# NumPy ops

[source]

### absolute function

keras.ops.absolute(x)

Compute the absolute value element-wise.

keras.ops.abs is a shorthand for this function.

Arguments

• x: Input tensor.

Returns

An array containing the absolute value of each element in x.

Example

>>> x = keras.ops.convert_to_tensor([-1.2, 1.2])
>>> keras.ops.absolute(x)
array([1.2, 1.2], dtype=float32)

[source]

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

The tensor containing the element-wise sum of x1 and x2.

Examples

>>> x1 = keras.ops.convert_to_tensor([1, 4])
>>> x2 = keras.ops.convert_to_tensor([5, 6])
array([6, 10], dtype=int32)

>>> x1 = keras.ops.convert_to_tensor(
...     [[5, 4],
...      [5, 6]]
... )
>>> x2 = keras.ops.convert_to_tensor([5, 6])
array([[10 10]
[10 12]], shape=(2, 2), dtype=int32)

[source]

### all function

keras.ops.all(x, axis=None, keepdims=False)

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

Arguments

• x: Input tensor.
• axis: An integer or tuple of integers that represent the axis 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 for the last to the first axis.
• keepdims: If True, 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. Defaults to False.

Returns

The tensor containing the logical AND reduction over the axis.

Examples

>>> x = keras.ops.convert_to_tensor([True, False])
>>> keras.ops.all(x)
array(False, shape=(), dtype=bool)
>>> x = keras.ops.convert_to_tensor([[True, False], [True, True]])
>>> keras.ops.all(x, axis=0)
array([ True False], shape=(2,), dtype=bool)

keepdims=True outputs a tensor with dimensions reduced to one.

>>> x = keras.ops.convert_to_tensor([[True, False], [True, True]])
>>> keras.ops.all(x, keepdims=True)
array([[False]], shape=(1, 1), dtype=bool)

[source]

### amax function

keras.ops.amax(x, axis=None, keepdims=False)

Returns the maximum of an array or maximum value along an axis.

Arguments

• x: Input tensor.
• axis: Axis along which to compute the maximum. By default (axis=None), find the maximum value in all the dimensions of the input array.
• keepdims: If True, axes which are reduced are left in the result as dimensions that are broadcast to the size of the original input tensor. Defaults to False.

Returns

An array with the maximum value. If axis=None, the result is a scalar value representing the maximum element in the entire array. If axis is given, the result is an array with the maximum values along the specified axis.

Examples

>>> x = keras.ops.convert_to_tensor([[1, 3, 5], [2, 3, 6]])
>>> keras.ops.amax(x)
array(6, dtype=int32)
>>> x = keras.ops.convert_to_tensor([[1, 6, 8], [1, 5, 2]])
>>> keras.ops.amax(x, axis=0)
array([1, 6, 8], dtype=int32)
>>> x = keras.ops.convert_to_tensor([[1, 6, 8], [1, 5, 2]])
>>> keras.ops.amax(x, axis=1, keepdims=True)
array([[8], [5]], dtype=int32)

[source]

### amin function

keras.ops.amin(x, axis=None, keepdims=False)

Returns the minimum of an array or minimum value along an axis.

Arguments

• x: Input tensor.
• axis: Axis along which to compute the minimum. By default (axis=None), find the minimum value in all the dimensions of the input array.
• keepdims: If True, axes which are reduced are left in the result as dimensions that are broadcast to the size of the original input tensor. Defaults to False.

Returns

An array with the minimum value. If axis=None, the result is a scalar value representing the minimum element in the entire array. If axis is given, the result is an array with the minimum values along the specified axis.

Examples

>>> x = keras.ops.convert_to_tensor([1, 3, 5, 2, 3, 6])
>>> keras.ops.amin(x)
array(1, dtype=int32)
>>> x = keras.ops.convert_to_tensor([[1, 6, 8], [7, 5, 3]])
>>> keras.ops.amin(x, axis=0)
array([1,5,3], dtype=int32)
>>> x = keras.ops.convert_to_tensor([[1, 6, 8], [7, 5, 3]])
>>> keras.ops.amin(x, axis=1, keepdims=True)
array([[1],[3]], dtype=int32)

[source]

### any function

keras.ops.any(x, axis=None, keepdims=False)

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

Arguments

• x: Input tensor.
• axis: An integer or tuple of integers that represent the axis 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 for the last to the first axis.
• keepdims: If True, 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. Defaults to False.

Returns

The tensor containing the logical OR reduction over the axis.

Examples

>>> x = keras.ops.convert_to_tensor([True, False])
>>> keras.ops.any(x)
array(True, shape=(), dtype=bool)
>>> x = keras.ops.convert_to_tensor([[True, False], [True, True]])
>>> keras.ops.any(x, axis=0)
array([ True  True], shape=(2,), dtype=bool)

keepdims=True outputs a tensor with dimensions reduced to one.

>>> x = keras.ops.convert_to_tensor([[True, False], [True, True]])
>>> keras.ops.all(x, keepdims=True)
array([[False]], shape=(1, 1), dtype=bool)

[source]

### append function

keras.ops.append(x1, x2, axis=None)

Append tensor x2 to the end of tensor x1.

Arguments

• x1: First input tensor.
• x2: Second input tensor.
• axis: Axis along which tensor x2 is appended to tensor x1. If None, both tensors are flattened before use.

Returns

A tensor with the values of x2 appended to x1.

Examples

>>> x1 = keras.ops.convert_to_tensor([1, 2, 3])
>>> x2 = keras.ops.convert_to_tensor([[4, 5, 6], [7, 8, 9]])
>>> keras.ops.append(x1, x2)
array([1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int32)

When axis is specified, x1 and x2 must have compatible shapes.

