row-wise and column-wise Pearson correlation coefficients, R. Since rowvar is true by default, we first find the row-wise Pearson correlation coefficients between the variables of xarr.

>>> import numpy as np  # doctest: +SKIP
>>> rng = np.random.default_rng(seed=42)  # doctest: +SKIP
>>> xarr = rng.random((3, 3))  # doctest: +SKIP
>>> xarr  # doctest: +SKIP
array([[0.77395605, 0.43887844, 0.85859792],
[0.69736803, 0.09417735, 0.97562235],
[0.7611397 , 0.78606431, 0.12811363]])
>>> R1 = np.corrcoef(xarr)  # doctest: +SKIP
>>> R1  # doctest: +SKIP
array([[ 1.        ,  0.99256089, -0.68080986],
[ 0.99256089,  1.        , -0.76492172],
[-0.68080986, -0.76492172,  1.        ]])


If we add another set of variables and observations yarr, we can compute the row-wise Pearson correlation coefficients between the variables in xarr and yarr.

>>> yarr = rng.random((3, 3))  # doctest: +SKIP
>>> yarr  # doctest: +SKIP
array([[0.45038594, 0.37079802, 0.92676499],
[0.64386512, 0.82276161, 0.4434142 ],
[0.22723872, 0.55458479, 0.06381726]])
>>> R2 = np.corrcoef(xarr, yarr)  # doctest: +SKIP
>>> R2  # doctest: +SKIP
array([[ 1.        ,  0.99256089, -0.68080986,  0.75008178, -0.934284  ,
-0.99004057],
[ 0.99256089,  1.        , -0.76492172,  0.82502011, -0.97074098,
-0.99981569],
[-0.68080986, -0.76492172,  1.        , -0.99507202,  0.89721355,
0.77714685],
[ 0.75008178,  0.82502011, -0.99507202,  1.        , -0.93657855,
-0.83571711],
[-0.934284  , -0.97074098,  0.89721355, -0.93657855,  1.        ,
0.97517215],
[-0.99004057, -0.99981569,  0.77714685, -0.83571711,  0.97517215,
1.        ]])


Finally if we use the option rowvar=False, the columns are now being treated as the variables and we will find the column-wise Pearson correlation coefficients between variables in xarr and yarr.

>>> R3 = np.corrcoef(xarr, yarr, rowvar=False)  # doctest: +SKIP
>>> R3  # doctest: +SKIP
array([[ 1.        ,  0.77598074, -0.47458546, -0.75078643, -0.9665554 ,
0.22423734],
[ 0.77598074,  1.        , -0.92346708, -0.99923895, -0.58826587,
-0.44069024],
[-0.47458546, -0.92346708,  1.        ,  0.93773029,  0.23297648,
0.75137473],
[-0.75078643, -0.99923895,  0.93773029,  1.        ,  0.55627469,
0.47536961],
[-0.9665554 , -0.58826587,  0.23297648,  0.55627469,  1.        ,
-0.46666491],
[ 0.22423734, -0.44069024,  0.75137473,  0.47536961, -0.46666491,
1.        ]])

dask.array.cos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.cos.

Some inconsistencies with the Dask version may exist.

Cosine element-wise.

Parameters: x : array_like Input array in radians. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray The corresponding cosine values. This is a scalar if x is a scalar.

Notes

If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)

References

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972.

Examples

>>> np.cos(np.array([0, np.pi/2, np.pi]))  # doctest: +SKIP
array([  1.00000000e+00,   6.12303177e-17,  -1.00000000e+00])
>>>
>>> # Example of providing the optional output parameter
>>> out1 = np.array([0], dtype='d')  # doctest: +SKIP
>>> out2 = np.cos([0.1], out1)  # doctest: +SKIP
>>> out2 is out1  # doctest: +SKIP
True
>>>
>>> # Example of ValueError due to provision of shape mis-matched out
>>> np.cos(np.zeros((3,3)),np.zeros((2,2)))  # doctest: +SKIP
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: operands could not be broadcast together with shapes (3,3) (2,2)

dask.array.cosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.cosh.

Some inconsistencies with the Dask version may exist.

Hyperbolic cosine, element-wise.

Equivalent to 1/2 * (np.exp(x) + np.exp(-x)) and np.cos(1j*x).

Parameters: x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array of same shape as x. This is a scalar if x is a scalar.

Examples

>>> np.cosh(0)  # doctest: +SKIP
1.0


The hyperbolic cosine describes the shape of a hanging cable:

>>> import matplotlib.pyplot as plt  # doctest: +SKIP
>>> x = np.linspace(-4, 4, 1000)  # doctest: +SKIP
>>> plt.plot(x, np.cosh(x))  # doctest: +SKIP
>>> plt.show()  # doctest: +SKIP

dask.array.count_nonzero(a, axis=None)[source]

Counts the number of non-zero values in the array a.

This docstring was copied from numpy.count_nonzero.

Some inconsistencies with the Dask version may exist.

The word “non-zero” is in reference to the Python 2.x built-in method __nonzero__() (renamed __bool__() in Python 3.x) of Python objects that tests an object’s “truthfulness”. For example, any number is considered truthful if it is nonzero, whereas any string is considered truthful if it is not the empty string. Thus, this function (recursively) counts how many elements in a (and in sub-arrays thereof) have their __nonzero__() or __bool__() method evaluated to True.

Parameters: a : array_like The array for which to count non-zeros. axis : int or tuple, optional Axis or tuple of axes along which to count non-zeros. Default is None, meaning that non-zeros will be counted along a flattened version of a. New in version 1.12.0. keepdims : bool, optional (Not supported in Dask) If this is set to True, the axes that are counted are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. New in version 1.19.0. count : int or array of int Number of non-zero values in the array along a given axis. Otherwise, the total number of non-zero values in the array is returned.

nonzero
Return the coordinates of all the non-zero values.

Examples

>>> np.count_nonzero(np.eye(4))  # doctest: +SKIP
4
>>> a = np.array([[0, 1, 7, 0],  # doctest: +SKIP
...               [3, 0, 2, 19]])
>>> np.count_nonzero(a)  # doctest: +SKIP
5
>>> np.count_nonzero(a, axis=0)  # doctest: +SKIP
array([1, 1, 2, 1])
>>> np.count_nonzero(a, axis=1)  # doctest: +SKIP
array([2, 3])
>>> np.count_nonzero(a, axis=1, keepdims=True)  # doctest: +SKIP
array([[2],
[3]])

dask.array.cov(m, y=None, rowvar=1, bias=0, ddof=None)[source]

Estimate a covariance matrix, given data and weights.

This docstring was copied from numpy.cov.

Some inconsistencies with the Dask version may exist.

Covariance indicates the level to which two variables vary together. If we examine N-dimensional samples, $$X = [x_1, x_2, ... x_N]^T$$, then the covariance matrix element $$C_{ij}$$ is the covariance of $$x_i$$ and $$x_j$$. The element $$C_{ii}$$ is the variance of $$x_i$$.

See the notes for an outline of the algorithm.

Parameters: m : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of m represents a variable, and each column a single observation of all those variables. Also see rowvar below. y : array_like, optional An additional set of variables and observations. y has the same form as that of m. rowvar : bool, optional If rowvar is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : bool, optional Default normalization (False) is by (N - 1), where N is the number of observations given (unbiased estimate). If bias is True, then normalization is by N. These values can be overridden by using the keyword ddof in numpy versions >= 1.5. ddof : int, optional If not None the default value implied by bias is overridden. Note that ddof=1 will return the unbiased estimate, even if both fweights and aweights are specified, and ddof=0 will return the simple average. See the notes for the details. The default value is None. New in version 1.5. fweights : array_like, int, optional (Not supported in Dask) 1-D array of integer frequency weights; the number of times each observation vector should be repeated. New in version 1.10. aweights : array_like, optional (Not supported in Dask) 1-D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. If ddof=0 the array of weights can be used to assign probabilities to observation vectors. New in version 1.10. dtype : data-type, optional (Not supported in Dask) Data-type of the result. By default, the return data-type will have at least numpy.float64 precision. New in version 1.20. out : ndarray The covariance matrix of the variables.

corrcoef
Normalized covariance matrix

Notes

Assume that the observations are in the columns of the observation array m and let f = fweights and a = aweights for brevity. The steps to compute the weighted covariance are as follows:

>>> m = np.arange(10, dtype=np.float64)
>>> f = np.arange(10) * 2
>>> a = np.arange(10) ** 2.
>>> ddof = 1
>>> w = f * a
>>> v1 = np.sum(w)
>>> v2 = np.sum(w * a)
>>> m -= np.sum(m * w, axis=None, keepdims=True) / v1
>>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2)


Note that when a == 1, the normalization factor v1 / (v1**2 - ddof * v2) goes over to 1 / (np.sum(f) - ddof) as it should.

Examples

Consider two variables, $$x_0$$ and $$x_1$$, which correlate perfectly, but in opposite directions:

>>> x = np.array([[0, 2], [1, 1], [2, 0]]).T  # doctest: +SKIP
>>> x  # doctest: +SKIP
array([[0, 1, 2],
[2, 1, 0]])


Note how $$x_0$$ increases while $$x_1$$ decreases. The covariance matrix shows this clearly:

>>> np.cov(x)  # doctest: +SKIP
array([[ 1., -1.],
[-1.,  1.]])


Note that element $$C_{0,1}$$, which shows the correlation between $$x_0$$ and $$x_1$$, is negative.

Further, note how x and y are combined:

>>> x = [-2.1, -1,  4.3]  # doctest: +SKIP
>>> y = [3,  1.1,  0.12]  # doctest: +SKIP
>>> X = np.stack((x, y), axis=0)  # doctest: +SKIP
>>> np.cov(X)  # doctest: +SKIP
array([[11.71      , -4.286     ], # may vary
[-4.286     ,  2.144133]])
>>> np.cov(x, y)  # doctest: +SKIP
array([[11.71      , -4.286     ], # may vary
[-4.286     ,  2.144133]])
>>> np.cov(x)  # doctest: +SKIP
array(11.71)

dask.array.cumprod(x, axis=None, dtype=None, out=None, method='sequential')[source]

Return the cumulative product of elements along a given axis.

This docstring was copied from numpy.cumprod.

Some inconsistencies with the Dask version may exist.

Dask added an additional keyword-only argument method.

method : {‘sequential’, ‘blelloch’}, optional

Choose which method to use to perform the cumprod. Default is ‘sequential’.

• ‘sequential’ performs the cumprod of each prior block before the current block.
• ‘blelloch’ is a work-efficient parallel cumprod. It exposes parallelism by first taking the product of each block and combines the products via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary.
Parameters: a : array_like (Not supported in Dask) Input array. axis : int, optional Axis along which the cumulative product is computed. By default the input is flattened. dtype : dtype, optional Type of the returned array, as well as of the accumulator in which the elements are multiplied. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary. cumprod : ndarray A new array holding the result is returned unless out is specified, in which case a reference to out is returned.

Notes

Arithmetic is modular when using integer types, and no error is raised on overflow.

Examples

>>> a = np.array([1,2,3])  # doctest: +SKIP
>>> np.cumprod(a) # intermediate results 1, 1*2  # doctest: +SKIP
...               # total product 1*2*3 = 6
array([1, 2, 6])
>>> a = np.array([[1, 2, 3], [4, 5, 6]])  # doctest: +SKIP
>>> np.cumprod(a, dtype=float) # specify type of output  # doctest: +SKIP
array([   1.,    2.,    6.,   24.,  120.,  720.])


The cumulative product for each column (i.e., over the rows) of a:

>>> np.cumprod(a, axis=0)  # doctest: +SKIP
array([[ 1,  2,  3],
[ 4, 10, 18]])


The cumulative product for each row (i.e. over the columns) of a:

>>> np.cumprod(a,axis=1)  # doctest: +SKIP
array([[  1,   2,   6],
[  4,  20, 120]])

dask.array.cumsum(x, axis=None, dtype=None, out=None, method='sequential')[source]

Return the cumulative sum of the elements along a given axis.

This docstring was copied from numpy.cumsum.

Some inconsistencies with the Dask version may exist.

Dask added an additional keyword-only argument method.

method : {‘sequential’, ‘blelloch’}, optional

Choose which method to use to perform the cumsum. Default is ‘sequential’.

• ‘sequential’ performs the cumsum of each prior block before the current block.
• ‘blelloch’ is a work-efficient parallel cumsum. It exposes parallelism by first taking the sum of each block and combines the sums via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary.
Parameters: a : array_like (Not supported in Dask) Input array. axis : int, optional Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. dtype : dtype, optional Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See Output type determination for more details. cumsum_along_axis : ndarray. A new array holding the result is returned unless out is specified, in which case a reference to out is returned. The result has the same size as a, and the same shape as a if axis is not None or a is a 1-d array.

sum
Sum array elements.
trapz
Integration of array values using the composite trapezoidal rule.
diff
Calculate the n-th discrete difference along given axis.

Notes

Arithmetic is modular when using integer types, and no error is raised on overflow.

Examples

>>> a = np.array([[1,2,3], [4,5,6]])  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[1, 2, 3],
[4, 5, 6]])
>>> np.cumsum(a)  # doctest: +SKIP
array([ 1,  3,  6, 10, 15, 21])
>>> np.cumsum(a, dtype=float)     # specifies type of output value(s)  # doctest: +SKIP
array([  1.,   3.,   6.,  10.,  15.,  21.])

>>> np.cumsum(a,axis=0)      # sum over rows for each of the 3 columns  # doctest: +SKIP
array([[1, 2, 3],
[5, 7, 9]])
>>> np.cumsum(a,axis=1)      # sum over columns for each of the 2 rows  # doctest: +SKIP
array([[ 1,  3,  6],
[ 4,  9, 15]])

dask.array.deg2rad(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.deg2rad.

Some inconsistencies with the Dask version may exist.

Convert angles from degrees to radians.

Parameters: x : array_like Angles in degrees. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray The corresponding angle in radians. This is a scalar if x is a scalar.

rad2deg
Convert angles from radians to degrees.
unwrap
Remove large jumps in angle by wrapping.

Notes

New in version 1.3.0.

deg2rad(x) is x * pi / 180.

Examples

>>> np.deg2rad(180)  # doctest: +SKIP
3.1415926535897931

dask.array.degrees(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.degrees.

