print(help(np.add))"""
Help on ufunc object:add = class ufunc(builtins.object)| Functions that operate element by element on whole arrays.| | To see the documentation for a specific ufunc, use `info`. For| example, ``np.info(np.sin)``. Because ufuncs are written in C| (for speed) and linked into Python with NumPy's ufunc facility,| Python's help() function finds this page whenever help() is called| on a ufunc.| | A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`.| | **Calling ufuncs:** ``op(*x[, out], where=True, **kwargs)``| | Apply `op` to the arguments `*x` elementwise, broadcasting the arguments.| | The broadcasting rules are:| | * Dimensions of length 1 may be prepended to either array.| * Arrays may be repeated along dimensions of length 1.| | Parameters| ----------| *x : array_like| Input arrays.| out : ndarray, None, or tuple of ndarray and None, optional| Alternate array object(s) in which to put the result; if provided, it| must have a shape that the inputs broadcast to. A tuple of arrays| (possible only as a keyword argument) must have length equal to the| number of outputs; use None for uninitialized outputs to be| allocated by the ufunc.| 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 :ref:`ufunc docs <ufuncs.kwargs>`.| | Returns| -------| r : ndarray or tuple of ndarray| `r` will have the shape that the arrays in `x` broadcast to; if `out` is| provided, it will be returned. If not, `r` will be allocated and| may contain uninitialized values. If the function has more than one| output, then the result will be a tuple of arrays.| | Methods defined here:| | __call__(self, /, *args, **kwargs)| Call self as a function.| | __repr__(self, /)| Return repr(self).| | __str__(self, /)| Return str(self).| | accumulate(...)| accumulate(array, axis=0, dtype=None, out=None)| | Accumulate the result of applying the operator to all elements.| | For a one-dimensional array, accumulate produces results equivalent to::| | r = np.empty(len(A))| t = op.identity # op = the ufunc being applied to A's elements| for i in range(len(A)):| t = op(t, A[i])| r[i] = t| return r| | For example, add.accumulate() is equivalent to np.cumsum().| | For a multi-dimensional array, accumulate is applied along only one| axis (axis zero by default; see Examples below) so repeated use is| necessary if one wants to accumulate over multiple axes.| | Parameters| ----------| array : array_like| The array to act on.| axis : int, optional| The axis along which to apply the accumulation; default is zero.| dtype : data-type code, optional| The data-type used to represent the intermediate results. Defaults| to the data-type of the output array if such is provided, or the| the data-type of the input array if no output array is provided.| out : ndarray, None, or tuple of ndarray and None, optional| A location into which the result is stored. If not provided or None,| a freshly-allocated array is returned. For consistency with| ``ufunc.__call__``, if given as a keyword, this may be wrapped in a| 1-element tuple.| | .. versionchanged:: 1.13.0| Tuples are allowed for keyword argument.| | Returns| -------| r : ndarray| The accumulated values. If `out` was supplied, `r` is a reference to| `out`.| | Examples| --------| 1-D array examples:| | >>> np.add.accumulate([2, 3, 5])| array([ 2, 5, 10])| >>> np.multiply.accumulate([2, 3, 5])| array([ 2, 6, 30])| | 2-D array examples:| | >>> I = np.eye(2)| >>> I| array([[1., 0.],| [0., 1.]])| | Accumulate along axis 0 (rows), down columns:| | >>> np.add.accumulate(I, 0)| array([[1., 0.],| [1., 1.]])| >>> np.add.accumulate(I) # no axis specified = axis zero| array([[1., 0.],| [1., 1.]])| | Accumulate along axis 1 (columns), through rows:| | >>> np.add.accumulate(I, 1)| array([[1., 1.],| [0., 1.]])| | at(...)| at(a, indices, b=None, /)| | Performs unbuffered in place operation on operand 'a' for elements| specified by 'indices'. For addition ufunc, this method is equivalent to| ``a[indices] += b``, except that results are accumulated for elements that| are indexed more than once. For example, ``a[[0,0]] += 1`` will only| increment the first element once because of buffering, whereas| ``add.at(a, [0,0], 1)`` will increment the first element twice.| | .. versionadded:: 1.8.0| | Parameters| ----------| a : array_like| The array to perform in place operation on.