>>> x1 = keras.ops.convert_to_tensor([[1, 2, 3], [4, 5, 6]])
>>> x2 = keras.ops.convert_to_tensor([[7, 8, 9]])
>>> keras.ops.append(x1, x2, axis=0)
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]], dtype=int32)
>>> x3 = keras.ops.convert_to_tensor([7, 8, 9])
>>> keras.ops.append(x1, x3, axis=0)
Traceback (most recent call last):
...
TypeError: Cannot concatenate arrays with different numbers of
dimensions: got (2, 3), (3,).

[source]

### arange function

keras.ops.arange(start, stop=None, step=1, dtype=None)

Return evenly spaced values within a given interval.

arange can be called with a varying number of positional arguments: * arange(stop): Values are generated within the half-open interval [0, stop) (in other words, the interval including start but excluding stop). * arange(start, stop): Values are generated within the half-open interval [start, stop). * arange(start, stop, step): Values are generated within the half-open interval [start, stop), with spacing between values given by step.

Arguments

• start: Integer or real, representing the start of the interval. The interval includes this value.
• stop: Integer or real, representing the end of the interval. The interval does not include this value, except in some cases where step is not an integer and floating point round-off affects the length of out. Defaults to None.
• step: Integer or real, represent the spacing between values. For any output out, this is the distance between two adjacent values, out[i+1] - out[i]. The default step size is 1. If step is specified as a position argument, start must also be given.
• dtype: The type of the output array. If dtype is not given, infer the data type from the other input arguments.

Returns

Tensor of evenly spaced values. For floating point arguments, the length of the result is ceil((stop - start)/step). Because of floating point overflow, this rule may result in the last element of out being greater than stop.

Examples

>>> keras.ops.arange(3)
array([0, 1, 2], dtype=int32)
>>> keras.ops.arange(3.0)
array([0., 1., 2.], dtype=float32)
>>> keras.ops.arange(3, 7)
array([3, 4, 5, 6], dtype=int32)
>>> keras.ops.arange(3, 7, 2)
array([3, 5], dtype=int32)

[source]

### arccos function

keras.ops.arccos(x)

Trigonometric inverse cosine, element-wise.

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

Arguments

• x: Input tensor.

Returns

Tensor of the angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi].

Example

>>> x = keras.ops.convert_to_tensor([1, -1])
>>> keras.ops.arccos(x)
array([0.0, 3.1415927], dtype=float32)

[source]

### arccosh function

keras.ops.arccosh(x)

Inverse hyperbolic cosine, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

Example

>>> x = keras.ops.convert_to_tensor([10, 100])
>>> keras.ops.arccosh(x)
array([2.993223, 5.298292], dtype=float32)

[source]

### arcsin function

keras.ops.arcsin(x)

Inverse sine, element-wise.

Arguments

• x: Input tensor.

Returns

Tensor of the inverse sine of each element in x, in radians and in the closed interval [-pi/2, pi/2].

Example

>>> x = keras.ops.convert_to_tensor([1, -1, 0])
>>> keras.ops.arcsin(x)
array([ 1.5707964, -1.5707964,  0.], dtype=float32)

[source]

### arcsinh function

keras.ops.arcsinh(x)

Inverse hyperbolic sine, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

Example

>>> x = keras.ops.convert_to_tensor([1, -1, 0])
>>> keras.ops.arcsinh(x)
array([0.88137364, -0.88137364, 0.0], dtype=float32)

[source]

### arctan function

keras.ops.arctan(x)

Trigonometric inverse tangent, element-wise.

Arguments

• x: Input tensor.

Returns

Tensor of the inverse tangent of each element in x, in the interval [-pi/2, pi/2].

Example

>>> x = keras.ops.convert_to_tensor([0, 1])
>>> keras.ops.arctan(x)
array([0., 0.7853982], dtype=float32)

[source]

### arctan2 function

keras.ops.arctan2(x1, x2)

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.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Tensor of angles in radians, in the range [-pi, pi].

Examples

Consider four points in different quadrants:

>>> x = keras.ops.convert_to_tensor([-1, +1, +1, -1])
>>> y = keras.ops.convert_to_tensor([-1, -1, +1, +1])
>>> keras.ops.arctan2(y, x) * 180 / numpy.pi
array([-135., -45., 45., 135.], dtype=float32)

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

>>> keras.ops.arctan2(
...     keras.ops.array([1., -1.]),
...     keras.ops.array([0., 0.]),
... )
array([ 1.5707964, -1.5707964], dtype=float32)
>>> keras.ops.arctan2(
...     keras.ops.array([0., 0., numpy.inf]),
...     keras.ops.array([+0., -0., numpy.inf]),
... )
array([0., 3.1415925, 0.7853982], dtype=float32)

[source]

### arctanh function

keras.ops.arctanh(x)

Inverse hyperbolic tangent, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### argmax function

keras.ops.argmax(x, axis=None, keepdims=False)

Returns the indices of the maximum values along an axis.

Arguments

• x: Input tensor.
• axis: By default, the index is into the flattened tensor, otherwise along the specified axis.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one. Defaults to False.

Returns

Tensor of indices. It has the same shape as x, with the dimension along axis removed.

Example

>>> x = keras.ops.arange(6).reshape(2, 3) + 10
>>> x
array([[10, 11, 12],
[13, 14, 15]], dtype=int32)
>>> keras.ops.argmax(x)
array(5, dtype=int32)
>>> keras.ops.argmax(x, axis=0)
array([1, 1, 1], dtype=int32)
>>> keras.ops.argmax(x, axis=1)
array([2, 2], dtype=int32)

[source]

### argmin function

keras.ops.argmin(x, axis=None, keepdims=False)

Returns the indices of the minium values along an axis.

Arguments

• x: Input tensor.
• axis: By default, the index is into the flattened tensor, otherwise along the specified axis.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one. Defaults to False.

Returns

Tensor of indices. It has the same shape as x, with the dimension along axis removed.