Some inconsistencies with the Dask version may exist.

Convert angles from radians to degrees.

Parameters: x : array_like Input array in radians. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray of floats The corresponding degree values; if out was supplied this is a reference to it. This is a scalar if x is a scalar.

rad2deg
equivalent function

Examples

Convert a radian array to degrees

>>> rad = np.arange(12.)*np.pi/6  # doctest: +SKIP
array([   0.,   30.,   60.,   90.,  120.,  150.,  180.,  210.,  240.,
270.,  300.,  330.])

>>> out = np.zeros((rad.shape))  # doctest: +SKIP
>>> r = np.degrees(rad, out)  # doctest: +SKIP
>>> np.all(r == out)  # doctest: +SKIP
True

dask.array.diag(v)[source]

Extract a diagonal or construct a diagonal array.

This docstring was copied from numpy.diag.

Some inconsistencies with the Dask version may exist.

See the more detailed documentation for numpy.diagonal if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using.

Parameters: v : array_like If v is a 2-D array, return a copy of its k-th diagonal. If v is a 1-D array, return a 2-D array with v on the k-th diagonal. k : int, optional (Not supported in Dask) Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. out : ndarray The extracted diagonal or constructed diagonal array.

diagonal
Return specified diagonals.
diagflat
Create a 2-D array with the flattened input as a diagonal.
trace
Sum along diagonals.
triu
Upper triangle of an array.
tril
Lower triangle of an array.

Examples

>>> x = np.arange(9).reshape((3,3))  # doctest: +SKIP
>>> x  # doctest: +SKIP
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])

>>> np.diag(x)  # doctest: +SKIP
array([0, 4, 8])
>>> np.diag(x, k=1)  # doctest: +SKIP
array([1, 5])
>>> np.diag(x, k=-1)  # doctest: +SKIP
array([3, 7])

>>> np.diag(np.diag(x))  # doctest: +SKIP
array([[0, 0, 0],
[0, 4, 0],
[0, 0, 8]])

dask.array.diagonal(a, offset=0, axis1=0, axis2=1)[source]

Return specified diagonals.

This docstring was copied from numpy.diagonal.

Some inconsistencies with the Dask version may exist.

If a is 2-D, returns the diagonal of a with the given offset, i.e., the collection of elements of the form a[i, i+offset]. If a has more than two dimensions, then the axes specified by axis1 and axis2 are used to determine the 2-D sub-array whose diagonal is returned. The shape of the resulting array can be determined by removing axis1 and axis2 and appending an index to the right equal to the size of the resulting diagonals.

In versions of NumPy prior to 1.7, this function always returned a new, independent array containing a copy of the values in the diagonal.

In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal, but depending on this fact is deprecated. Writing to the resulting array continues to work as it used to, but a FutureWarning is issued.

Starting in NumPy 1.9 it returns a read-only view on the original array. Attempting to write to the resulting array will produce an error.

In some future release, it will return a read/write view and writing to the returned array will alter your original array. The returned array will have the same type as the input array.

If you don’t write to the array returned by this function, then you can just ignore all of the above.

If you depend on the current behavior, then we suggest copying the returned array explicitly, i.e., use np.diagonal(a).copy() instead of just np.diagonal(a). This will work with both past and future versions of NumPy.

Parameters: a : array_like Array from which the diagonals are taken. offset : int, optional Offset of the diagonal from the main diagonal. Can be positive or negative. Defaults to main diagonal (0). axis1 : int, optional Axis to be used as the first axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults to first axis (0). axis2 : int, optional Axis to be used as the second axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults to second axis (1). array_of_diagonals : ndarray If a is 2-D, then a 1-D array containing the diagonal and of the same type as a is returned unless a is a matrix, in which case a 1-D array rather than a (2-D) matrix is returned in order to maintain backward compatibility. If a.ndim > 2, then the dimensions specified by axis1 and axis2 are removed, and a new axis inserted at the end corresponding to the diagonal. ValueError If the dimension of a is less than 2.

diag
MATLAB work-a-like for 1-D and 2-D arrays.
diagflat
Create diagonal arrays.
trace
Sum along diagonals.

Examples

>>> a = np.arange(4).reshape(2,2)  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[0, 1],
[2, 3]])
>>> a.diagonal()  # doctest: +SKIP
array([0, 3])
>>> a.diagonal(1)  # doctest: +SKIP
array([1])


A 3-D example:

>>> a = np.arange(8).reshape(2,2,2); a  # doctest: +SKIP
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> a.diagonal(0,  # Main diagonals of two arrays created by skipping  # doctest: +SKIP
...            0,  # across the outer(left)-most axis last and
...            1)  # the "middle" (row) axis first.
array([[0, 6],
[1, 7]])


The sub-arrays whose main diagonals we just obtained; note that each corresponds to fixing the right-most (column) axis, and that the diagonals are “packed” in rows.

>>> a[:,:,0]  # main diagonal is [0 6]  # doctest: +SKIP
array([[0, 2],
[4, 6]])
>>> a[:,:,1]  # main diagonal is [1 7]  # doctest: +SKIP
array([[1, 3],
[5, 7]])


The anti-diagonal can be obtained by reversing the order of elements using either numpy.flipud or numpy.fliplr.

>>> a = np.arange(9).reshape(3, 3)  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
>>> np.fliplr(a).diagonal()  # Horizontal flip  # doctest: +SKIP
array([2, 4, 6])
>>> np.flipud(a).diagonal()  # Vertical flip  # doctest: +SKIP
array([6, 4, 2])


Note that the order in which the diagonal is retrieved varies depending on the flip function.

dask.array.diff(a, n=1, axis=-1)[source]

Calculate the n-th discrete difference along the given axis.

This docstring was copied from numpy.diff.

Some inconsistencies with the Dask version may exist.

The first difference is given by out[i] = a[i+1] - a[i] along the given axis, higher differences are calculated by using diff recursively.

Parameters: a : array_like Input array n : int, optional The number of times values are differenced. If zero, the input is returned as-is. axis : int, optional The axis along which the difference is taken, default is the last axis. prepend, append : array_like, optional Values to prepend or append to a along axis prior to performing the difference. Scalar values are expanded to arrays with length 1 in the direction of axis and the shape of the input array in along all other axes. Otherwise the dimension and shape must match a except along axis. New in version 1.16.0. diff : ndarray The n-th differences. The shape of the output is the same as a except along axis where the dimension is smaller by n. The type of the output is the same as the type of the difference between any two elements of a. This is the same as the type of a in most cases. A notable exception is datetime64, which results in a timedelta64 output array.

Notes

Type is preserved for boolean arrays, so the result will contain False when consecutive elements are the same and True when they differ.

For unsigned integer arrays, the results will also be unsigned. This should not be surprising, as the result is consistent with calculating the difference directly:

>>> u8_arr = np.array([1, 0], dtype=np.uint8)  # doctest: +SKIP
>>> np.diff(u8_arr)  # doctest: +SKIP
array([255], dtype=uint8)
>>> u8_arr[1,...] - u8_arr[0,...]  # doctest: +SKIP
255


If this is not desirable, then the array should be cast to a larger integer type first:

>>> i16_arr = u8_arr.astype(np.int16)  # doctest: +SKIP
>>> np.diff(i16_arr)  # doctest: +SKIP
array([-1], dtype=int16)


Examples

>>> x = np.array([1, 2, 4, 7, 0])  # doctest: +SKIP
>>> np.diff(x)  # doctest: +SKIP
array([ 1,  2,  3, -7])
>>> np.diff(x, n=2)  # doctest: +SKIP
array([  1,   1, -10])

>>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])  # doctest: +SKIP
>>> np.diff(x)  # doctest: +SKIP
array([[2, 3, 4],
[5, 1, 2]])
>>> np.diff(x, axis=0)  # doctest: +SKIP
array([[-1,  2,  0, -2]])

>>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64)  # doctest: +SKIP
>>> np.diff(x)  # doctest: +SKIP
array([1, 1], dtype='timedelta64[D]')

dask.array.digitize(a, bins, right=False)[source]

Return the indices of the bins to which each value in input array belongs.

This docstring was copied from numpy.digitize.

Some inconsistencies with the Dask version may exist.

right order of bins returned index i satisfies
False increasing bins[i-1] <= x < bins[i]
True increasing bins[i-1] < x <= bins[i]
False decreasing bins[i-1] > x >= bins[i]
True decreasing bins[i-1] >= x > bins[i]

If values in x are beyond the bounds of bins, 0 or len(bins) is returned as appropriate.

Parameters: x : array_like (Not supported in Dask) Input array to be binned. Prior to NumPy 1.10.0, this array had to be 1-dimensional, but can now have any shape. bins : array_like Array of bins. It has to be 1-dimensional and monotonic. right : bool, optional Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i-1] <= x < bins[i] is the default behavior for monotonically increasing bins. indices : ndarray of ints Output array of indices, of same shape as x. ValueError If bins is not monotonic. TypeError If the type of the input is complex.

Notes

If values in x are such that they fall outside the bin range, attempting to index bins with the indices that digitize returns will result in an IndexError.

New in version 1.10.0.

np.digitize is implemented in terms of np.searchsorted. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1-dimensional.

For monotonically _increasing_ bins, the following are equivalent:

np.digitize(x, bins, right=True)
np.searchsorted(bins, x, side='left')


Note that as the order of the arguments are reversed, the side must be too. The searchsorted call is marginally faster, as it does not do any monotonicity checks. Perhaps more importantly, it supports all dtypes.

Examples

>>> x = np.array([0.2, 6.4, 3.0, 1.6])  # doctest: +SKIP
>>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])  # doctest: +SKIP
>>> inds = np.digitize(x, bins)  # doctest: +SKIP
>>> inds  # doctest: +SKIP
array([1, 4, 3, 2])
>>> for n in range(x.size):  # doctest: +SKIP
...   print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]])
...
0.0 <= 0.2 < 1.0
4.0 <= 6.4 < 10.0
2.5 <= 3.0 < 4.0
1.0 <= 1.6 < 2.5

>>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.])  # doctest: +SKIP
>>> bins = np.array([0, 5, 10, 15, 20])  # doctest: +SKIP
>>> np.digitize(x,bins,right=True)  # doctest: +SKIP
array([1, 2, 3, 4, 4])
>>> np.digitize(x,bins,right=False)  # doctest: +SKIP
array([1, 3, 3, 4, 5])

dask.array.dot(a, b, out=None)[source]

This docstring was copied from numpy.dot.

Some inconsistencies with the Dask version may exist.

Dot product of two arrays. Specifically,

• If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation).

• If both a and b are 2-D arrays, it is matrix multiplication, but using matmul() or a @ b is preferred.

• If either a or b is 0-D (scalar), it is equivalent to multiply() and using numpy.multiply(a, b) or a * b is preferred.

• If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.

• If a is an N-D array and b is an M-D array (where M>=2), it is a sum product over the last axis of a and the second-to-last axis of b:

dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

Parameters: a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. output : ndarray Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned. ValueError If the last dimension of a is not the same size as the second-to-last dimension of b.

vdot
Complex-conjugating dot product.
tensordot
Sum products over arbitrary axes.
einsum
Einstein summation convention.
matmul
‘@’ operator as method with out parameter.
linalg.multi_dot
Chained dot product.

Examples

>>> np.dot(3, 4)  # doctest: +SKIP
12


Neither argument is complex-conjugated:

>>> np.dot([2j, 3j], [2j, 3j])  # doctest: +SKIP
(-13+0j)


For 2-D arrays it is the matrix product:

>>> a = [[1, 0], [0, 1]]  # doctest: +SKIP
>>> b = [[4, 1], [2, 2]]  # doctest: +SKIP
>>> np.dot(a, b)  # doctest: +SKIP
array([[4, 1],
[2, 2]])

>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))  # doctest: +SKIP
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))  # doctest: +SKIP
>>> np.dot(a, b)[2,3,2,1,2,2]  # doctest: +SKIP
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])  # doctest: +SKIP
499128

dask.array.dstack(tup, allow_unknown_chunksizes=False)[source]

Stack arrays in sequence depth wise (along third axis).

This docstring was copied from numpy.dstack.

Some inconsistencies with the Dask version may exist.

This is equivalent to concatenation along the third axis after 2-D arrays of shape (M,N) have been reshaped to (M,N,1) and 1-D arrays of shape (N,) have been reshaped to (1,N,1). Rebuilds arrays divided by dsplit.

This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.

Parameters: tup : sequence of arrays The arrays must have the same shape along all but the third axis. 1-D or 2-D arrays must have the same shape. stacked : ndarray The array formed by stacking the given arrays, will be at least 3-D.

concatenate
Join a sequence of arrays along an existing axis.
stack
Join a sequence of arrays along a new axis.
block
Assemble an nd-array from nested lists of blocks.
vstack
Stack arrays in sequence vertically (row wise).
hstack
Stack arrays in sequence horizontally (column wise).
column_stack
Stack 1-D arrays as columns into a 2-D array.
dsplit
Split array along third axis.

Examples

>>> a = np.array((1,2,3))  # doctest: +SKIP
>>> b = np.array((2,3,4))  # doctest: +SKIP
>>> np.dstack((a,b))  # doctest: +SKIP
array([[[1, 2],
[2, 3],
[3, 4]]])

>>> a = np.array([[1],[2],[3]])  # doctest: +SKIP
>>> b = np.array([[2],[3],[4]])  # doctest: +SKIP
>>> np.dstack((a,b))  # doctest: +SKIP
array([[[1, 2]],
[[2, 3]],
[[3, 4]]])

dask.array.ediff1d(ary, to_end=None, to_begin=None)[source]

The differences between consecutive elements of an array.

This docstring was copied from numpy.ediff1d.

Some inconsistencies with the Dask version may exist.

Parameters: ary : array_like If necessary, will be flattened before the differences are taken. to_end : array_like, optional Number(s) to append at the end of the returned differences. to_begin : array_like, optional Number(s) to prepend at the beginning of the returned differences. ediff1d : ndarray The differences. Loosely, this is ary.flat[1:] - ary.flat[:-1].

Notes

When applied to masked arrays, this function drops the mask information if the to_begin and/or to_end parameters are used.