| indices : array_like or tuple| Array like index object or slice object for indexing into first| operand. If first operand has multiple dimensions, indices can be a| tuple of array like index objects or slice objects.| b : array_like| Second operand for ufuncs requiring two operands. Operand must be| broadcastable over first operand after indexing or slicing.| | Examples| --------| Set items 0 and 1 to their negative values:| | >>> a = np.array([1, 2, 3, 4])| >>> np.negative.at(a, [0, 1])| >>> a| array([-1, -2, 3, 4])| | Increment items 0 and 1, and increment item 2 twice:| | >>> a = np.array([1, 2, 3, 4])| >>> np.add.at(a, [0, 1, 2, 2], 1)| >>> a| array([2, 3, 5, 4])| | Add items 0 and 1 in first array to second array,| and store results in first array:| | >>> a = np.array([1, 2, 3, 4])| >>> b = np.array([1, 2])| >>> np.add.at(a, [0, 1], b)| >>> a| array([2, 4, 3, 4])| | outer(...)| outer(A, B, /, **kwargs)| | Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`.| | Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of| ``op.outer(A, B)`` is an array of dimension M + N such that:| | .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =| op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])| | For `A` and `B` one-dimensional, this is equivalent to::| | r = empty(len(A),len(B))| for i in range(len(A)):| for j in range(len(B)):| r[i,j] = op(A[i], B[j]) # op = ufunc in question| | Parameters| ----------| A : array_like| First array| B : array_like| Second array| kwargs : any| Arguments to pass on to the ufunc. Typically `dtype` or `out`.| See `ufunc` for a comprehensive overview of all available arguments.| | Returns| -------| r : ndarray| Output array| | See Also| --------| numpy.outer : A less powerful version of ``np.multiply.outer``| that `ravel`\ s all inputs to 1D. This exists| primarily for compatibility with old code.| | tensordot : ``np.tensordot(a, b, axes=((), ()))`` and| ``np.multiply.outer(a, b)`` behave same for all| dimensions of a and b.| | Examples| --------| >>> np.multiply.outer([1, 2, 3], [4, 5, 6])| array([[ 4, 5, 6],| [ 8, 10, 12],| [12, 15, 18]])| | A multi-dimensional example:| | >>> A = np.array([[1, 2, 3], [4, 5, 6]])| >>> A.shape| (2, 3)| >>> B = np.array([[1, 2, 3, 4]])| >>> B.shape| (1, 4)| >>> C = np.multiply.outer(A, B)| >>> C.shape; C| (2, 3, 1, 4)| array([[[[ 1, 2, 3, 4]],| [[ 2, 4, 6, 8]],| [[ 3, 6, 9, 12]]],| [[[ 4, 8, 12, 16]],| [[ 5, 10, 15, 20]],| [[ 6, 12, 18, 24]]]])| | reduce(...)| reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)| | Reduces `array`'s dimension by one, by applying ufunc along one axis.| | Let :math:`array.shape = (N_0, ..., N_i, ..., N_{M-1})`. Then| :math:`ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` =| the result of iterating `j` over :math:`range(N_i)`, cumulatively applying| ufunc to each :math:`array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`.| For a one-dimensional array, reduce produces results equivalent to:| ::| | r = op.identity # op = ufunc| for i in range(len(A)):| r = op(r, A[i])| return r| | For example, add.reduce() is equivalent to sum().| | Parameters| ----------| array : array_like| The array to act on.| axis : None or int or tuple of ints, optional| Axis or axes along which a reduction is performed.| The default (`axis` = 0) is perform a reduction over the first| dimension of the input array. `axis` may be negative, in| which case it counts from the last to the first axis.| | .. versionadded:: 1.7.0| | If this is None, a reduction is performed over all the axes.| 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.| | For operations which are either not commutative or not associative,| doing a reduction over multiple axes is not well-defined. The| ufuncs do not currently raise an exception in this case, but will| likely do so in the future.| dtype : data-type code, optional| The type used to represent the intermediate results. Defaults| to the data-type of the output array if this is provided, or| the data-type of the input array if no output array is provided.| out : ndarray, None, or tuple of ndarray and None, optional| A location into which the result is stored. If not provided or None,| a freshly-allocated array is returned. For consistency with| ``ufunc.__call__``, if given as a keyword, this may be wrapped in a| 1-element tuple.| | .. versionchanged:: 1.13.0| Tuples are allowed for keyword argument.| 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 original `array`.