Example

>>> x = keras.ops.arange(6).reshape(2, 3) + 10
>>> x
array([[10, 11, 12],
[13, 14, 15]], dtype=int32)
>>> keras.ops.argmin(x)
array(0, dtype=int32)
>>> keras.ops.argmin(x, axis=0)
array([0, 0, 0], dtype=int32)
>>> keras.ops.argmin(x, axis=1)
array([0, 0], dtype=int32)

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### argsort function

keras.ops.argsort(x, axis=-1)

Returns the indices that would sort a tensor.

Arguments

• x: Input tensor.
• axis: Axis along which to sort. Defaults to-1 (the last axis). If None, the flattened tensor is used.

Returns

Tensor of indices that sort x along the specified axis.

Examples

One dimensional array:

>>> x = keras.ops.array([3, 1, 2])
>>> keras.ops.argsort(x)
array([1, 2, 0], dtype=int32)

Two-dimensional array:

>>> x = keras.ops.array([[0, 3], [3, 2], [4, 5]])
>>> x
array([[0, 3],
[3, 2],
[4, 5]], dtype=int32)
>>> keras.ops.argsort(x, axis=0)
array([[0, 1],
[1, 0],
[2, 2]], dtype=int32)
>>> keras.ops.argsort(x, axis=1)
array([[0, 1],
[1, 0],
[0, 1]], dtype=int32)

[source]

### array function

keras.ops.array(x, dtype=None)

Create a tensor.

Arguments

• x: Input tensor.
• dtype: The desired data-type for the tensor.

Returns

A tensor.

Examples

>>> keras.ops.array([1, 2, 3])
array([1, 2, 3], dtype=int32)
>>> keras.ops.array([1, 2, 3], dtype="float32")
array([1., 2., 3.], dtype=float32)

[source]

### average function

keras.ops.average(x, axis=None, weights=None)

Compute the weighted average along the specified axis.

Arguments

• x: Input tensor.
• axis: Integer along which to average x. The default, axis=None, will average over all of the elements of the input tensor. If axis is negative it counts from the last to the first axis.
• weights: Tensor of wieghts associated with the values in x. Each value in x 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 x. If weights=None (default), then all data in x 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.

Returns

Return the average along the specified axis.

Examples

>>> data = keras.ops.arange(1, 5)
>>> data
array([1, 2, 3, 4], dtype=int32)
>>> keras.ops.average(data)
array(2.5, dtype=float32)
>>> keras.ops.average(
...     keras.ops.arange(1, 11),
...     weights=keras.ops.arange(10, 0, -1)
... )
array(4., dtype=float32)
>>> data = keras.ops.arange(6).reshape((3, 2))
>>> data
array([[0, 1],
[2, 3],
[4, 5]], dtype=int32)
>>> keras.ops.average(
...     data,
...     axis=1,
...     weights=keras.ops.array([1./4, 3./4])
... )
array([0.75, 2.75, 4.75], dtype=float32)
>>> keras.ops.average(
...     data,
...     weights=keras.ops.array([1./4, 3./4])
... )
Traceback (most recent call last):
...
ValueError: Axis must be specified when shapes of a and weights differ.

[source]

### bincount function

keras.ops.bincount(x, weights=None, minlength=0, sparse=False)

Count the number of occurrences of each value in a tensor of integers.

Arguments

• x: Input tensor. It must be of dimension 1, and it must only contain non-negative integer(s).
• weights: Weight tensor. It must have the same length as x. The default value is None. If specified, x is weighted by it, i.e. if n = x[i], out[n] += weight[i] instead of the default behavior out[n] += 1.
• minlength: An integer. The default value is 0. If specified, there will be at least this number of bins in the output tensor. If greater than max(x) + 1, each value of the output at an index higher than max(x) is set to 0.
• sparse: Whether to return a sparse tensor; for backends that support sparse tensors.

Returns

1D tensor where each element gives the number of occurrence(s) of its index value in x. Its length is the maximum between max(x) + 1 and minlength.

Examples

>>> x = keras.ops.array([1, 2, 2, 3], dtype="uint8")
>>> keras.ops.bincount(x)
array([0, 1, 2, 1], dtype=int32)
>>> weights = x / 2
>>> weights
array([0.5, 1., 1., 1.5], dtype=float64)
>>> keras.ops.bincount(x, weights=weights)
array([0., 0.5, 2., 1.5], dtype=float64)
>>> minlength = (keras.ops.max(x).numpy() + 1) + 2 # 6
>>> keras.ops.bincount(x, minlength=minlength)
array([0, 1, 2, 1, 0, 0], dtype=int32)

[source]

Broadcast a tensor to a new shape.

Arguments

• x: The tensor to broadcast.
• shape: The shape of the desired tensor. A single integer i is interpreted as (i,).

Returns

A tensor with the desired shape.

Examples

>>> x = keras.ops.array([1, 2, 3])
array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]])

[source]

### ceil function

keras.ops.ceil(x)

Return the ceiling of the input, element-wise.

The ceil of the scalar x is the smallest integer i, such that i >= x.

Arguments

• x: Input tensor.

Returns

The ceiling of each element in x, with float dtype.

[source]

### clip function

keras.ops.clip(x, x_min, x_max)

Clip (limit) the values in a tensor.

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.

Arguments

• x: Input tensor.
• x_min: Minimum value.
• x_max: Maximum value.

Returns

The clipped tensor.

[source]

### concatenate function

keras.ops.concatenate(xs, axis=0)

Join a sequence of tensors along an existing axis.

Arguments

• xs: The sequence of tensors to concatenate.
• axis: The axis along which the tensors will be joined. Defaults to 0.

Returns

The concatenated tensor.

[source]

### conj function

keras.ops.conj(x)

Shorthand for keras.ops.conjugate.

[source]

### conjugate function

keras.ops.conjugate(x)

Returns the complex conjugate, element-wise.

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

keras.ops.conj is a shorthand for this function.

Arguments

• x: Input tensor.