Examples

>>> x = np.array([1, 2, 4, 7, 0])  # doctest: +SKIP
>>> np.ediff1d(x)  # doctest: +SKIP
array([ 1,  2,  3, -7])

>>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))  # doctest: +SKIP
array([-99,   1,   2, ...,  -7,  88,  99])


The returned array is always 1D.

>>> y = [[1, 2, 4], [1, 6, 24]]  # doctest: +SKIP
>>> np.ediff1d(y)  # doctest: +SKIP
array([ 1,  2, -3,  5, 18])

dask.array.empty(*args, **kwargs)

Blocked variant of empty

Follows the signature of empty exactly except that it also features optional keyword arguments chunks: int, tuple, or dict and name: str.

Original signature follows below.

Return np.empty_like(a, shape=shape, **kwargs) if the shape argument is supported (requires NumPy >= 1.17), otherwise falls back to using the old behavior, returning np.empty(shape, **kwargs).

dask.array.empty_like(a, dtype=None, order='C', chunks=None, name=None, shape=None)[source]

Return a new array with the same shape and type as a given array.

Parameters: a : array_like The shape and data-type of a define these same attributes of the returned array. dtype : data-type, optional Overrides the data type of the result. order : {‘C’, ‘F’}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. chunks : sequence of ints The number of samples on each block. Note that the last block will have fewer samples if len(array) % chunks != 0. name : str, optional An optional keyname for the array. Defaults to hashing the input keyword arguments. shape : int or sequence of ints, optional. Overrides the shape of the result. out : ndarray Array of uninitialized (arbitrary) data with the same shape and type as a.

ones_like
Return an array of ones with shape and type of input.
zeros_like
Return an array of zeros with shape and type of input.
empty
Return a new uninitialized array.
ones
Return a new array setting values to one.
zeros
Return a new array setting values to zero.

Notes

This function does not initialize the returned array; to do that use zeros_like or ones_like instead. It may be marginally faster than the functions that do set the array values.

dask.array.equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.equal.

Some inconsistencies with the Dask version may exist.

Return (x1 == x2) element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array, element-wise comparison of x1 and x2. Typically of type bool, unless dtype=object is passed. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.equal([0, 1, 3], np.arange(3))  # doctest: +SKIP
array([ True,  True, False])


What is compared are values, not types. So an int (1) and an array of length one can evaluate as True:

>>> np.equal(1, np.ones(1))  # doctest: +SKIP
array([ True])


The == operator can be used as a shorthand for np.equal on ndarrays.

>>> a = np.array([2, 4, 6])  # doctest: +SKIP
>>> b = np.array([2, 4, 2])  # doctest: +SKIP
>>> a == b  # doctest: +SKIP
array([ True,  True, False])

dask.array.einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe', optimize=False)[source]

This docstring was copied from numpy.einsum.

Some inconsistencies with the Dask version may exist.

Evaluates the Einstein summation convention on the operands.

Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.

In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical Einstein summation operations, by disabling, or forcing summation over specified subscript labels.

See the notes and examples for clarification.

Parameters: subscripts : str Specifies the subscripts for summation as comma separated list of subscript labels. An implicit (classical Einstein summation) calculation is performed unless the explicit indicator ‘->’ is included as well as subscript labels of the precise output form. operands : list of array_like These are the arrays for the operation. out : ndarray, optional (Not supported in Dask) If provided, the calculation is done into this array. dtype : {data-type, None}, optional If provided, forces the calculation to use the data type specified. Note that you may have to also give a more liberal casting parameter to allow the conversions. Default is None. order : {‘C’, ‘F’, ‘A’, ‘K’}, optional Controls the memory layout of the output. ‘C’ means it should be C contiguous. ‘F’ means it should be Fortran contiguous, ‘A’ means it should be ‘F’ if the inputs are all ‘F’, ‘C’ otherwise. ‘K’ means it should be as close to the layout as the inputs as is possible, including arbitrarily permuted axes. Default is ‘K’. casting : {‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional Controls what kind of data casting may occur. Setting this to ‘unsafe’ is not recommended, as it can adversely affect accumulations. ‘no’ means the data types should not be cast at all. ‘equiv’ means only byte-order changes are allowed. ‘safe’ means only casts which can preserve values are allowed. ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed. ‘unsafe’ means any data conversions may be done. Default is ‘safe’. optimize : {False, True, ‘greedy’, ‘optimal’}, optional (Not supported in Dask) Controls if intermediate optimization should occur. No optimization will occur if False and True will default to the ‘greedy’ algorithm. Also accepts an explicit contraction list from the np.einsum_path function. See np.einsum_path for more details. Defaults to False. output : ndarray The calculation based on the Einstein summation convention.

einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
einops
similar verbose interface is provided by einops package to cover additional operations: transpose, reshape/flatten, repeat/tile, squeeze/unsqueeze and reductions.
opt_einsum
opt_einsum optimizes contraction order for einsum-like expressions in backend-agnostic manner.

Notes

New in version 1.6.0.

The Einstein summation convention can be used to compute many multi-dimensional, linear algebraic array operations. einsum provides a succinct way of representing these.

A non-exhaustive list of these operations, which can be computed by einsum, is shown below along with examples:

The subscripts string is a comma-separated list of subscript labels, where each label refers to a dimension of the corresponding operand. Whenever a label is repeated it is summed, so np.einsum('i,i', a, b) is equivalent to np.inner(a,b). If a label appears only once, it is not summed, so np.einsum('i', a) produces a view of a with no changes. A further example np.einsum('ij,jk', a, b) describes traditional matrix multiplication and is equivalent to np.matmul(a,b). Repeated subscript labels in one operand take the diagonal. For example, np.einsum('ii', a) is equivalent to np.trace(a).

In implicit mode, the chosen subscripts are important since the axes of the output are reordered alphabetically. This means that np.einsum('ij', a) doesn’t affect a 2D array, while np.einsum('ji', a) takes its transpose. Additionally, np.einsum('ij,jk', a, b) returns a matrix multiplication, while, np.einsum('ij,jh', a, b) returns the transpose of the multiplication since subscript ‘h’ precedes subscript ‘i’.

In explicit mode the output can be directly controlled by specifying output subscript labels. This requires the identifier ‘->’ as well as the list of output subscript labels. This feature increases the flexibility of the function since summing can be disabled or forced when required. The call np.einsum('i->', a) is like np.sum(a, axis=-1), and np.einsum('ii->i', a) is like np.diag(a). The difference is that einsum does not allow broadcasting by default. Additionally np.einsum('ij,jh->ih', a, b) directly specifies the order of the output subscript labels and therefore returns matrix multiplication, unlike the example above in implicit mode.

To enable and control broadcasting, use an ellipsis. Default NumPy-style broadcasting is done by adding an ellipsis to the left of each term, like np.einsum('...ii->...i', a). To take the trace along the first and last axes, you can do np.einsum('i...i', a), or to do a matrix-matrix product with the left-most indices instead of rightmost, one can do np.einsum('ij...,jk...->ik...', a, b).

When there is only one operand, no axes are summed, and no output parameter is provided, a view into the operand is returned instead of a new array. Thus, taking the diagonal as np.einsum('ii->i', a) produces a view (changed in version 1.10.0).

einsum also provides an alternative way to provide the subscripts and operands as einsum(op0, sublist0, op1, sublist1, ..., [sublistout]). If the output shape is not provided in this format einsum will be calculated in implicit mode, otherwise it will be performed explicitly. The examples below have corresponding einsum calls with the two parameter methods.

New in version 1.10.0.

Views returned from einsum are now writeable whenever the input array is writeable. For example, np.einsum('ijk...->kji...', a) will now have the same effect as np.swapaxes(a, 0, 2) and np.einsum('ii->i', a) will return a writeable view of the diagonal of a 2D array.

New in version 1.12.0.

Added the optimize argument which will optimize the contraction order of an einsum expression. For a contraction with three or more operands this can greatly increase the computational efficiency at the cost of a larger memory footprint during computation.

Typically a ‘greedy’ algorithm is applied which empirical tests have shown returns the optimal path in the majority of cases. In some cases ‘optimal’ will return the superlative path through a more expensive, exhaustive search. For iterative calculations it may be advisable to calculate the optimal path once and reuse that path by supplying it as an argument. An example is given below.

See numpy.einsum_path() for more details.

Examples

>>> a = np.arange(25).reshape(5,5)  # doctest: +SKIP
>>> b = np.arange(5)  # doctest: +SKIP
>>> c = np.arange(6).reshape(2,3)  # doctest: +SKIP


Trace of a matrix:

>>> np.einsum('ii', a)  # doctest: +SKIP
60
>>> np.einsum(a, [0,0])  # doctest: +SKIP
60
>>> np.trace(a)  # doctest: +SKIP
60


Extract the diagonal (requires explicit form):

>>> np.einsum('ii->i', a)  # doctest: +SKIP
array([ 0,  6, 12, 18, 24])
>>> np.einsum(a, [0,0], [0])  # doctest: +SKIP
array([ 0,  6, 12, 18, 24])
>>> np.diag(a)  # doctest: +SKIP
array([ 0,  6, 12, 18, 24])


Sum over an axis (requires explicit form):

>>> np.einsum('ij->i', a)  # doctest: +SKIP
array([ 10,  35,  60,  85, 110])
>>> np.einsum(a, [0,1], [0])  # doctest: +SKIP
array([ 10,  35,  60,  85, 110])
>>> np.sum(a, axis=1)  # doctest: +SKIP
array([ 10,  35,  60,  85, 110])


For higher dimensional arrays summing a single axis can be done with ellipsis:

>>> np.einsum('...j->...', a)  # doctest: +SKIP
array([ 10,  35,  60,  85, 110])
>>> np.einsum(a, [Ellipsis,1], [Ellipsis])  # doctest: +SKIP
array([ 10,  35,  60,  85, 110])


Compute a matrix transpose, or reorder any number of axes:

>>> np.einsum('ji', c)  # doctest: +SKIP
array([[0, 3],
[1, 4],
[2, 5]])
>>> np.einsum('ij->ji', c)  # doctest: +SKIP
array([[0, 3],
[1, 4],
[2, 5]])
>>> np.einsum(c, [1,0])  # doctest: +SKIP
array([[0, 3],
[1, 4],
[2, 5]])
>>> np.transpose(c)  # doctest: +SKIP
array([[0, 3],
[1, 4],
[2, 5]])


Vector inner products:

>>> np.einsum('i,i', b, b)  # doctest: +SKIP
30
>>> np.einsum(b, [0], b, [0])  # doctest: +SKIP
30
>>> np.inner(b,b)  # doctest: +SKIP
30


Matrix vector multiplication:

>>> np.einsum('ij,j', a, b)  # doctest: +SKIP
array([ 30,  80, 130, 180, 230])
>>> np.einsum(a, [0,1], b, [1])  # doctest: +SKIP
array([ 30,  80, 130, 180, 230])
>>> np.dot(a, b)  # doctest: +SKIP
array([ 30,  80, 130, 180, 230])
>>> np.einsum('...j,j', a, b)  # doctest: +SKIP
array([ 30,  80, 130, 180, 230])


>>> np.einsum('..., ...', 3, c)  # doctest: +SKIP
array([[ 0,  3,  6],
[ 9, 12, 15]])
>>> np.einsum(',ij', 3, c)  # doctest: +SKIP
array([[ 0,  3,  6],
[ 9, 12, 15]])
>>> np.einsum(3, [Ellipsis], c, [Ellipsis])  # doctest: +SKIP
array([[ 0,  3,  6],
[ 9, 12, 15]])
>>> np.multiply(3, c)  # doctest: +SKIP
array([[ 0,  3,  6],
[ 9, 12, 15]])


Vector outer product:

>>> np.einsum('i,j', np.arange(2)+1, b)  # doctest: +SKIP
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
>>> np.einsum(np.arange(2)+1, [0], b, [1])  # doctest: +SKIP
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
>>> np.outer(np.arange(2)+1, b)  # doctest: +SKIP
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])


Tensor contraction:

>>> a = np.arange(60.).reshape(3,4,5)  # doctest: +SKIP
>>> b = np.arange(24.).reshape(4,3,2)  # doctest: +SKIP
>>> np.einsum('ijk,jil->kl', a, b)  # doctest: +SKIP
array([[4400., 4730.],
[4532., 4874.],
[4664., 5018.],
[4796., 5162.],
[4928., 5306.]])
>>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])  # doctest: +SKIP
array([[4400., 4730.],
[4532., 4874.],
[4664., 5018.],
[4796., 5162.],
[4928., 5306.]])
>>> np.tensordot(a,b, axes=([1,0],[0,1]))  # doctest: +SKIP
array([[4400., 4730.],
[4532., 4874.],
[4664., 5018.],
[4796., 5162.],
[4928., 5306.]])


Writeable returned arrays (since version 1.10.0):

>>> a = np.zeros((3, 3))  # doctest: +SKIP
>>> np.einsum('ii->i', a)[:] = 1  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])


Example of ellipsis use:

>>> a = np.arange(6).reshape((3,2))  # doctest: +SKIP
>>> b = np.arange(12).reshape((4,3))  # doctest: +SKIP
>>> np.einsum('ki,jk->ij', a, b)  # doctest: +SKIP
array([[10, 28, 46, 64],
[13, 40, 67, 94]])
>>> np.einsum('ki,...k->i...', a, b)  # doctest: +SKIP
array([[10, 28, 46, 64],
[13, 40, 67, 94]])
>>> np.einsum('k...,jk', a, b)  # doctest: +SKIP
array([[10, 28, 46, 64],
[13, 40, 67, 94]])


Chained array operations. For more complicated contractions, speed ups might be achieved by repeatedly computing a ‘greedy’ path or pre-computing the ‘optimal’ path and repeatedly applying it, using an einsum_path insertion (since version 1.12.0). Performance improvements can be particularly significant with larger arrays:

>>> a = np.ones(64).reshape(2,4,8)  # doctest: +SKIP


Basic einsum: ~1520ms (benchmarked on 3.1GHz Intel i5.)

>>> for iteration in range(500):  # doctest: +SKIP
...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)


Sub-optimal einsum (due to repeated path calculation time): ~330ms

>>> for iteration in range(500):  # doctest: +SKIP
...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')


Greedy einsum (faster optimal path approximation): ~160ms

>>> for iteration in range(500):  # doctest: +SKIP
...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy')


Optimal einsum (best usage pattern in some use cases): ~110ms

>>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')[0]  # doctest: +SKIP
>>> for iteration in range(500):  # doctest: +SKIP
...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path)

dask.array.exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.exp.