| | .. versionadded:: 1.7.0| initial : scalar, optional| The value with which to start the reduction.| If the ufunc has no identity or the dtype is object, this defaults| to None - otherwise it defaults to ufunc.identity.| If ``None`` is given, the first element of the reduction is used,| and an error is thrown if the reduction is empty.| | .. versionadded:: 1.15.0| | where : array_like of bool, optional| A boolean array which is broadcasted to match the dimensions| of `array`, and selects elements to include in the reduction. Note| that for ufuncs like ``minimum`` that do not have an identity| defined, one has to pass in also ``initial``.| | .. versionadded:: 1.17.0| | Returns| -------| r : ndarray| The reduced array. If `out` was supplied, `r` is a reference to it.| | Examples| --------| >>> np.multiply.reduce([2,3,5])| 30| | A multi-dimensional array example:| | >>> X = np.arange(8).reshape((2,2,2))| >>> X| array([[[0, 1],| [2, 3]],| [[4, 5],| [6, 7]]])| >>> np.add.reduce(X, 0)| array([[ 4, 6],| [ 8, 10]])| >>> np.add.reduce(X) # confirm: default axis value is 0| array([[ 4, 6],| [ 8, 10]])| >>> np.add.reduce(X, 1)| array([[ 2, 4],| [10, 12]])| >>> np.add.reduce(X, 2)| array([[ 1, 5],| [ 9, 13]])| | You can use the ``initial`` keyword argument to initialize the reduction| with a different value, and ``where`` to select specific elements to include:| | >>> np.add.reduce([10], initial=5)| 15| >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)| array([14., 14.])| >>> a = np.array([10., np.nan, 10])| >>> np.add.reduce(a, where=~np.isnan(a))| 20.0| | Allows reductions of empty arrays where they would normally fail, i.e.| for ufuncs without an identity.| | >>> np.minimum.reduce([], initial=np.inf)| inf| >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])| array([ 1., 10.])| >>> np.minimum.reduce([])| Traceback (most recent call last):| ...| ValueError: zero-size array to reduction operation minimum which has no identity| | reduceat(...)| reduceat(array, indices, axis=0, dtype=None, out=None)| | Performs a (local) reduce with specified slices over a single axis.| | For i in ``range(len(indices))``, `reduceat` computes| ``ufunc.reduce(array[indices[i]:indices[i+1]])``, which becomes the i-th| generalized "row" parallel to `axis` in the final result (i.e., in a| 2-D array, for example, if `axis = 0`, it becomes the i-th row, but if| `axis = 1`, it becomes the i-th column). There are three exceptions to this:| | * when ``i = len(indices) - 1`` (so for the last index),| ``indices[i+1] = array.shape[axis]``.| * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is| simply ``array[indices[i]]``.| * if ``indices[i] >= len(array)`` or ``indices[i] < 0``, an error is raised.| | The shape of the output depends on the size of `indices`, and may be| larger than `array` (this happens if ``len(indices) > array.shape[axis]``).| | Parameters| ----------| array : array_like| The array to act on.| indices : array_like| Paired indices, comma separated (not colon), specifying slices to| reduce.| axis : int, optional| The axis along which to apply the reduceat.| dtype : data-type code, optional| The type used to represent the intermediate results. Defaults| to the data type of the output array if this is provided, or| the data type of the input array if no output array is provided.| out : ndarray, None, or tuple of ndarray and None, optional| A location into which the result is stored. If not provided or None,| a freshly-allocated array is returned. For consistency with| ``ufunc.__call__``, if given as a keyword, this may be wrapped in a| 1-element tuple.| | .. versionchanged:: 1.13.0| Tuples are allowed for keyword argument.| | Returns| -------| r : ndarray| The reduced values. If `out` was supplied, `r` is a reference to| `out`.| | Notes| -----| A descriptive example:| | If `array` is 1-D, the function `ufunc.accumulate(array)` is the same as| ``ufunc.reduceat(array, indices)[::2]`` where `indices` is| ``range(len(array) - 1)`` with a zero placed| in every other element:| ``indices = zeros(2 * len(array) - 1)``,| ``indices[1::2] = range(1, len(array))``.| | Don't be fooled by this attribute's name: `reduceat(array)` is not| necessarily smaller than `array`.