Returns

The complex conjugate of each element in x.

[source]

### copy function

keras.ops.copy(x)

Returns a copy of x.

Arguments

• x: Input tensor.

Returns

A copy of x.

[source]

### cos function

keras.ops.cos(x)

Cosine, element-wise.

Arguments

• x: Input tensor.

Returns

The corresponding cosine values.

[source]

### cosh function

keras.ops.cosh(x)

Hyperbolic cosine, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### count_nonzero function

keras.ops.count_nonzero(x, axis=None)

Counts the number of non-zero values in x along the given axis.

If no axis is specified then all non-zeros in the tensor are counted.

Arguments

• x: Input tensor.
• axis: Axis or tuple of axes along which to count the number of non-zeros. Defaults to None.

Returns

int or tensor of ints.

Examples

>>> x = keras.ops.array([[0, 1, 7, 0], [3, 0, 2, 19]])
>>> keras.ops.count_nonzero(x)
5
>>> keras.ops.count_nonzero(x, axis=0)
array([1, 1, 2, 1], dtype=int64)
>>> keras.ops.count_nonzero(x, axis=1)
array([2, 3], dtype=int64)

[source]

### cross function

keras.ops.cross(x1, x2, axisa=-1, axisb=-1, axisc=-1, axis=None)

Returns the cross product of two (arrays of) vectors.

The cross product of x1 and x2 in R^3 is a vector perpendicular to both x1 and x2. If x1 and x2 are arrays of vectors, the vectors are defined by the last axis of x1 and x2 by default, and these axes can have dimensions 2 or 3.

Where the dimension of either x1 or x2 is 2, the third component of the input vector is assumed to be zero and the cross product calculated accordingly.

In cases where both input vectors have dimension 2, the z-component of the cross product is returned.

Arguments

• x1: Components of the first vector(s).
• x2: Components of the second vector(s).
• axisa: Axis of x1 that defines the vector(s). Defaults to -1.
• axisb: Axis of x2 that defines the vector(s). Defaults to -1.
• axisc: Axis of the result containing the cross product vector(s). Ignored if both input vectors have dimension 2, as the return is scalar. By default, the last axis.
• axis: If defined, the axis of x1, x2 and the result that defines the vector(s) and cross product(s). Overrides axisa, axisb and axisc.

Note: Torch backend does not support two dimensional vectors, or the arguments axisa, axisb and axisc. Use axis instead.

Returns

Vector cross product(s).

[source]

### cumprod function

keras.ops.cumprod(x, axis=None, dtype=None)

Return the cumulative product of elements along a given axis.

Arguments

• x: Input tensor.
• axis: Axis along which the cumulative product is computed. By default the input is flattened.
• dtype: dtype of returned tensor. Defaults to x.dtype.

Returns

Output tensor.

[source]

### cumsum function

keras.ops.cumsum(x, axis=None, dtype=None)

Returns the cumulative sum of elements along a given axis.

Arguments

• x: Input tensor.
• axis: Axis along which the cumulative sum is computed. By default the input is flattened.
• dtype: dtype of returned tensor. Defaults to x.dtype.

Returns

Output tensor.

[source]

### diag function

keras.ops.diag(x, k=0)

Extract a diagonal or construct a diagonal array.

Arguments

• x: Input tensor. If x is 2-D, returns the k-th diagonal of x. If x is 1-D, return a 2-D tensor with x on the k-th diagonal.
• k: The diagonal to consider. Defaults to 0. Use k > 0 for diagonals above the main diagonal, and k < 0 for diagonals below the main diagonal.

Returns

The extracted diagonal or constructed diagonal tensor.

Examples

>>> from keras.src import ops
>>> x = ops.arange(9).reshape((3, 3))
>>> x
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
>>> ops.diag(x)
array([0, 4, 8])
>>> ops.diag(x, k=1)
array([1, 5])
>>> ops.diag(x, k=-1)
array([3, 7])
>>> ops.diag(ops.diag(x)))
array([[0, 0, 0],
[0, 4, 0],
[0, 0, 8]])

[source]

### diagonal function

keras.ops.diagonal(x, offset=0, axis1=0, axis2=1)

Return specified diagonals.

If x is 2-D, returns the diagonal of x with the given offset, i.e., the collection of elements of the form x[i, i+offset].

If x has more than two dimensions, 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.

Arguments

• x: Input tensor.
• offset: Offset of the diagonal from the main diagonal. Can be positive or negative. Defaults to 0.(main diagonal).
• axis1: Axis to be used as the first axis of the 2-D sub-arrays. Defaults to 0.(first axis).
• axis2: Axis to be used as the second axis of the 2-D sub-arrays. Defaults to 1 (second axis).

Returns

Tensor of diagonals.

Examples

>>> from keras.src import ops
>>> x = ops.arange(4).reshape((2, 2))
>>> x
array([[0, 1],
[2, 3]])
>>> x.diagonal()
array([0, 3])
>>> x.diagonal(1)
array([1])
>>> x = ops.arange(8).reshape((2, 2, 2))
>>> x
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> x.diagonal(0, 0, 1)
array([[0, 6],
[1, 7]])

[source]

### diff function

keras.ops.diff(a, n=1, axis=-1)

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

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.

Arguments

• a: Input tensor.
• n: The number of times values are differenced. Defaults to 1.
• axis: Axis to compute discrete difference(s) along. Defaults to -1.(last axis).

Returns

Tensor of diagonals.

Examples

>>> from keras.src import ops
>>> x = ops.convert_to_tensor([1, 2, 4, 7, 0])
>>> ops.diff(x)
array([ 1,  2,  3, -7])
>>> ops.diff(x, n=2)
array([  1,   1, -10])
>>> x = ops.convert_to_tensor([[1, 3, 6, 10], [0, 5, 6, 8]])
>>> ops.diff(x)
array([[2, 3, 4],
[5, 1, 2]])
>>> ops.diff(x, axis=0)
array([[-1,  2,  0, -2]])

[source]

### digitize function

keras.ops.digitize(x, bins)

Returns the indices of the bins to which each value in x belongs.