Some inconsistencies with the Dask version may exist.

Calculate the exponential of all elements in the input array.

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array, element-wise exponential of x. This is a scalar if x is a scalar.

expm1
Calculate exp(x) - 1 for all elements in the array.
exp2
Calculate 2**x for all elements in the array.

Notes

The irrational number e is also known as Euler’s number. It is approximately 2.718281, and is the base of the natural logarithm, ln (this means that, if $$x = \ln y = \log_e y$$, then $$e^x = y$$. For real input, exp(x) is always positive.

For complex arguments, x = a + ib, we can write $$e^x = e^a e^{ib}$$. The first term, $$e^a$$, is already known (it is the real argument, described above). The second term, $$e^{ib}$$, is $$\cos b + i \sin b$$, a function with magnitude 1 and a periodic phase.

References

 [1] Wikipedia, “Exponential function”, https://en.wikipedia.org/wiki/Exponential_function
 [2] M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” Dover, 1964, p. 69, http://www.math.sfu.ca/~cbm/aands/page_69.htm

Examples

Plot the magnitude and phase of exp(x) in the complex plane:

>>> import matplotlib.pyplot as plt  # doctest: +SKIP

>>> x = np.linspace(-2*np.pi, 2*np.pi, 100)  # doctest: +SKIP
>>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane  # doctest: +SKIP
>>> out = np.exp(xx)  # doctest: +SKIP

>>> plt.subplot(121)  # doctest: +SKIP
>>> plt.imshow(np.abs(out),  # doctest: +SKIP
...            extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='gray')
>>> plt.title('Magnitude of exp(x)')  # doctest: +SKIP

>>> plt.subplot(122)  # doctest: +SKIP
>>> plt.imshow(np.angle(out),  # doctest: +SKIP
...            extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='hsv')
>>> plt.title('Phase (angle) of exp(x)')  # doctest: +SKIP
>>> plt.show()  # doctest: +SKIP

dask.array.exp2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.exp2.

Some inconsistencies with the Dask version may exist.

Calculate 2**p for all p in the input array.

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Element-wise 2 to the power x. This is a scalar if x is a scalar.

Notes

New in version 1.3.0.

Examples

>>> np.exp2([2, 3])  # doctest: +SKIP
array([ 4.,  8.])

dask.array.expm1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.expm1.

Some inconsistencies with the Dask version may exist.

Calculate exp(x) - 1 for all elements in the array.

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Element-wise exponential minus one: out = exp(x) - 1. This is a scalar if x is a scalar.

log1p
log(1 + x), the inverse of expm1.

Notes

This function provides greater precision than exp(x) - 1 for small values of x.

Examples

The true value of exp(1e-10) - 1 is 1.00000000005e-10 to about 32 significant digits. This example shows the superiority of expm1 in this case.

>>> np.expm1(1e-10)  # doctest: +SKIP
1.00000000005e-10
>>> np.exp(1e-10) - 1  # doctest: +SKIP
1.000000082740371e-10

dask.array.eye(N, chunks='auto', M=None, k=0, dtype=<class 'float'>)[source]

Return a 2-D Array with ones on the diagonal and zeros elsewhere.

Parameters: N : int Number of rows in the output. chunks : int, str How to chunk the array. Must be one of the following forms: A blocksize like 1000. A size in bytes, like “100 MiB” which will choose a uniform block-like shape The word “auto” which acts like the above, but uses a configuration value array.chunk-size for the chunk size M : int, optional Number of columns in the output. If None, defaults to N. k : int, optional Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : data-type, optional Data-type of the returned array. I : Array of shape (N,M) An array where all elements are equal to zero, except for the k-th diagonal, whose values are equal to one.
dask.array.fabs(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.fabs.

Some inconsistencies with the Dask version may exist.

Compute the absolute values element-wise.

This function returns the absolute values (positive magnitude) of the data in x. Complex values are not handled, use absolute to find the absolute values of complex data.

Parameters: x : array_like The array of numbers for which the absolute values are required. If x is a scalar, the result y will also be a scalar. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or scalar The absolute values of x, the returned values are always floats. This is a scalar if x is a scalar.

absolute
Absolute values including complex types.

Examples

>>> np.fabs(-1)  # doctest: +SKIP
1.0
>>> np.fabs([-1.2, 1.2])  # doctest: +SKIP
array([ 1.2,  1.2])

dask.array.fix(*args, **kwargs)

Round to nearest integer towards zero.

This docstring was copied from numpy.fix.

Some inconsistencies with the Dask version may exist.

Round an array of floats element-wise to nearest integer towards zero. The rounded values are returned as floats.

Parameters: x : array_like (Not supported in Dask) An array of floats to be rounded out : ndarray, optional A location into which the result is stored. If provided, it must have a shape that the input broadcasts to. If not provided or None, a freshly-allocated array is returned. out : ndarray of floats A float array with the same dimensions as the input. If second argument is not supplied then a float array is returned with the rounded values. If a second argument is supplied the result is stored there. The return value out is then a reference to that array.

Examples

>>> np.fix(3.14)  # doctest: +SKIP
3.0
>>> np.fix(3)  # doctest: +SKIP
3.0
>>> np.fix([2.1, 2.9, -2.1, -2.9])  # doctest: +SKIP
array([ 2.,  2., -2., -2.])

dask.array.flatnonzero(a)[source]

Return indices that are non-zero in the flattened version of a.

This docstring was copied from numpy.flatnonzero.

Some inconsistencies with the Dask version may exist.

This is equivalent to np.nonzero(np.ravel(a))[0].

Parameters: a : array_like Input data. res : ndarray Output array, containing the indices of the elements of a.ravel() that are non-zero.

nonzero
Return the indices of the non-zero elements of the input array.
ravel
Return a 1-D array containing the elements of the input array.

Examples

>>> x = np.arange(-2, 3)  # doctest: +SKIP
>>> x  # doctest: +SKIP
array([-2, -1,  0,  1,  2])
>>> np.flatnonzero(x)  # doctest: +SKIP
array([0, 1, 3, 4])


Use the indices of the non-zero elements as an index array to extract these elements:

>>> x.ravel()[np.flatnonzero(x)]  # doctest: +SKIP
array([-2, -1,  1,  2])

dask.array.flip(m, axis)[source]

Reverse element order along axis.

Parameters: axis : int Axis to reverse element order of. reversed array : ndarray
dask.array.flipud(m)[source]

Flip array in the up/down direction.

This docstring was copied from numpy.flipud.

Some inconsistencies with the Dask version may exist.

Flip the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before.

Parameters: m : array_like Input array. out : array_like A view of m with the rows reversed. Since a view is returned, this operation is $$\mathcal O(1)$$.

fliplr
Flip array in the left/right direction.
rot90
Rotate array counterclockwise.

Notes

Equivalent to m[::-1,...]. Does not require the array to be two-dimensional.

Examples

>>> A = np.diag([1.0, 2, 3])  # doctest: +SKIP
>>> A  # doctest: +SKIP
array([[1.,  0.,  0.],
[0.,  2.,  0.],
[0.,  0.,  3.]])
>>> np.flipud(A)  # doctest: +SKIP
array([[0.,  0.,  3.],
[0.,  2.,  0.],
[1.,  0.,  0.]])

>>> A = np.random.randn(2,3,5)  # doctest: +SKIP
>>> np.all(np.flipud(A) == A[::-1,...])  # doctest: +SKIP
True

>>> np.flipud([1,2])  # doctest: +SKIP
array([2, 1])

dask.array.fliplr(m)[source]

Flip array in the left/right direction.

This docstring was copied from numpy.fliplr.

Some inconsistencies with the Dask version may exist.

Flip the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before.

Parameters: m : array_like Input array, must be at least 2-D. f : ndarray A view of m with the columns reversed. Since a view is returned, this operation is $$\mathcal O(1)$$.

flipud
Flip array in the up/down direction.
rot90
Rotate array counterclockwise.

Notes

Equivalent to m[:,::-1]. Requires the array to be at least 2-D.

Examples

>>> A = np.diag([1.,2.,3.])  # doctest: +SKIP
>>> A  # doctest: +SKIP
array([[1.,  0.,  0.],
[0.,  2.,  0.],
[0.,  0.,  3.]])
>>> np.fliplr(A)  # doctest: +SKIP
array([[0.,  0.,  1.],
[0.,  2.,  0.],
[3.,  0.,  0.]])

>>> A = np.random.randn(2,3,5)  # doctest: +SKIP
>>> np.all(np.fliplr(A) == A[:,::-1,...])  # doctest: +SKIP
True

dask.array.float_power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.float_power.

Some inconsistencies with the Dask version may exist.

First array elements raised to powers from second array, element-wise.

Raise each base in x1 to the positionally-corresponding power in x2. x1 and x2 must be broadcastable to the same shape. This differs from the power function in that integers, float16, and float32 are promoted to floats with a minimum precision of float64 so that the result is always inexact. The intent is that the function will return a usable result for negative powers and seldom overflow for positive powers.

New in version 1.12.0.

Parameters: x1 : array_like The bases. x2 : array_like The exponents. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray The bases in x1 raised to the exponents in x2. This is a scalar if both x1 and x2 are scalars.

power
power function that preserves type

Examples

Cube each element in a list.

>>> x1 = range(6)  # doctest: +SKIP
>>> x1  # doctest: +SKIP
[0, 1, 2, 3, 4, 5]
>>> np.float_power(x1, 3)  # doctest: +SKIP
array([   0.,    1.,    8.,   27.,   64.,  125.])


Raise the bases to different exponents.

>>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]  # doctest: +SKIP
>>> np.float_power(x1, x2)  # doctest: +SKIP
array([  0.,   1.,   8.,  27.,  16.,   5.])


>>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])  # doctest: +SKIP
>>> x2  # doctest: +SKIP
array([[1, 2, 3, 3, 2, 1],
[1, 2, 3, 3, 2, 1]])
>>> np.float_power(x1, x2)  # doctest: +SKIP
array([[  0.,   1.,   8.,  27.,  16.,   5.],
[  0.,   1.,   8.,  27.,  16.,   5.]])

dask.array.floor(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.floor.

Some inconsistencies with the Dask version may exist.

Return the floor of the input, element-wise.

The floor of the scalar x is the largest integer i, such that i <= x. It is often denoted as $$\lfloor x \rfloor$$.

Parameters: x : array_like Input data. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or scalar The floor of each element in x. This is a scalar if x is a scalar.

Notes

Some spreadsheet programs calculate the “floor-towards-zero”, in other words floor(-2.5) == -2. NumPy instead uses the definition of floor where floor(-2.5) == -3.

Examples

>>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])  # doctest: +SKIP
>>> np.floor(a)  # doctest: +SKIP
array([-2., -2., -1.,  0.,  1.,  1.,  2.])

dask.array.floor_divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.floor_divide.

Some inconsistencies with the Dask version may exist.

Return the largest integer smaller or equal to the division of the inputs. It is equivalent to the Python // operator and pairs with the Python % (remainder), function so that a = a % b + b * (a // b) up to roundoff.

Parameters: x1 : array_like Numerator. x2 : array_like Denominator. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray y = floor(x1/x2) This is a scalar if both x1 and x2 are scalars.

remainder
Remainder complementary to floor_divide.
divmod
Simultaneous floor division and remainder.
divide
Standard division.
floor
Round a number to the nearest integer toward minus infinity.
ceil
Round a number to the nearest integer toward infinity.

Examples

>>> np.floor_divide(7,3)  # doctest: +SKIP
2
>>> np.floor_divide([1., 2., 3., 4.], 2.5)  # doctest: +SKIP
array([ 0.,  0.,  1.,  1.])


The // operator can be used as a shorthand for np.floor_divide on ndarrays.

>>> x1 = np.array([1., 2., 3., 4.])  # doctest: +SKIP
>>> x1 // 2.5  # doctest: +SKIP
array([0., 0., 1., 1.])

dask.array.fmax(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.fmax.

Some inconsistencies with the Dask version may exist.

Element-wise maximum of array elements.

Compare two arrays and returns a new array containing the element-wise maxima. If one of the elements being compared is a NaN, then the non-nan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible.

Parameters: x1, x2 : array_like The arrays holding the elements to be compared. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or scalar The maximum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

fmin
Element-wise minimum of two arrays, ignores NaNs.
maximum
Element-wise maximum of two arrays, propagates NaNs.
amax
The maximum value of an array along a given axis, propagates NaNs.
nanmax
The maximum value of an array along a given axis, ignores NaNs.
minimum, amin, nanmin

Notes

New in version 1.3.0.

The fmax is equivalent to np.where(x1 >= x2, x1, x2) when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.

Examples

>>> np.fmax([2, 3, 4], [1, 5, 2])  # doctest: +SKIP
array([ 2.,  5.,  4.])

>>> np.fmax(np.eye(2), [0.5, 2])  # doctest: +SKIP
array([[ 1. ,  2. ],
[ 0.5,  2. ]])

>>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan])  # doctest: +SKIP
array([ 0.,  0., nan])

dask.array.fmin(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.fmin.

Some inconsistencies with the Dask version may exist.

Element-wise minimum of array elements.

Compare two arrays and returns a new array containing the element-wise minima. If one of the elements being compared is a NaN, then the non-nan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible.

Parameters: x1, x2 : array_like The arrays holding the elements to be compared. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or scalar The minimum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.

fmax
Element-wise maximum of two arrays, ignores NaNs.
minimum
Element-wise minimum of two arrays, propagates NaNs.
amin
The minimum value of an array along a given axis, propagates NaNs.
nanmin
The minimum value of an array along a given axis, ignores NaNs.
maximum, amax, nanmax

Notes

New in version 1.3.0.

The fmin is equivalent to np.where(x1 <= x2, x1, x2) when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.

Examples

>>> np.fmin([2, 3, 4], [1, 5, 2])  # doctest: +SKIP
array([1, 3, 2])

>>> np.fmin(np.eye(2), [0.5, 2])  # doctest: +SKIP
array([[ 0.5,  0. ],
[ 0. ,  1. ]])

>>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan])  # doctest: +SKIP
array([ 0.,  0., nan])

dask.array.fmod(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.fmod.