| | Examples| --------| To take the running sum of four successive values:| | >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2]| array([ 6, 10, 14, 18])| | A 2-D example:| | >>> x = np.linspace(0, 15, 16).reshape(4,4)| >>> x| array([[ 0., 1., 2., 3.],| [ 4., 5., 6., 7.],| [ 8., 9., 10., 11.],| [12., 13., 14., 15.]])| | ::| | # reduce such that the result has the following five rows:| # [row1 + row2 + row3]| # [row4]| # [row2]| # [row3]| # [row1 + row2 + row3 + row4]| | >>> np.add.reduceat(x, [0, 3, 1, 2, 0])| array([[12., 15., 18., 21.],| [12., 13., 14., 15.],| [ 4., 5., 6., 7.],| [ 8., 9., 10., 11.],| [24., 28., 32., 36.]])| | ::| | # reduce such that result has the following two columns:| # [col1 * col2 * col3, col4]| | >>> np.multiply.reduceat(x, [0, 3], 1)| array([[ 0., 3.],| [ 120., 7.],| [ 720., 11.],| [2184., 15.]])| | ----------------------------------------------------------------------| Data descriptors defined here:| | identity| The identity value.| | Data attribute containing the identity element for the ufunc, if it has one.| If it does not, the attribute value is None.| | Examples| --------| >>> np.add.identity| 0| >>> np.multiply.identity| 1| >>> np.power.identity| 1| >>> print(np.exp.identity)| None| | nargs| The number of arguments.| | Data attribute containing the number of arguments the ufunc takes, including| optional ones.| | Notes| -----| Typically this value will be one more than what you might expect because all| ufuncs take the optional "out" argument.| | Examples| --------| >>> np.add.nargs| 3| >>> np.multiply.nargs| 3| >>> np.power.nargs| 3| >>> np.exp.nargs| 2| | nin| The number of inputs.| | Data attribute containing the number of arguments the ufunc treats as input.| | Examples| --------| >>> np.add.nin| 2| >>> np.multiply.nin| 2| >>> np.power.nin| 2| >>> np.exp.nin| 1| | nout| The number of outputs.| | Data attribute containing the number of arguments the ufunc treats as output.| | Notes| -----| Since all ufuncs can take output arguments, this will always be (at least) 1.| | Examples| --------| >>> np.add.nout| 1| >>> np.multiply.nout| 1| >>> np.power.nout| 1| >>> np.exp.nout| 1| | ntypes| The number of types.| | The number of numerical NumPy types - of which there are 18 total - on which| the ufunc can operate.| | See Also| --------| numpy.ufunc.types| | Examples| --------| >>> np.add.ntypes| 18| >>> np.multiply.ntypes| 18| >>> np.power.ntypes| 17| >>> np.exp.ntypes| 7| >>> np.remainder.ntypes| 14| | signature| Definition of the core elements a generalized ufunc operates on.| | The signature determines how the dimensions of each input/output array| are split into core and loop dimensions:| | 1. Each dimension in the signature is matched to a dimension of the| corresponding passed-in array, starting from the end of the shape tuple.| 2. Core dimensions assigned to the same label in the signature must have| exactly matching sizes, no broadcasting is performed.| 3. The core dimensions are removed from all inputs and the remaining| dimensions are broadcast together, defining the loop dimensions.| | Notes| -----| Generalized ufuncs are used internally in many linalg functions, and in| the testing suite; the examples below are taken from these.| For ufuncs that operate on scalars, the signature is None, which is| equivalent to '()' for every argument.| | Examples| --------| >>> np.core.umath_tests.matrix_multiply.signature| '(m,n),(n,p)->(m,p)'| >>> np.linalg._umath_linalg.det.signature| '(m,m)->()'| >>> np.add.signature is None| True # equivalent to '(),()->()'| | types| Returns a list with types grouped input->output.| | Data attribute listing the data-type "Domain-Range" groupings the ufunc can| deliver. The data-types are given using the character codes.| | See Also| --------| numpy.ufunc.ntypes| | Examples| --------| >>> np.add.types| ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',| 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',| 'GG->G', 'OO->O']| | >>> np.multiply.types| ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',| 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',| 'GG->G', 'OO->O']| | >>> np.power.types| ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',| 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G',| 'OO->O']| | >>> np.exp.types| ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O']| | >>> np.remainder.types| ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',| 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O']None
"""
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