Arguments

• x: Input array to be binned.
• bins: Array of bins. It has to be one-dimensional and monotonically increasing.

Returns

Output array of indices, of same shape as x.

Example

>>> x = np.array([0.0, 1.0, 3.0, 1.6])
>>> bins = np.array([0.0, 3.0, 4.5, 7.0])
>>> keras.ops.digitize(x, bins)
array([1, 1, 2, 1])

[source]

### divide function

keras.ops.divide(x1, x2)

Divide arguments element-wise.

keras.ops.true_divide is an alias for this function.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, the quotient x1/x2, element-wise.

[source]

### divide_no_nan function

keras.ops.divide_no_nan(x1, x2)

Safe element-wise division which returns 0 where the denominator is 0.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

The quotient x1/x2, element-wise, with zero where x2 is zero.

[source]

### dot function

keras.ops.dot(x1, x2)

Dot product of two tensors.

• If both x1 and x2 are 1-D tensors, it is inner product of vectors (without complex conjugation).
• If both x1 and x2 are 2-D tensors, it is matrix multiplication.
• If either x1 or x2 is 0-D (scalar), it is equivalent to x1 * x2.
• If x1 is an N-D tensor and x2 is a 1-D tensor, it is a sum product over the last axis of x1 and x2.
• If x1 is an N-D tensor and x2 is an M-D tensor (where M>=2), it is a sum product over the last axis of x1 and the second-to-last axis of x2: dot(x1, x2)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m]).

Arguments

• x1: First argument.
• x2: Second argument.

Note: Torch backend does not accept 0-D tensors as arguments.

Returns

Dot product of x1 and x2.

[source]

### einsum function

keras.ops.einsum(subscripts, *operands)

Evaluates the Einstein summation convention on the operands.

Arguments

• subscripts: 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: The operands to compute the Einstein sum of.

Returns

The calculation based on the Einstein summation convention.

Example

>>> from keras.src import ops
>>> a = ops.arange(25).reshape(5, 5)
>>> b = ops.arange(5)
>>> c = ops.arange(6).reshape(2, 3)

Trace of a matrix:

>>> ops.einsum("ii", a)
60
>>> ops.einsum(a, [0, 0])
60
>>> ops.trace(a)
60

Extract the diagonal:

>>> ops.einsum("ii -> i", a)
array([ 0,  6, 12, 18, 24])
>>> ops.einsum(a, [0, 0], [0])
array([ 0,  6, 12, 18, 24])
>>> ops.diag(a)
array([ 0,  6, 12, 18, 24])

Sum over an axis:

>>> ops.einsum("ij -> i", a)
array([ 10,  35,  60,  85, 110])
>>> ops.einsum(a, [0, 1], [0])
array([ 10,  35,  60,  85, 110])
>>> ops.sum(a, axis=1)
array([ 10,  35,  60,  85, 110])

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

>>> ops.einsum("...j -> ...", a)
array([ 10,  35,  60,  85, 110])
>>> np.einsum(a, [..., 1], [...])
array([ 10,  35,  60,  85, 110])

Compute a matrix transpose or reorder any number of axes:

>>> ops.einsum("ji", c)
array([[0, 3],
[1, 4],
[2, 5]])
>>> ops.einsum("ij -> ji", c)
array([[0, 3],
[1, 4],
[2, 5]])
>>> ops.einsum(c, [1, 0])
array([[0, 3],
[1, 4],
[2, 5]])
>>> ops.transpose(c)
array([[0, 3],
[1, 4],
[2, 5]])

Matrix vector multiplication:

>>> ops.einsum("ij, j", a, b)
array([ 30,  80, 130, 180, 230])
>>> ops.einsum(a, [0, 1], b, [1])
array([ 30,  80, 130, 180, 230])
>>> ops.einsum("...j, j", a, b)
array([ 30,  80, 130, 180, 230])

[source]

### empty function

keras.ops.empty(shape, dtype=None)

Return a tensor of given shape and type filled with uninitialized data.

Arguments

• shape: Shape of the empty tensor.
• dtype: Desired data type of the empty tensor.

Returns

The empty tensor.

[source]

### equal function

keras.ops.equal(x1, x2)

Returns (x1 == x2) element-wise.

Arguments

• x1: Tensor to compare.
• x2: Tensor to compare.

Returns

Output tensor, element-wise comparison of x1 and x2.

[source]

### exp function

keras.ops.exp(x)

Calculate the exponential of all elements in the input tensor.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise exponential of x.

[source]

### expand_dims function

keras.ops.expand_dims(x, axis)

Expand the shape of a tensor.

Insert a new axis at the axis position in the expanded tensor shape.

Arguments

• x: Input tensor.
• axis: Position in the expanded axes where the new axis (or axes) is placed.

Returns

Output tensor with the number of dimensions increased.

[source]

### expm1 function

keras.ops.expm1(x)

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

Arguments

• x: Input values.

Returns

Output tensor, element-wise exponential minus one.

[source]

### eye function

keras.ops.eye(N, M=None, k=0, dtype=None)

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

Arguments

• N: Number of rows in the output.
• M: Number of columns in the output. If None, defaults to N.
• k: 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 of the returned tensor.

Returns

Tensor with ones on the k-th diagonal and zeros elsewhere.

[source]

### flip function

keras.ops.flip(x, axis=None)

Reverse the order of elements in the tensor along the given axis.

The shape of the tensor is preserved, but the elements are reordered.

Arguments

• x: Input tensor.
• axis: Axis or axes along which to flip the tensor. The default, axis=None, will flip over all of the axes of the input tensor.

Returns

Output tensor with entries of axis reversed.