Some inconsistencies with the Dask version may exist.

Return the element-wise remainder of division.

This is the NumPy implementation of the C library function fmod, the remainder has the same sign as the dividend x1. It is equivalent to the Matlab(TM) rem function and should not be confused with the Python modulus operator x1 % x2.

Parameters: x1 : array_like Dividend. x2 : array_like Divisor. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : array_like The remainder of the division of x1 by x2. This is a scalar if both x1 and x2 are scalars.

remainder
Equivalent to the Python % operator.
divide

Notes

The result of the modulo operation for negative dividend and divisors is bound by conventions. For fmod, the sign of result is the sign of the dividend, while for remainder the sign of the result is the sign of the divisor. The fmod function is equivalent to the Matlab(TM) rem function.

Examples

>>> np.fmod([-3, -2, -1, 1, 2, 3], 2)  # doctest: +SKIP
array([-1,  0, -1,  1,  0,  1])
>>> np.remainder([-3, -2, -1, 1, 2, 3], 2)  # doctest: +SKIP
array([1, 0, 1, 1, 0, 1])

>>> np.fmod([5, 3], [2, 2.])  # doctest: +SKIP
array([ 1.,  1.])
>>> a = np.arange(-3, 3).reshape(3, 2)  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[-3, -2],
[-1,  0],
[ 1,  2]])
>>> np.fmod(a, [2,2])  # doctest: +SKIP
array([[-1,  0],
[-1,  0],
[ 1,  0]])

dask.array.frexp(x, [out1, out2, ]/, [out=(None, None), ]*, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])[source]

This docstring was copied from numpy.frexp.

Some inconsistencies with the Dask version may exist.

Decompose the elements of x into mantissa and twos exponent.

Returns (mantissa, exponent), where x = mantissa * 2**exponent. The mantissa is lies in the open interval(-1, 1), while the twos exponent is a signed integer.

Parameters: x : array_like Array of numbers to be decomposed. out1 : ndarray, optional Output array for the mantissa. Must have the same shape as x. out2 : ndarray, optional Output array for the exponent. Must have the same shape as x. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. mantissa : ndarray Floating values between -1 and 1. This is a scalar if x is a scalar. exponent : ndarray Integer exponents of 2. This is a scalar if x is a scalar.

ldexp
Compute y = x1 * 2**x2, the inverse of frexp.

Notes

Complex dtypes are not supported, they will raise a TypeError.

Examples

>>> x = np.arange(9)  # doctest: +SKIP
>>> y1, y2 = np.frexp(x)  # doctest: +SKIP
>>> y1  # doctest: +SKIP
array([ 0.   ,  0.5  ,  0.5  ,  0.75 ,  0.5  ,  0.625,  0.75 ,  0.875,
0.5  ])
>>> y2  # doctest: +SKIP
array([0, 1, 2, 2, 3, 3, 3, 3, 4])
>>> y1 * 2**y2  # doctest: +SKIP
array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.])

dask.array.fromfunction(func, chunks='auto', shape=None, dtype=None, **kwargs)[source]

Construct an array by executing a function over each coordinate.

This docstring was copied from numpy.fromfunction.

Some inconsistencies with the Dask version may exist.

The resulting array therefore has a value fn(x, y, z) at coordinate (x, y, z).

Parameters: function : callable (Not supported in Dask) The function is called with N parameters, where N is the rank of shape. Each parameter represents the coordinates of the array varying along a specific axis. For example, if shape were (2, 2), then the parameters would be array([[0, 0], [1, 1]]) and array([[0, 1], [0, 1]]) shape : (N,) tuple of ints Shape of the output array, which also determines the shape of the coordinate arrays passed to function. dtype : data-type, optional Data-type of the coordinate arrays passed to function. By default, dtype is float. like : array_like (Not supported in Dask) Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as like supports the __array_function__ protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. Note The like keyword is an experimental feature pending on acceptance of NEP 35. New in version 1.20.0. fromfunction : any The result of the call to function is passed back directly. Therefore the shape of fromfunction is completely determined by function. If function returns a scalar value, the shape of fromfunction would not match the shape parameter.

Notes

Keywords other than dtype are passed to function.

Examples

>>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int)  # doctest: +SKIP
array([[ True, False, False],
[False,  True, False],
[False, False,  True]])

>>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)  # doctest: +SKIP
array([[0, 1, 2],
[1, 2, 3],
[2, 3, 4]])

dask.array.frompyfunc(func, nin, nout, *[, identity])[source]

This docstring was copied from numpy.frompyfunc.

Some inconsistencies with the Dask version may exist.

Takes an arbitrary Python function and returns a NumPy ufunc.

Can be used, for example, to add broadcasting to a built-in Python function (see Examples section).

Parameters: func : Python function object An arbitrary Python function. nin : int The number of input arguments. nout : int The number of objects returned by func. identity : object, optional The value to use for the ~numpy.ufunc.identity attribute of the resulting object. If specified, this is equivalent to setting the underlying C identity field to PyUFunc_IdentityValue. If omitted, the identity is set to PyUFunc_None. Note that this is _not_ equivalent to setting the identity to None, which implies the operation is reorderable. out : ufunc Returns a NumPy universal function (ufunc) object.

vectorize
Evaluates pyfunc over input arrays using broadcasting rules of numpy.

Notes

The returned ufunc always returns PyObject arrays.

Examples

Use frompyfunc to add broadcasting to the Python function oct:

>>> oct_array = np.frompyfunc(oct, 1, 1)  # doctest: +SKIP
>>> oct_array(np.array((10, 30, 100)))  # doctest: +SKIP
array(['0o12', '0o36', '0o144'], dtype=object)
>>> np.array((oct(10), oct(30), oct(100))) # for comparison  # doctest: +SKIP
array(['0o12', '0o36', '0o144'], dtype='<U5')

dask.array.full(shape, fill_value, *args, **kwargs)[source]

Blocked variant of full

Follows the signature of full exactly except that it also features optional keyword arguments chunks: int, tuple, or dict and name: str.

Original signature follows below.

Return np.full_like(a, fill_value, shape=shape, **kwargs) if the shape argument is supported (requires NumPy >= 1.17), otherwise falls back to using the old behavior, returning np.full(shape, fill_value, **kwargs).

dask.array.full_like(a, fill_value, order='C', dtype=None, chunks=None, name=None, shape=None)[source]

Return a full array with the same shape and type as a given array.

Parameters: a : array_like The shape and data-type of a define these same attributes of the returned array. fill_value : scalar Fill value. dtype : data-type, optional Overrides the data type of the result. order : {‘C’, ‘F’}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. chunks : sequence of ints The number of samples on each block. Note that the last block will have fewer samples if len(array) % chunks != 0. name : str, optional An optional keyname for the array. Defaults to hashing the input keyword arguments. shape : int or sequence of ints, optional. Overrides the shape of the result. out : ndarray Array of fill_value with the same shape and type as a.

zeros_like
Return an array of zeros with shape and type of input.
ones_like
Return an array of ones with shape and type of input.
empty_like
Return an empty array with shape and type of input.
zeros
Return a new array setting values to zero.
ones
Return a new array setting values to one.
empty
Return a new uninitialized array.
full
Fill a new array.
dask.array.gradient(f, *varargs, **kwargs)[source]

Return the gradient of an N-dimensional array.

This docstring was copied from numpy.gradient.

Some inconsistencies with the Dask version may exist.

The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.

Parameters: f : array_like An N-dimensional array containing samples of a scalar function. varargs : list of scalar or array, optional Spacing between f values. Default unitary spacing for all dimensions. Spacing can be specified using: single scalar to specify a sample distance for all dimensions. N scalars to specify a constant sample distance for each dimension. i.e. dx, dy, dz, … N arrays to specify the coordinates of the values along each dimension of F. The length of the array must match the size of the corresponding dimension Any combination of N scalars/arrays with the meaning of 2. and 3. If axis is given, the number of varargs must equal the number of axes. Default: 1. edge_order : {1, 2}, optional (Not supported in Dask) Gradient is calculated using N-th order accurate differences at the boundaries. Default: 1. New in version 1.9.1. axis : None or int or tuple of ints, optional (Not supported in Dask) Gradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis. New in version 1.11.0. gradient : ndarray or list of ndarray A set of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f.

Notes

Assuming that $$f\in C^{3}$$ (i.e., $$f$$ has at least 3 continuous derivatives) and let $$h_{*}$$ be a non-homogeneous stepsize, we minimize the “consistency error” $$\eta_{i}$$ between the true gradient and its estimate from a linear combination of the neighboring grid-points:

$\eta_{i} = f_{i}^{\left(1\right)} - \left[ \alpha f\left(x_{i}\right) + \beta f\left(x_{i} + h_{d}\right) + \gamma f\left(x_{i}-h_{s}\right) \right]$

By substituting $$f(x_{i} + h_{d})$$ and $$f(x_{i} - h_{s})$$ with their Taylor series expansion, this translates into solving the following the linear system:

$\begin{split}\left\{ \begin{array}{r} \alpha+\beta+\gamma=0 \\ \beta h_{d}-\gamma h_{s}=1 \\ \beta h_{d}^{2}+\gamma h_{s}^{2}=0 \end{array} \right.\end{split}$

The resulting approximation of $$f_{i}^{(1)}$$ is the following:

$\hat f_{i}^{(1)} = \frac{ h_{s}^{2}f\left(x_{i} + h_{d}\right) + \left(h_{d}^{2} - h_{s}^{2}\right)f\left(x_{i}\right) - h_{d}^{2}f\left(x_{i}-h_{s}\right)} { h_{s}h_{d}\left(h_{d} + h_{s}\right)} + \mathcal{O}\left(\frac{h_{d}h_{s}^{2} + h_{s}h_{d}^{2}}{h_{d} + h_{s}}\right)$

It is worth noting that if $$h_{s}=h_{d}$$ (i.e., data are evenly spaced) we find the standard second order approximation:

$\hat f_{i}^{(1)}= \frac{f\left(x_{i+1}\right) - f\left(x_{i-1}\right)}{2h} + \mathcal{O}\left(h^{2}\right)$

With a similar procedure the forward/backward approximations used for boundaries can be derived.

References

 [1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics (Texts in Applied Mathematics). New York: Springer.
 [2] Durran D. R. (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. New York: Springer.
 [3] Fornberg B. (1988) Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, Mathematics of Computation 51, no. 184 : 699-706. PDF.

Examples

>>> f = np.array([1, 2, 4, 7, 11, 16], dtype=float)  # doctest: +SKIP
array([1. , 1.5, 2.5, 3.5, 4.5, 5. ])
>>> np.gradient(f, 2)  # doctest: +SKIP
array([0.5 ,  0.75,  1.25,  1.75,  2.25,  2.5 ])


Spacing can be also specified with an array that represents the coordinates of the values F along the dimensions. For instance a uniform spacing:

>>> x = np.arange(f.size)  # doctest: +SKIP
>>> np.gradient(f, x)  # doctest: +SKIP
array([1. ,  1.5,  2.5,  3.5,  4.5,  5. ])


Or a non uniform one:

>>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float)  # doctest: +SKIP
>>> np.gradient(f, x)  # doctest: +SKIP
array([1. ,  3. ,  3.5,  6.7,  6.9,  2.5])


For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction:

>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float))  # doctest: +SKIP
[array([[ 2.,  2., -1.],
[ 2.,  2., -1.]]), array([[1. , 2.5, 4. ],
[1. , 1. , 1. ]])]


In this example the spacing is also specified: uniform for axis=0 and non uniform for axis=1

>>> dx = 2.  # doctest: +SKIP
>>> y = [1., 1.5, 3.5]  # doctest: +SKIP
>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y)  # doctest: +SKIP
[array([[ 1. ,  1. , -0.5],
[ 1. ,  1. , -0.5]]), array([[2. , 2. , 2. ],
[2. , 1.7, 0.5]])]


It is possible to specify how boundaries are treated using edge_order

>>> x = np.array([0, 1, 2, 3, 4])  # doctest: +SKIP
>>> f = x**2  # doctest: +SKIP
>>> np.gradient(f, edge_order=1)  # doctest: +SKIP
array([1.,  2.,  4.,  6.,  7.])
>>> np.gradient(f, edge_order=2)  # doctest: +SKIP
array([0., 2., 4., 6., 8.])


The axis keyword can be used to specify a subset of axes of which the gradient is calculated

>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), axis=0)  # doctest: +SKIP
array([[ 2.,  2., -1.],
[ 2.,  2., -1.]])

dask.array.greater(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.greater.

Some inconsistencies with the Dask version may exist.

Return the truth value of (x1 > x2) element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array, element-wise comparison of x1 and x2. Typically of type bool, unless dtype=object is passed. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.greater([4,2],[2,2])  # doctest: +SKIP
array([ True, False])


The > operator can be used as a shorthand for np.greater on ndarrays.

>>> a = np.array([4, 2])  # doctest: +SKIP
>>> b = np.array([2, 2])  # doctest: +SKIP
>>> a > b  # doctest: +SKIP
array([ True, False])

dask.array.greater_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.greater_equal.

Some inconsistencies with the Dask version may exist.

Return the truth value of (x1 >= x2) element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : bool or ndarray of bool Output array, element-wise comparison of x1 and x2. Typically of type bool, unless dtype=object is passed. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.greater_equal([4, 2, 1], [2, 2, 2])  # doctest: +SKIP
array([ True, True, False])


The >= operator can be used as a shorthand for np.greater_equal on ndarrays.

>>> a = np.array([4, 2, 1])  # doctest: +SKIP
>>> b = np.array([2, 2, 2])  # doctest: +SKIP
>>> a >= b  # doctest: +SKIP
array([ True,  True, False])

dask.array.histogram(a, bins=None, range=None, normed=False, weights=None, density=None)[source]

Blocked variant of numpy.histogram().

Parameters: a : dask.array.Array Input data; the histogram is computed over the flattened array. If the weights argument is used, the chunks of a are accessed to check chunking compatibility between a and weights. If weights is None, a dask.dataframe.Series object can be passed as input data. bins : int or sequence of scalars, optional Either an iterable specifying the bins or the number of bins and a range argument is required as computing min and max over blocked arrays is an expensive operation that must be performed explicitly. If bins is an int, it defines the number of equal-width bins in the given range (10, by default). If bins is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing for non-uniform bin widths. range : (float, float), optional The lower and upper range of the bins. If not provided, range is simply (a.min(), a.max()). Values outside the range are ignored. The first element of the range must be less than or equal to the second. range affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within range, the bin count will fill the entire range including portions containing no data. normed : bool, optional This is equivalent to the density argument, but produces incorrect results for unequal bin widths. It should not be used. weights : dask.array.Array, optional A dask.array.Array of weights, of the same block structure as a. Each value in a only contributes its associated weight towards the bin count (instead of 1). If density is True, the weights are normalized, so that the integral of the density over the range remains 1. density : bool, optional If False, the result will contain the number of samples in each bin. If True, the result is the value of the probability density function at the bin, normalized such that the integral over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability mass function. Overrides the normed keyword if given. If density is True, bins cannot be a single-number delayed value. It must be a concrete number, or a (possibly-delayed) array/sequence of the bin edges. hist : dask Array The values of the histogram. See density and weights for a description of the possible semantics. bin_edges : dask Array of dtype float Return the bin edges (length(hist)+1).

Examples

Using number of bins and range:

>>> import dask.array as da
>>> import numpy as np
>>> x = da.from_array(np.arange(10000), chunks=10)
>>> h, bins = da.histogram(x, bins=10, range=[0, 10000])
>>> bins
array([    0.,  1000.,  2000.,  3000.,  4000.,  5000.,  6000.,  7000.,
8000.,  9000., 10000.])
>>> h.compute()
array([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000])


Explicitly specifying the bins:

>>> h, bins = da.histogram(x, bins=np.array([0, 5000, 10000]))
>>> bins
array([    0,  5000, 10000])
>>> h.compute()
array([5000, 5000])

dask.array.histogramdd(sample, bins, range=None, normed=None, weights=None, density=None)[source]

Blocked variant of numpy.histogramdd().

Chunking of the input data (sample) is only allowed along the 0th (row) axis (the axis corresponding to the total number of samples). Data chunked along the 1st axis (column) axis is not compatible with this function. If weights are used, they must be chunked along the 0th axis identically to the input sample.

A proper example setup for a three dimensional histogram, where the sample shape is (8, 3) and weights are shape (8,), sample chunks would be ((4, 4), (3,)) and the weights chunks would be ((4, 4),) a table of the structure:

sample (8 x 3) weights
chunk row x y z row w
0 0 5 6 6 0 0.5
1 8 9 2 1 0.8
2 3 3 1 2 0.3
3 2 5 6 3 0.7
1 4 3 1 1 4 0.3
5 3 2 9 5 1.3
6 8 1 5 6 0.8
7 3 5 3 7 0.7

If the sample 0th dimension and weight 0th (row) dimension are chunked differently, a ValueError will be raised. If coordinate groupings ((x, y, z) trios) are separated by a chunk boundry, then a ValueError will be raised. We suggest that you rechunk your data if it is of that form.

The chunks property of the data (and optional weights) are used to check for compatibility with the blocked algorithm (as described above); therefore, you must call to_dask_array on a collection from dask.dataframe, i.e. dask.dataframe.Series or dask.dataframe.DataFrame.

Parameters: sample : dask.array.Array (N, D) or sequence of dask.array.Array Multidimensional data to be histogrammed. Note the unusual interpretation of a sample when it is a sequence of dask Arrays: When a (N, D) dask Array, each row is an entry in the sample (coordinate in D dimensional space). When a sequence of dask Arrays, each element in the sequence is the array of values for a single coordinate. This type of input will be automatically rechunked along the column axis if necessary. This may induce a runtime increase. bins : sequence of arrays describing bin edges, int, or sequence of ints The bin specification. The possible binning configurations are: A sequence of arrays describing the monotonically increasing bin edges along each dimension. A single int describing the total number of bins that will be used in each dimension (this requires the range argument to be defined). A sequence of ints describing the total number of bins to be used in each dimension (this requires the range argument to be defined). When bins are described by arrays, the rightmost edge is included. Bins described by arrays also allows for non-uniform bin widths. range : sequence of pairs, optional A sequence of length D, each a (min, max) tuple giving the outer bin edges to be used if the edges are not given explicitly in bins. If defined, this argument is required to have an entry for each dimension. Unlike numpy.histogramdd(), if bins does not define bin edges, this argument is required (this function will not automatically use the min and max of of the value in a given dimension because the input data may be lazy in dask). normed : bool, optional An alias for the density argument that behaves identically. To avoid confusion with the broken argument to histogram, density should be preferred. weights : dask.array.Array, optional An array of values weighing each sample in the input data. The chunks of the weights must be identical to the chunking along the 0th (row) axis of the data sample. density : bool, optional If False (default), the returned array represents the number of samples in each bin. If True, the returned array represents the probability density function at each bin.

Examples

Computing the histogram in 5 blocks using different bin edges along each dimension:

>>> import dask.array as da
>>> x = da.random.uniform(0, 1, size=(1000, 3), chunks=(200, 3))
>>> edges = [
...     np.linspace(0, 1, 5), # 4 bins in 1st dim
...     np.linspace(0, 1, 6), # 5 in the 2nd
...     np.linspace(0, 1, 4), # 3 in the 3rd
... ]
>>> h, edges = da.histogramdd(x, bins=edges)
>>> result = h.compute()
>>> result.shape
(4, 5, 3)


Defining the bins by total number and their ranges, along with using weights:

>>> bins = (4, 5, 3)
>>> ranges = ((0, 1),) * 3  # expands to ((0, 1), (0, 1), (0, 1))
>>> w = da.random.uniform(0, 1, size=(1000,), chunks=x.chunksize[0])
>>> h, edges = da.histogramdd(x, bins=bins, range=ranges, weights=w)
>>> np.isclose(h.sum().compute(), w.sum().compute())
True

dask.array.hstack(tup, allow_unknown_chunksizes=False)[source]

Stack arrays in sequence horizontally (column wise).

This docstring was copied from numpy.hstack.

Some inconsistencies with the Dask version may exist.

This is equivalent to concatenation along the second axis, except for 1-D arrays where it concatenates along the first axis. Rebuilds arrays divided by hsplit.

This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.

Parameters: tup : sequence of ndarrays The arrays must have the same shape along all but the second axis, except 1-D arrays which can be any length. stacked : ndarray The array formed by stacking the given arrays.

concatenate
Join a sequence of arrays along an existing axis.
stack
Join a sequence of arrays along a new axis.
block
Assemble an nd-array from nested lists of blocks.
vstack
Stack arrays in sequence vertically (row wise).
dstack
Stack arrays in sequence depth wise (along third axis).
column_stack
Stack 1-D arrays as columns into a 2-D array.
hsplit
Split an array into multiple sub-arrays horizontally (column-wise).

Examples

>>> a = np.array((1,2,3))  # doctest: +SKIP
>>> b = np.array((2,3,4))  # doctest: +SKIP
>>> np.hstack((a,b))  # doctest: +SKIP
array([1, 2, 3, 2, 3, 4])
>>> a = np.array([[1],[2],[3]])  # doctest: +SKIP
>>> b = np.array([[2],[3],[4]])  # doctest: +SKIP
>>> np.hstack((a,b))  # doctest: +SKIP
array([[1, 2],
[2, 3],
[3, 4]])

dask.array.hypot(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.hypot.

Some inconsistencies with the Dask version may exist.

Given the “legs” of a right triangle, return its hypotenuse.

Equivalent to sqrt(x1**2 + x2**2), element-wise. If x1 or x2 is scalar_like (i.e., unambiguously cast-able to a scalar type), it is broadcast for use with each element of the other argument. (See Examples)

Parameters: x1, x2 : array_like Leg of the triangle(s). If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. z : ndarray The hypotenuse of the triangle(s). This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3)))  # doctest: +SKIP
array([[ 5.,  5.,  5.],
[ 5.,  5.,  5.],
[ 5.,  5.,  5.]])


Example showing broadcast of scalar_like argument:

>>> np.hypot(3*np.ones((3, 3)), [4])  # doctest: +SKIP
array([[ 5.,  5.,  5.],
[ 5.,  5.,  5.],
[ 5.,  5.,  5.]])

dask.array.imag(*args, **kwargs)

Return the imaginary part of the complex argument.

This docstring was copied from numpy.imag.

Some inconsistencies with the Dask version may exist.

Parameters: val : array_like (Not supported in Dask) Input array. out : ndarray or scalar The imaginary component of the complex argument. If val is real, the type of val is used for the output. If val has complex elements, the returned type is float.

real, angle, real_if_close

Examples

>>> a = np.array([1+2j, 3+4j, 5+6j])  # doctest: +SKIP
>>> a.imag  # doctest: +SKIP
array([2.,  4.,  6.])
>>> a.imag = np.array([8, 10, 12])  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([1. +8.j,  3.+10.j,  5.+12.j])
>>> np.imag(1 + 1j)  # doctest: +SKIP
1.0

dask.array.indices(dimensions, dtype=<class 'int'>, chunks='auto')[source]

Implements NumPy’s indices for Dask Arrays.

Generates a grid of indices covering the dimensions provided.

The final array has the shape (len(dimensions), *dimensions). The chunks are used to specify the chunking for axis 1 up to len(dimensions). The 0th axis always has chunks of length 1.

Parameters: dimensions : sequence of ints The shape of the index grid. dtype : dtype, optional Type to use for the array. Default is int. chunks : sequence of ints, str The size of each block. Must be one of the following forms: A blocksize like (500, 1000) A size in bytes, like “100 MiB” which will choose a uniform block-like shape The word “auto” which acts like the above, but uses a configuration value array.chunk-size for the chunk size Note that the last block will have fewer samples if len(array) % chunks != 0. grid : dask array
dask.array.insert(arr, obj, values, axis)[source]

Insert values along the given axis before the given indices.

This docstring was copied from numpy.insert.

Some inconsistencies with the Dask version may exist.

Parameters: arr : array_like Input array. obj : int, slice or sequence of ints Object that defines the index or indices before which values is inserted. New in version 1.8.0. Support for multiple insertions when obj is a single scalar or a sequence with one element (similar to calling insert multiple times). values : array_like Values to insert into arr. If the type of values is different from that of arr, values is converted to the type of arr. values should be shaped so that arr[...,obj,...] = values is legal. axis : int, optional Axis along which to insert values. If axis is None then arr is flattened first. out : ndarray A copy of arr with values inserted. Note that insert does not occur in-place: a new array is returned. If axis is None, out is a flattened array.

append
Append elements at the end of an array.
concatenate
Join a sequence of arrays along an existing axis.
delete
Delete elements from an array.

Notes

Note that for higher dimensional inserts obj=0 behaves very different from obj=[0] just like arr[:,0,:] = values is different from arr[:,[0],:] = values.

Examples

>>> a = np.array([[1, 1], [2, 2], [3, 3]])  # doctest: +SKIP
>>> a  # doctest: +SKIP
array([[1, 1],
[2, 2],
[3, 3]])
>>> np.insert(a, 1, 5)  # doctest: +SKIP
array([1, 5, 1, ..., 2, 3, 3])
>>> np.insert(a, 1, 5, axis=1)  # doctest: +SKIP
array([[1, 5, 1],
[2, 5, 2],
[3, 5, 3]])


Difference between sequence and scalars:

>>> np.insert(a, [1], [[1],[2],[3]], axis=1)  # doctest: +SKIP
array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])
>>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1),  # doctest: +SKIP
...                np.insert(a, [1], [[1],[2],[3]], axis=1))
True

>>> b = a.flatten()  # doctest: +SKIP
>>> b  # doctest: +SKIP
array([1, 1, 2, 2, 3, 3])
>>> np.insert(b, [2, 2], [5, 6])  # doctest: +SKIP
array([1, 1, 5, ..., 2, 3, 3])

>>> np.insert(b, slice(2, 4), [5, 6])  # doctest: +SKIP
array([1, 1, 5, ..., 2, 3, 3])

>>> np.insert(b, [2, 2], [7.13, False]) # type casting  # doctest: +SKIP
array([1, 1, 7, ..., 2, 3, 3])

>>> x = np.arange(8).reshape(2, 4)  # doctest: +SKIP
>>> idx = (1, 3)  # doctest: +SKIP
>>> np.insert(x, idx, 999, axis=1)  # doctest: +SKIP
array([[  0, 999,   1,   2, 999,   3],
[  4, 999,   5,   6, 999,   7]])

dask.array.invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.invert.

Some inconsistencies with the Dask version may exist.

Compute bit-wise inversion, or bit-wise NOT, element-wise.

Computes the bit-wise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ~.

For signed integer inputs, the two’s complement is returned. In a two’s-complement system negative numbers are represented by the two’s complement of the absolute value. This is the most common method of representing signed integers on computers [1]. A N-bit two’s-complement system can represent every integer in the range $$-2^{N-1}$$ to $$+2^{N-1}-1$$.

Parameters: x : array_like Only integer and boolean types are handled. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Result. This is a scalar if x is a scalar.

bitwise_and, bitwise_or, bitwise_xor
logical_not
binary_repr
Return the binary representation of the input number as a string.

Notes

bitwise_not is an alias for invert:

>>> np.bitwise_not is np.invert  # doctest: +SKIP
True


References

 [1] Wikipedia, “Two’s complement”, https://en.wikipedia.org/wiki/Two’s_complement

Examples

We’ve seen that 13 is represented by 00001101. The invert or bit-wise NOT of 13 is then:

>>> x = np.invert(np.array(13, dtype=np.uint8))  # doctest: +SKIP
>>> x  # doctest: +SKIP
242
>>> np.binary_repr(x, width=8)  # doctest: +SKIP
'11110010'


The result depends on the bit-width:

>>> x = np.invert(np.array(13, dtype=np.uint16))  # doctest: +SKIP
>>> x  # doctest: +SKIP
65522
>>> np.binary_repr(x, width=16)  # doctest: +SKIP
'1111111111110010'


When using signed integer types the result is the two’s complement of the result for the unsigned type:

>>> np.invert(np.array([13], dtype=np.int8))  # doctest: +SKIP
array([-14], dtype=int8)
>>> np.binary_repr(-14, width=8)  # doctest: +SKIP
'11110010'


Booleans are accepted as well:

>>> np.invert(np.array([True, False]))  # doctest: +SKIP
array([False,  True])


The ~ operator can be used as a shorthand for np.invert on ndarrays.