[source]

### floor function

keras.ops.floor(x)

Return the floor of the input, element-wise.

The floor of the scalar x is the largest integer i, such that i <= x.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise floor of x.

[source]

### floor_divide function

keras.ops.floor_divide(x1, x2)

Returns the largest integer smaller or equal to the division of inputs.

Arguments

• x1: Numerator.
• x2: Denominator.

Returns

Output tensor, y = floor(x1/x2)

[source]

### full function

keras.ops.full(shape, fill_value, dtype=None)

Return a new tensor of given shape and type, filled with fill_value.

Arguments

• shape: Shape of the new tensor.
• fill_value: Fill value.
• dtype: Desired data type of the tensor.

Returns

Output tensor.

[source]

### full_like function

keras.ops.full_like(x, fill_value, dtype=None)

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

Arguments

• x: Input tensor.
• fill_value: Fill value.
• dtype: Overrides data type of the result.

Returns

Tensor of fill_value with the same shape and type as x.

[source]

### get_item function

keras.ops.get_item(x, key)

Return x[key].

[source]

### greater function

keras.ops.greater(x1, x2)

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

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise comparison of x1 and x2.

[source]

### greater_equal function

keras.ops.greater_equal(x1, x2)

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

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise comparison of x1 and x2.

[source]

### hstack function

keras.ops.hstack(xs)

Stack tensors in sequence horizontally (column wise).

This is equivalent to concatenation along the first axis for 1-D tensors, and along the second axis for all other tensors.

Arguments

• xs: Sequence of tensors.

Returns

The tensor formed by stacking the given tensors.

[source]

### identity function

keras.ops.identity(n, dtype=None)

Return the identity tensor.

The identity tensor is a square tensor with ones on the main diagonal and zeros elsewhere.

Arguments

• n: Number of rows (and columns) in the n x n output tensor.
• dtype: Data type of the output tensor.

Returns

The identity tensor.

[source]

### imag function

keras.ops.imag(x)

Return the imaginary part of the complex argument.

Arguments

• x: Input tensor.

Returns

The imaginary component of the complex argument.

[source]

### isclose function

keras.ops.isclose(x1, x2)

Return whether two tensors are element-wise almost equal.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output boolean tensor.

[source]

### isfinite function

keras.ops.isfinite(x)

Return whether a tensor is finite, element-wise.

Real values are finite when they are not NaN, not positive infinity, and not negative infinity. Complex values are finite when both their real and imaginary parts are finite.

Arguments

• x: Input tensor.

Returns

Output boolean tensor.

[source]

### isinf function

keras.ops.isinf(x)

Test element-wise for positive or negative infinity.

Arguments

• x: Input tensor.

Returns

Output boolean tensor.

[source]

### isnan function

keras.ops.isnan(x)

Test element-wise for NaN and return result as a boolean tensor.

Arguments

• x: Input tensor.

Returns

Output boolean tensor.

[source]

### less function

keras.ops.less(x1, x2)

Return the truth value of x1 < x2 element-wise.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise comparison of x1 and x2.

[source]

### less_equal function

keras.ops.less_equal(x1, x2)

Return the truth value of x1 <= x2 element-wise.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise comparison of x1 and x2.

[source]

### linspace function

keras.ops.linspace(
start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0
)

Return evenly spaced numbers over a specified interval.

Returns num evenly spaced samples, calculated over the interval [start, stop].

The endpoint of the interval can optionally be excluded.

Arguments

• start: The starting value of the sequence.
• stop: The end value of the sequence, unless endpoint is set to False. In that case, the sequence consists of all but the last of num + 1 evenly spaced samples, so that stop is excluded. Note that the step size changes when endpoint is False.
• num: Number of samples to generate. Defaults to 50. Must be non-negative.
• endpoint: If True, stop is the last sample. Otherwise, it is not included. Defaults to True.
• retstep: If True, return (samples, step), where step is the spacing between samples.
• dtype: The type of the output tensor.
• axis: The axis in the result to store the samples. Relevant only if start or stop are array-like. Defaults to 0.

Note: Torch backend does not support axis argument.

Returns

A tensor of evenly spaced numbers. If retstep is True, returns (samples, step)

[source]

### log function

keras.ops.log(x)

Natural logarithm, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise natural logarithm of x.

[source]

### log10 function

keras.ops.log10(x)

Return the base 10 logarithm of the input tensor, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise base 10 logarithm of x.

[source]

### log1p function

keras.ops.log1p(x)

Returns the natural logarithm of one plus the x, element-wise.

Calculates log(1 + x).

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise natural logarithm of 1 + x.

[source]

### log2 function

keras.ops.log2(x)

Base-2 logarithm of x, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise base-2 logarithm of x.

[source]

Logarithm of the sum of exponentiations of the inputs.

Calculates log(exp(x1) + exp(x2)).

Arguments

• x1: Input tensor.
• x2: Input tensor.

Returns

Output tensor, element-wise logarithm of the sum of exponentiations of the inputs.

[source]

### logical_and function

keras.ops.logical_and(x1, x2)

Computes the element-wise logical AND of the given input tensors.

Zeros are treated as False and non-zeros are treated as True.

Arguments

• x1: Input tensor.
• x2: Input tensor.

Returns

Output tensor, element-wise logical AND of the inputs.

[source]

### logical_not function

keras.ops.logical_not(x)

Computes the element-wise NOT of the given input tensor.

Zeros are treated as False and non-zeros are treated as True.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise logical NOT of the input.

[source]

### logical_or function

keras.ops.logical_or(x1, x2)

Computes the element-wise logical OR of the given input tensors.

Zeros are treated as False and non-zeros are treated as True.

Arguments

• x1: Input tensor.
• x2: Input tensor.

Returns

Output tensor, element-wise logical OR of the inputs.