>>> x1 = np.array([True, False])  # doctest: +SKIP
>>> ~x1  # doctest: +SKIP
array([False,  True])

dask.array.isclose(arr1, arr2, rtol=1e-05, atol=1e-08, equal_nan=False)[source]

Returns a boolean array where two arrays are element-wise equal within a tolerance.

This docstring was copied from numpy.isclose.

Some inconsistencies with the Dask version may exist.

The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.

Warning

The default atol is not appropriate for comparing numbers that are much smaller than one (see Notes).

Parameters: a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array. y : array_like Returns a boolean array of where a and b are equal within the given tolerance. If both a and b are scalars, returns a single boolean value.

allclose
math.isclose

Notes

New in version 1.7.0.

For finite values, isclose uses the following equation to test whether two floating point values are equivalent.

absolute(a - b) <= (atol + rtol * absolute(b))

Unlike the built-in math.isclose, the above equation is not symmetric in a and b – it assumes b is the reference value – so that isclose(a, b) might be different from isclose(b, a). Furthermore, the default value of atol is not zero, and is used to determine what small values should be considered close to zero. The default value is appropriate for expected values of order unity: if the expected values are significantly smaller than one, it can result in false positives. atol should be carefully selected for the use case at hand. A zero value for atol will result in False if either a or b is zero.

isclose is not defined for non-numeric data types.

Examples

>>> np.isclose([1e10,1e-7], [1.00001e10,1e-8])  # doctest: +SKIP
array([ True, False])
>>> np.isclose([1e10,1e-8], [1.00001e10,1e-9])  # doctest: +SKIP
array([ True, True])
>>> np.isclose([1e10,1e-8], [1.0001e10,1e-9])  # doctest: +SKIP
array([False,  True])
>>> np.isclose([1.0, np.nan], [1.0, np.nan])  # doctest: +SKIP
array([ True, False])
>>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)  # doctest: +SKIP
array([ True, True])
>>> np.isclose([1e-8, 1e-7], [0.0, 0.0])  # doctest: +SKIP
array([ True, False])
>>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0)  # doctest: +SKIP
array([False, False])
>>> np.isclose([1e-10, 1e-10], [1e-20, 0.0])  # doctest: +SKIP
array([ True,  True])
>>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0)  # doctest: +SKIP
array([False,  True])

dask.array.iscomplex(*args, **kwargs)

Returns a bool array, where True if input element is complex.

This docstring was copied from numpy.iscomplex.

Some inconsistencies with the Dask version may exist.

What is tested is whether the input has a non-zero imaginary part, not if the input type is complex.

Parameters: x : array_like (Not supported in Dask) Input array. out : ndarray of bools Output array.

isreal
iscomplexobj
Return True if x is a complex type or an array of complex numbers.

Examples

>>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j])  # doctest: +SKIP
array([ True, False, False, False, False,  True])

dask.array.isfinite(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.isfinite.

Some inconsistencies with the Dask version may exist.

Test element-wise for finiteness (not infinity or not Not a Number).

The result is returned as a boolean array.

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray, bool True where x is not positive infinity, negative infinity, or NaN; false otherwise. This is a scalar if x is a scalar.

Notes

Not a Number, positive infinity and negative infinity are considered to be non-finite.

NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Errors result if the second argument is also supplied when x is a scalar input, or if first and second arguments have different shapes.

Examples

>>> np.isfinite(1)  # doctest: +SKIP
True
>>> np.isfinite(0)  # doctest: +SKIP
True
>>> np.isfinite(np.nan)  # doctest: +SKIP
False
>>> np.isfinite(np.inf)  # doctest: +SKIP
False
>>> np.isfinite(np.NINF)  # doctest: +SKIP
False
>>> np.isfinite([np.log(-1.),1.,np.log(0)])  # doctest: +SKIP
array([False,  True, False])

>>> x = np.array([-np.inf, 0., np.inf])  # doctest: +SKIP
>>> y = np.array([2, 2, 2])  # doctest: +SKIP
>>> np.isfinite(x, y)  # doctest: +SKIP
array([0, 1, 0])
>>> y  # doctest: +SKIP
array([0, 1, 0])

dask.array.isin(element, test_elements, assume_unique=False, invert=False)

Calculates element in test_elements, broadcasting over element only. Returns a boolean array of the same shape as element that is True where an element of element is in test_elements and False otherwise.

Parameters: element : array_like Input array. test_elements : array_like The values against which to test each value of element. This argument is flattened if it is an array or array_like. See notes for behavior with non-array-like parameters. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted, as if calculating element not in test_elements. Default is False. np.isin(a, b, invert=True) is equivalent to (but faster than) np.invert(np.isin(a, b)). isin : ndarray, bool Has the same shape as element. The values element[isin] are in test_elements.

in1d
Flattened version of this function.
numpy.lib.arraysetops
Module with a number of other functions for performing set operations on arrays.

Notes

isin is an element-wise function version of the python keyword in. isin(a, b) is roughly equivalent to np.array([item in b for item in a]) if a and b are 1-D sequences.

element and test_elements are converted to arrays if they are not already. If test_elements is a set (or other non-sequence collection) it will be converted to an object array with one element, rather than an array of the values contained in test_elements. This is a consequence of the array constructor’s way of handling non-sequence collections. Converting the set to a list usually gives the desired behavior.

New in version 1.13.0.

Examples

>>> element = 2*np.arange(4).reshape((2, 2))
>>> element
array([[0, 2],
[4, 6]])
>>> test_elements = [1, 2, 4, 8]
array([[False,  True],
[ True, False]])
array([2, 4])


The indices of the matched values can be obtained with nonzero:

>>> np.nonzero(mask)
(array([0, 1]), array([1, 0]))


The test can also be inverted:

>>> mask = np.isin(element, test_elements, invert=True)
array([[ True, False],
[False,  True]])
array([0, 6])


Because of how array handles sets, the following does not work as expected:

>>> test_set = {1, 2, 4, 8}
>>> np.isin(element, test_set)
array([[False, False],
[False, False]])


Casting the set to a list gives the expected result:

>>> np.isin(element, list(test_set))
array([[False,  True],
[ True, False]])

dask.array.isinf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.isinf.

Some inconsistencies with the Dask version may exist.

Test element-wise for positive or negative infinity.

Returns a boolean array of the same shape as x, True where x == +/-inf, otherwise False.

Parameters: x : array_like Input values out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : bool (scalar) or boolean ndarray True where x is positive or negative infinity, false otherwise. This is a scalar if x is a scalar.

Notes

NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754).

Errors result if the second argument is supplied when the first argument is a scalar, or if the first and second arguments have different shapes.

Examples

>>> np.isinf(np.inf)  # doctest: +SKIP
True
>>> np.isinf(np.nan)  # doctest: +SKIP
False
>>> np.isinf(np.NINF)  # doctest: +SKIP
True
>>> np.isinf([np.inf, -np.inf, 1.0, np.nan])  # doctest: +SKIP
array([ True,  True, False, False])

>>> x = np.array([-np.inf, 0., np.inf])  # doctest: +SKIP
>>> y = np.array([2, 2, 2])  # doctest: +SKIP
>>> np.isinf(x, y)  # doctest: +SKIP
array([1, 0, 1])
>>> y  # doctest: +SKIP
array([1, 0, 1])

dask.array.isneginf(*args, **kwargs)

This docstring was copied from numpy.equal.

Some inconsistencies with the Dask version may exist.

Return (x1 == x2) element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array, element-wise comparison of x1 and x2. Typically of type bool, unless dtype=object is passed. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.equal([0, 1, 3], np.arange(3))  # doctest: +SKIP
array([ True,  True, False])


What is compared are values, not types. So an int (1) and an array of length one can evaluate as True:

>>> np.equal(1, np.ones(1))  # doctest: +SKIP
array([ True])


The == operator can be used as a shorthand for np.equal on ndarrays.

>>> a = np.array([2, 4, 6])  # doctest: +SKIP
>>> b = np.array([2, 4, 2])  # doctest: +SKIP
>>> a == b  # doctest: +SKIP
array([ True,  True, False])

dask.array.isnan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.isnan.

Some inconsistencies with the Dask version may exist.

Test element-wise for NaN and return result as a boolean array.

Parameters: x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or bool True where x is NaN, false otherwise. This is a scalar if x is a scalar.

Notes

NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity.

Examples

>>> np.isnan(np.nan)  # doctest: +SKIP
True
>>> np.isnan(np.inf)  # doctest: +SKIP
False
>>> np.isnan([np.log(-1.),1.,np.log(0)])  # doctest: +SKIP
array([ True, False, False])

dask.array.isnull(values)[source]

dask.array.isposinf(*args, **kwargs)

This docstring was copied from numpy.equal.

Some inconsistencies with the Dask version may exist.

Return (x1 == x2) element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array, element-wise comparison of x1 and x2. Typically of type bool, unless dtype=object is passed. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.equal([0, 1, 3], np.arange(3))  # doctest: +SKIP
array([ True,  True, False])


What is compared are values, not types. So an int (1) and an array of length one can evaluate as True:

>>> np.equal(1, np.ones(1))  # doctest: +SKIP
array([ True])


The == operator can be used as a shorthand for np.equal on ndarrays.

>>> a = np.array([2, 4, 6])  # doctest: +SKIP
>>> b = np.array([2, 4, 2])  # doctest: +SKIP
>>> a == b  # doctest: +SKIP
array([ True,  True, False])

dask.array.isreal(*args, **kwargs)

Returns a bool array, where True if input element is real.

This docstring was copied from numpy.isreal.

Some inconsistencies with the Dask version may exist.

If element has complex type with zero complex part, the return value for that element is True.

Parameters: x : array_like (Not supported in Dask) Input array. out : ndarray, bool Boolean array of same shape as x.

iscomplex
isrealobj
Return True if x is not a complex type.

Examples

>>> np.isreal([1+1j, 1+0j, 4.5, 3, 2, 2j])  # doctest: +SKIP
array([False,  True,  True,  True,  True, False])

dask.array.ldexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.ldexp.

Some inconsistencies with the Dask version may exist.

Returns x1 * 2**x2, element-wise.

The mantissas x1 and twos exponents x2 are used to construct floating point numbers x1 * 2**x2.

Parameters: x1 : array_like Array of multipliers. x2 : array_like, int Array of twos exponents. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or scalar The result of x1 * 2**x2. This is a scalar if both x1 and x2 are scalars.

frexp
Return (y1, y2) from x = y1 * 2**y2, inverse to ldexp.

Notes

Complex dtypes are not supported, they will raise a TypeError.

ldexp is useful as the inverse of frexp, if used by itself it is more clear to simply use the expression x1 * 2**x2.

Examples

>>> np.ldexp(5, np.arange(4))  # doctest: +SKIP
array([ 5., 10., 20., 40.], dtype=float16)

>>> x = np.arange(6)  # doctest: +SKIP
>>> np.ldexp(*np.frexp(x))  # doctest: +SKIP
array([ 0.,  1.,  2.,  3.,  4.,  5.])

dask.array.less(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.less.

Some inconsistencies with the Dask version may exist.

Return the truth value of (x1 < x2) element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. out : ndarray or scalar Output array, element-wise comparison of x1 and x2. Typically of type bool, unless dtype=object is passed. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.less([1, 2], [2, 2])  # doctest: +SKIP
array([ True, False])


The < operator can be used as a shorthand for np.less on ndarrays.

>>> a = np.array([1, 2])  # doctest: +SKIP
>>> b = np.array([2, 2])  # doctest: +SKIP
>>> a < b  # doctest: +SKIP
array([ True, False])

dask.array.linspace(start, stop, num=50, endpoint=True, retstep=False, chunks='auto', dtype=None)[source]

Return num evenly spaced values over the closed interval [start, stop].

Parameters: start : scalar The starting value of the sequence. stop : scalar The last value of the sequence. num : int, optional Number of samples to include in the returned dask array, including the endpoints. Default is 50. endpoint : bool, optional If True, stop is the last sample. Otherwise, it is not included. Default is True. retstep : bool, optional If True, return (samples, step), where step is the spacing between samples. Default is False. chunks : int The number of samples on each block. Note that the last block will have fewer samples if num % blocksize != 0 dtype : dtype, optional The type of the output array. samples : dask array step : float, optional Only returned if retstep is True. Size of spacing between samples.
dask.array.log(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.log.

Some inconsistencies with the Dask version may exist.

Natural logarithm, element-wise.

The natural logarithm log is the inverse of the exponential function, so that log(exp(x)) = x. The natural logarithm is logarithm in base e.

Parameters: x : array_like Input value. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray The natural logarithm of x, element-wise. This is a scalar if x is a scalar.

log10, log2, log1p, emath.log

Notes

Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = x. The convention is to return the z whose imaginary part lies in [-pi, pi].

For real-valued input data types, log always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, log is a complex analytical function that has a branch cut [-inf, 0] and is continuous from above on it. log handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm

Examples

>>> np.log([1, np.e, np.e**2, 0])  # doctest: +SKIP
array([  0.,   1.,   2., -Inf])

dask.array.log10(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.log10.

Some inconsistencies with the Dask version may exist.

Return the base 10 logarithm of the input array, element-wise.

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray The logarithm to the base 10 of x, element-wise. NaNs are returned where x is negative. This is a scalar if x is a scalar.

emath.log10

Notes

Logarithm is a multivalued function: for each x there is an infinite number of z such that 10**z = x. The convention is to return the z whose imaginary part lies in [-pi, pi].

For real-valued input data types, log10 always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, log10 is a complex analytical function that has a branch cut [-inf, 0] and is continuous from above on it. log10 handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm

Examples

>>> np.log10([1e-15, -3.])  # doctest: +SKIP
array([-15.,  nan])

dask.array.log1p(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.log1p.

Some inconsistencies with the Dask version may exist.

Return the natural logarithm of one plus the input array, element-wise.

Calculates log(1 + x).

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray Natural logarithm of 1 + x, element-wise. This is a scalar if x is a scalar.

expm1
exp(x) - 1, the inverse of log1p.

Notes

For real-valued input, log1p is accurate also for x so small that 1 + x == 1 in floating-point accuracy.

Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = 1 + x. The convention is to return the z whose imaginary part lies in [-pi, pi].

For real-valued input data types, log1p always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, log1p is a complex analytical function that has a branch cut [-inf, -1] and is continuous from above on it. log1p handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.

References

 [1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/
 [2] Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm

Examples

>>> np.log1p(1e-99)  # doctest: +SKIP
1e-99
>>> np.log(1 + 1e-99)  # doctest: +SKIP
0.0

dask.array.log2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.log2.

Some inconsistencies with the Dask version may exist.

Base-2 logarithm of x.

Parameters: x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray Base-2 logarithm of x. This is a scalar if x is a scalar.

log, log10, log1p, emath.log2

Notes

New in version 1.3.0.

Logarithm is a multivalued function: for each x there is an infinite number of z such that 2**z = x. The convention is to return the z whose imaginary part lies in [-pi, pi].

For real-valued input data types, log2 always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, log2 is a complex analytical function that has a branch cut [-inf, 0] and is continuous from above on it. log2 handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.

Examples

>>> x = np.array([0, 1, 2, 2**4])  # doctest: +SKIP
>>> np.log2(x)  # doctest: +SKIP
array([-Inf,   0.,   1.,   4.])

>>> xi = np.array([0+1.j, 1, 2+0.j, 4.j])  # doctest: +SKIP
>>> np.log2(xi)  # doctest: +SKIP
array([ 0.+2.26618007j,  0.+0.j        ,  1.+0.j        ,  2.+2.26618007j])

dask.array.logaddexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.logaddexp.

Some inconsistencies with the Dask version may exist.

Logarithm of the sum of exponentiations of the inputs.

Calculates log(exp(x1) + exp(x2)). This function is useful in statistics where the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the logarithm of the calculated probability is stored. This function allows adding probabilities stored in such a fashion.

Parameters: x1, x2 : array_like Input values. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. result : ndarray Logarithm of exp(x1) + exp(x2). This is a scalar if both x1 and x2 are scalars.

logaddexp2
Logarithm of the sum of exponentiations of inputs in base 2.

Notes

New in version 1.3.0.

Examples

>>> prob1 = np.log(1e-50)  # doctest: +SKIP
>>> prob2 = np.log(2.5e-50)  # doctest: +SKIP
>>> prob12 = np.logaddexp(prob1, prob2)  # doctest: +SKIP
>>> prob12  # doctest: +SKIP
-113.87649168120691
>>> np.exp(prob12)  # doctest: +SKIP
3.5000000000000057e-50

dask.array.logaddexp2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.logaddexp2.

Some inconsistencies with the Dask version may exist.

Logarithm of the sum of exponentiations of the inputs in base-2.

Calculates log2(2**x1 + 2**x2). This function is useful in machine learning when the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the base-2 logarithm of the calculated probability can be used instead. This function allows adding probabilities stored in such a fashion.

Parameters: x1, x2 : array_like Input values. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. result : ndarray Base-2 logarithm of 2**x1 + 2**x2. This is a scalar if both x1 and x2 are scalars.

logaddexp
Logarithm of the sum of exponentiations of the inputs.

Notes

New in version 1.3.0.

Examples

>>> prob1 = np.log2(1e-50)  # doctest: +SKIP
>>> prob2 = np.log2(2.5e-50)  # doctest: +SKIP
>>> prob12 = np.logaddexp2(prob1, prob2)  # doctest: +SKIP
>>> prob1, prob2, prob12  # doctest: +SKIP
(-166.09640474436813, -164.77447664948076, -164.28904982231052)
>>> 2**prob12  # doctest: +SKIP
3.4999999999999914e-50

dask.array.logical_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.logical_and.

Some inconsistencies with the Dask version may exist.

Compute the truth value of x1 AND x2 element-wise.

Parameters: x1, x2 : array_like Input arrays. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or bool Boolean result of the logical AND operation applied to the elements of x1 and x2; the shape is determined by broadcasting. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.logical_and(True, False)  # doctest: +SKIP
False
>>> np.logical_and([True, False], [False, False])  # doctest: +SKIP
array([False, False])

>>> x = np.arange(5)  # doctest: +SKIP
>>> np.logical_and(x>1, x<4)  # doctest: +SKIP
array([False, False,  True,  True, False])


The & operator can be used as a shorthand for np.logical_and on boolean ndarrays.

>>> a = np.array([True, False])  # doctest: +SKIP
>>> b = np.array([False, False])  # doctest: +SKIP
>>> a & b  # doctest: +SKIP
array([False, False])

dask.array.logical_not(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.logical_not.

Some inconsistencies with the Dask version may exist.

Compute the truth value of NOT x element-wise.

Parameters: x : array_like Logical NOT is applied to the elements of x. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : bool or ndarray of bool Boolean result with the same shape as x of the NOT operation on elements of x. This is a scalar if x is a scalar.

Examples

>>> np.logical_not(3)  # doctest: +SKIP
False
>>> np.logical_not([True, False, 0, 1])  # doctest: +SKIP
array([False,  True,  True, False])

>>> x = np.arange(5)  # doctest: +SKIP
>>> np.logical_not(x<3)  # doctest: +SKIP
array([False, False, False,  True,  True])

dask.array.logical_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.logical_or.

Some inconsistencies with the Dask version may exist.

Compute the truth value of x1 OR x2 element-wise.

Parameters: x1, x2 : array_like Logical OR is applied to the elements of x1 and x2. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : ndarray or bool Boolean result of the logical OR operation applied to the elements of x1 and x2; the shape is determined by broadcasting. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.logical_or(True, False)  # doctest: +SKIP
True
>>> np.logical_or([True, False], [False, False])  # doctest: +SKIP
array([ True, False])

>>> x = np.arange(5)  # doctest: +SKIP
>>> np.logical_or(x < 1, x > 3)  # doctest: +SKIP
array([ True, False, False, False,  True])


The | operator can be used as a shorthand for np.logical_or on boolean ndarrays.

>>> a = np.array([True, False])  # doctest: +SKIP
>>> b = np.array([False, False])  # doctest: +SKIP
>>> a | b  # doctest: +SKIP
array([ True, False])

dask.array.logical_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

This docstring was copied from numpy.logical_xor.

Some inconsistencies with the Dask version may exist.

Compute the truth value of x1 XOR x2, element-wise.

Parameters: x1, x2 : array_like Logical XOR is applied to the elements of x1 and x2. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs. y : bool or ndarray of bool Boolean result of the logical XOR operation applied to the elements of x1 and x2; the shape is determined by broadcasting. This is a scalar if both x1 and x2 are scalars.

Examples

>>> np.logical_xor(True, False)  # doctest: +SKIP
True
>>> np.logical_xor([True, True, False, False], [True, False, True, False])  # doctest: +SKIP
array([False,  True,  True, False])

>>> x = np.arange(5)  # doctest: +SKIP
>>> np.logical_xor(x < 1, x > 3)  # doctest: +SKIP
array([ True, False, False, False,  True])


Simple example showing support of broadcasting

>>> np.logical_xor(0, np.eye(2))  # doctest: +SKIP
array([[ True, False],
[False,  True]])

dask.array.map_blocks(func, *args, name=None, token=None, dtype=None, chunks=None, drop_axis=[], new_axis=None, meta=None, **kwargs)[source]

Map a function across all blocks of a dask array.

Note that map_blocks will attempt to automatically determine the output array type by calling func on 0-d versions of the inputs. Please refer to the meta keyword argument below if you expect that the function will not succeed when operating on 0-d arrays.

Parameters: func : callable Function to apply to every block in the array. args : dask arrays or other objects dtype : np.dtype, optional The dtype of the output array. It is recommended to provide this. If not provided, will be inferred by applying the function to a small set of fake data. chunks : tuple, optional Chunk shape of resulting blocks if the function does not preserve shape. If not provided, the resulting array is assumed to have the same block structure as the first input array. drop_axis : number or iterable, optional Dimensions lost by the function. new_axis : number or iterable, optional New dimensions created by the function. Note that these are applied after drop_axis (if present). token : string, optional The key prefix to use for the output array. If not provided, will be determined from the function name. name : string, optional The key name to use for the output array. Note that this fully specifies the output key name, and must be unique. If not provided, will be determined by a hash of the arguments. meta : array-like, optional The meta of the output array, when specified is expected to be an array of the same type and dtype of that returned when calling .compute() on the array returned by this function. When not provided, meta will be inferred by applying the function to a small set of fake data, usually a 0-d array. It’s important to ensure that func can successfully complete computation without raising exceptions when 0-d is passed to it, providing meta will be required otherwise. If the output type is known beforehand (e.g., np.ndarray, cupy.ndarray), an empty array of such type dtype can be passed, for example: meta=np.array((), dtype=np.int32). **kwargs : Other keyword arguments to pass to function. Values must be constants (not dask.arrays)

dask.array.blockwise
Generalized operation with control over block alignment.

Examples

>>> import dask.array as da
>>> x = da.arange(6, chunks=3)

>>> x.map_blocks(lambda x: x * 2).compute()
array([ 0,  2,  4,  6,  8, 10])


The da.map_blocks function can also accept multiple arrays.

>>> d = da.arange(5, chunks=2)
>>> e = da.arange(5, chunks=2)

>>> f = da.map_blocks(lambda a, b: a + b**2, d, e)
>>> f.compute()
array([ 0,  2,  6, 12, 20])


If the function changes shape of the blocks then you must provide chunks explicitly.

>>> y = x.map_blocks(lambda x: x[::2], chunks=((2, 2),))


You have a bit of freedom in specifying chunks. If all of the output chunk sizes are the same, you can provide just that chunk size as a single tuple.

>>> a = da.arange(18, chunks=(6,))
>>> b = a.map_blocks(lambda x: x[:3], chunks=(3,))


If the function changes the dimension of the blocks you must specify the created or destroyed dimensions.

>>> b = a.map_blocks(lambda x: x[None, :, None], chunks=(1, 6, 1),
...                  new_axis=[0, 2])


If chunks is specified but new_axis is not, then it is inferred to add the necessary number of axes on the left.

Map_blocks aligns blocks by block positions without regard to shape. In the following example we have two arrays with the same number of blocks but with different shape and chunk sizes.

>>> x = da.arange(1000, chunks=(100,))
>>> y = da.arange(100, chunks=(10,))


The relevant attribute to match is numblocks.

>>> x.numblocks
(10,)
>>> y.numblocks
(10,)


If these match (up to broadcasting rules) then we can map arbitrary functions across blocks

>>> def func(a, b):
...     return np.array([a.max(), b.max()])

>>> da.map_blocks(func, x, y, chunks=(2,), dtype='i8')

>>> _.compute()
array([ 99,   9, 199,  19, 299,  29, 399,  39, 499,  49, 599,  59, 699,
69, 799,  79, 899,  89, 999,  99])


Your block function get information about where it is in the array by accepting a special block_info or block_id keyword argument.

>>> def func(block_info=None):
...     pass


This will receive the following information:

>>> block_info  # doctest: +SKIP
{0: {'shape': (1000,),
'num-chunks': (10,),
'chunk-location': (4,),
'array-location': [(400, 500)]},
None: {'shape': (1000,),
'num-chunks': (10,),
'chunk-location': (4,),
'array-location': [(400, 500)],
'chunk-shape': (100,),
'dtype': dtype('float64')}}


For each argument and keyword arguments that are dask arrays (the positions of which are the first index), you will receive the shape of the full array, the number of chunks of the full array in each dimension, the chunk location (for example the fourth chunk over in the first dimension), and the array location (for example the slice corresponding to 40:50). The same information is provided for the output, with the key None, plus the shape and dtype that should be returned.

These features can be combined to synthesize an array from scratch, for example:

>>> def func(block_info=None):
...     loc = block_info[None]['array-location'][0]
...     return np.arange(loc[0], loc[1])

>>> da.map_blocks(func, chunks=((4, 4),), dtype=np.float_)

>>> _.compute()
array([0, 1, 2, 3, 4, 5, 6, 7])


block_id is similar to block_info but contains only the chunk_location:

>>> def func(block_id=None):
...     pass


This will receive the following information:

>>> block_id  # doctest: +SKIP
(4, 3)


You may specify the key name prefix of the resulting task in the graph with the optional token keyword argument.

>>> x.map_blocks(lambda x: x + 1, name='increment')  # doctest: +SKIP


For functions that may not handle 0-d arrays, it’s also possible to specify meta with an empty array matching the type of the expected result. In the example below, func will result in an IndexError when computing meta:

>>> da.map_blocks(lambda x: x[2], da.random.random(5), meta=np.array(()))


Similarly, it’s possible to specify a non-NumPy array to meta, and provide a dtype:

>>> import cupy  # doctest: +SKIP
>>> rs = da.random.RandomState(RandomState=cupy.random.RandomState)  # doctest: +SKIP
>>> dt = np.float32
>>> da.map_blocks(lambda x: x[2], rs.random(5, dtype=dt), meta=cupy.array((), dtype=dt))  # doctest: +SKIP

dask.array.matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])[source]

This docstring was copied from numpy.matmul.

Some inconsistencies with the Dask version may exist.

Matrix product of two arrays.

Parameters: x1, x2 : array_like Input arrays, scalars not allowed. out : ndarray, optional A location into which the result is stored. If provided, it must have a shape that matches the signature (n,k),(k,m)->(n,m). If not provided or None, a freshly-allocated array is returned. **kwargs For other keyword-only arguments, see the ufunc docs. New in version 1.16: Now handles ufunc kwargs y : ndarray The matrix product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors. ValueError If the last dimension of x1 is not the same size as the second-to-last dimension of x2. If a scalar value is passed in.

vdot
Complex-conjugating dot product.
tensordot
Sum products over arbitrary axes.
einsum
Einstein summation convention.
dot
alternative matrix product with different broadcasting rules.

Notes

The behavior depends on the arguments in the following way.

• If both arguments are 2-D they are multiplied like conventional matrices.
• If either argument is N-D, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly.
• If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
• If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.

matmul differs from dot in two important ways:

• Multiplication by scalars is not allowed, use * instead.

• Stacks of matrices are broadcast together as if the matrices were elements, respecting the signature (n,k),(k,m)->(n,m):

>>> a = np.ones([9, 5, 7, 4])  # doctest: +SKIP
>>> c = np.ones([9, 5, 4, 3])  # doctest: +SKIP
>>> np.dot(a, c).shape  # d`