[source]

### logical_xor function

keras.ops.logical_xor(x1, x2)

Compute the truth value of x1 XOR x2, element-wise.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output boolean tensor.

[source]

### logspace function

keras.ops.logspace(start, stop, num=50, endpoint=True, base=10, dtype=None, axis=0)

Returns numbers spaced evenly on a log scale.

In linear space, the sequence starts at base ** start and ends with base ** stop (see endpoint below).

Arguments

• start: The starting value of the sequence.
• stop: The final value of the sequence, unless endpoint is False. In that case, num + 1 values are spaced over the interval in log-space, of which all but the last (a sequence of length num) are returned.
• num: Number of samples to generate. Defaults to 50.
• endpoint: If True, stop is the last sample. Otherwise, it is not included. Defaults to True.
• base: The base of the log space. Defaults to 10.
• dtype: The type of the output tensor.
• axis: The axis in the result to store the samples. Relevant only if start or stop are array-like.

Note: Torch backend does not support axis argument.

Returns

A tensor of evenly spaced samples on a log scale.

[source]

### matmul function

keras.ops.matmul(x1, x2)

Matrix product of two tensors.

• If both tensors are 1-dimensional, the dot product (scalar) is returned.
• If either tensor 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 tensor 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 tensor is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.

Arguments

• x1: First tensor.
• x2: Second tensor.

Returns

Output tensor, matrix product of the inputs.

[source]

### max function

keras.ops.max(x, axis=None, keepdims=False, initial=None)

Return the maximum of a tensor or maximum along an axis.

Arguments

• x: Input tensor.
• axis: Axis or axes along which to operate. By default, flattened input is used.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one. Defaults to False.
• initial: The minimum value of an output element. Defaults to None.

Returns

Maximum of x.

[source]

### maximum function

keras.ops.maximum(x1, x2)

Element-wise maximum of x1 and x2.

Arguments

• x1: First tensor.
• x2: Second tensor.

Returns

Output tensor, element-wise maximum of x1 and x2.

[source]

### mean function

keras.ops.mean(x, axis=None, keepdims=False)

Compute the arithmetic mean along the specified axes.

Arguments

• x: Input tensor.
• axis: Axis or axes along which the means are computed. The default is to compute the mean of the flattened tensor.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

Output tensor containing the mean values.

[source]

### median function

keras.ops.median(x, axis=None, keepdims=False)

Compute the median along the specified axis.

Arguments

• x: Input tensor.
• axis: Axis or axes along which the medians are computed. Defaults to axis=None which is to compute the median(s) along a flattened version of the array.
• keepdims: If this is set to True, the axes which are reduce are left in the result as dimensions with size one.

Returns

The output tensor.

[source]

### meshgrid function

keras.ops.meshgrid(*x, indexing="xy")

Creates grids of coordinates from coordinate vectors.

Given N 1-D tensors T0, T1, ..., TN-1 as inputs with corresponding lengths S0, S1, ..., SN-1, this creates an N N-dimensional tensors G0, G1, ..., GN-1 each with shape (S0, ..., SN-1) where the output Gi is constructed by expanding Ti to the result shape.

Arguments

• x: 1-D tensors representing the coordinates of a grid.
• indexing: "xy" or "ij". "xy" is cartesian; "ij" is matrix indexing of output. Defaults to "xy".

Returns

Sequence of N tensors.

Example

>>> from keras.src import ops
>>> x = ops.array([1, 2, 3])
>>> y = ops.array([4, 5, 6])
>>> grid_x, grid_y = ops.meshgrid(x, y, indexing="ij")
>>> grid_x
array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])
>>> grid_y
array([[4, 5, 6],
[4, 5, 6],
[4, 5, 6]])

[source]

### min function

keras.ops.min(x, axis=None, keepdims=False, initial=None)

Return the minimum of a tensor or minimum along an axis.

Arguments

• x: Input tensor.
• axis: Axis or axes along which to operate. By default, flattened input is used.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one. Defaults to False.
• initial: The maximum value of an output element. Defaults to None.

Returns

Minimum of x.

[source]

### minimum function

keras.ops.minimum(x1, x2)

Element-wise minimum of x1 and x2.

Arguments

• x1: First tensor.
• x2: Second tensor.

Returns

Output tensor, element-wise minimum of x1 and x2.

[source]

### mod function

keras.ops.mod(x1, x2)

Returns the element-wise remainder of division.

Arguments

• x1: First tensor.
• x2: Second tensor.

Returns

Output tensor, element-wise remainder of division.

[source]

### moveaxis function

keras.ops.moveaxis(x, source, destination)

Move axes of a tensor to new positions.

Other axes remain in their original order.

Arguments

• x: Tensor whose axes should be reordered.
• source: Original positions of the axes to move. These must be unique.
• destination: Destinations positions for each of the original axes. These must also be unique.

Returns

Tensor with moved axes.

[source]

### multiply function

keras.ops.multiply(x1, x2)

Multiply arguments element-wise.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise product of x1 and x2.

[source]

### nan_to_num function

keras.ops.nan_to_num(x, nan=0.0, posinf=None, neginf=None)

Replace NaN with zero and infinity with large finite numbers.

Arguments

• x: Input data.
• nan: Optional float or int. Value to replace NaN entries with.
• posinf: Optional float or int. Value to replace positive infinity with.
• neginf: Optional float or int. Value to replace negative infinity with.

Returns

x, with non-finite values replaced.

[source]

### ndim function

keras.ops.ndim(x)

Return the number of dimensions of a tensor.

Arguments

• x: Input tensor.

Returns

The number of dimensions in x.

[source]

### negative function

keras.ops.negative(x)

Numerical negative, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor, y = -x.

[source]

### nonzero function

keras.ops.nonzero(x)

Return the indices of the elements that are non-zero.

Arguments

• x: Input tensor.

Returns

Indices of elements that are non-zero.

[source]

### norm function

keras.ops.norm(x, ord=None, axis=None, keepdims=False)

Matrix or vector norm.

This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter.

Arguments

• x: Input tensor.
• ord: Order of the norm (see table under Notes). The default is None.
• axis: If axis is an integer, it specifies the axis of x along which to compute the vector norms. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Note: For values of ord < 1, the result is, strictly speaking, not a mathematical 'norm', but it may still be useful for various numerical purposes. The following norms can be calculated: - For matrices: - ord=None: Frobenius norm - ord="fro": Frobenius norm - ord="nuc": nuclear norm - ord=np.inf: max(sum(abs(x), axis=1)) - ord=-np.inf: min(sum(abs(x), axis=1)) - ord=0: not supported - ord=1: max(sum(abs(x), axis=0)) - ord=-1: min(sum(abs(x), axis=0)) - ord=2: 2-norm (largest sing. value) - ord=-2: smallest singular value - other: not supported - For vectors: - ord=None: 2-norm - ord="fro": not supported - ord="nuc": not supported - ord=np.inf: max(abs(x)) - ord=-np.inf: min(abs(x)) - ord=0: sum(x != 0) - ord=1: as below - ord=-1: as below - ord=2: as below - ord=-2: as below - other: sum(abs(x)**ord)**(1./ord)

Returns

Norm of the matrix or vector(s).

Example

>>> x = keras.ops.reshape(keras.ops.arange(9, dtype="float32") - 4, (3, 3))
>>> keras.ops.linalg.norm(x)
7.7459664

[source]

### not_equal function

keras.ops.not_equal(x1, x2)

Return (x1 != x2) element-wise.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise comparsion of x1 and x2.

[source]

### ones function

keras.ops.ones(shape, dtype=None)

Return a new tensor of given shape and type, filled with ones.

Arguments

• shape: Shape of the new tensor.
• dtype: Desired data type of the tensor.

Returns

Tensor of ones with the given shape and dtype.

[source]

### ones_like function

keras.ops.ones_like(x, dtype=None)

Return a tensor of ones with the same shape and type of x.

Arguments

• x: Input tensor.
• dtype: Overrides the data type of the result.

Returns

A tensor of ones with the same shape and type as x.

[source]

### outer function

keras.ops.outer(x1, x2)

Compute the outer product of two vectors.

Given two vectors x1 and x2, the outer product is:

out[i, j] = x1[i] * x2[j]

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Outer product of x1 and x2.

[source]

Arguments

• pad_width: Number of values padded to the edges of each axis. ((before_1, after_1), ...(before_N, after_N)) unique pad widths for each axis. ((before, after),) yields same before and after pad for each axis. (pad,) or int is a shortcut for before = after = pad width for all axes.
• mode: One of "constant", "edge", "linear_ramp", "maximum", "mean", "median", "minimum", "reflect", "symmetric", "wrap", "empty", "circular". Defaults to"constant".
• constant_values: value to pad with if mode == "constant". Defaults to 0. A ValueError is raised if not None and mode != "constant".

Note: Torch backend only supports modes "constant", "reflect", "symmetric" and "circular". Only Torch backend supports "circular" mode.

Note: Tensorflow backend only supports modes "constant", "reflect" and "symmetric".

Returns

[source]

### power function

keras.ops.power(x1, x2)

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

Arguments

• x1: The bases.
• x2: The exponents.

Returns

Output tensor, the bases in x1 raised to the exponents in x2.

[source]

### prod function

keras.ops.prod(x, axis=None, keepdims=False, dtype=None)

Return the product of tensor elements over a given axis.

Arguments

• x: Input tensor.
• axis: Axis or axes along which a product is performed. The default, axis=None, will compute the product of all elements in the input tensor.
• keepdims: If this is set to True, the axes which are reduce are left in the result as dimensions with size one.
• dtype: Data type of the returned tensor.

Returns

Product of elements of x over the given axis or axes.

[source]

### quantile function

keras.ops.quantile(x, q, axis=None, method="linear", keepdims=False)

Compute the q-th quantile(s) of the data along the specified axis.

Arguments

• x: Input tensor.
• q: Probability or sequence of probabilities for the quantiles to compute. Values must be between 0 and 1 inclusive.
• axis: Axis or axes along which the quantiles are computed. Defaults to axis=None which is to compute the quantile(s) along a flattened version of the array.
• method: A string specifies the method to use for estimating the quantile. Available methods are "linear", "lower", "higher", "midpoint", and "nearest". Defaults to "linear". If the desired quantile lies between two data points i < j:
• "linear": i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.
• "lower": i.
• "higher": j.
• "midpoint": (i + j) / 2
• "nearest": i or j, whichever is nearest.
• keepdims: If this is set to True, the axes which are reduce are left in the result as dimensions with size one.

Returns

The quantile(s). If q is a single probability and axis=None, then the result is a scalar. If multiple probabilies levels are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of x.

[source]

### ravel function

keras.ops.ravel(x)

Return a contiguous flattened tensor.

A 1-D tensor, containing the elements of the input, is returned.

Arguments

• x: Input tensor.

Returns

Output tensor.

[source]

### real function

keras.ops.real(x)

Return the real part of the complex argument.

Arguments

• x: Input tensor.

Returns

The real component of the complex argument.

[source]

### reciprocal function

keras.ops.reciprocal(x)

Return the reciprocal of the argument, element-wise.

Calculates 1/x.

Arguments

• x: Input tensor.

Returns

Output tensor, element-wise reciprocal of x.

[source]

### repeat function

keras.ops.repeat(x, repeats, axis=None)

Repeat each element of a tensor after themselves.

Arguments

• x: Input tensor.
• repeats: The number of repetitions for each element.
• axis: The axis along which to repeat values. By default, use the flattened input array, and return a flat output array.

Returns

Output tensor.

[source]

### reshape function

keras.ops.reshape(x, newshape)

Gives a new shape to a tensor without changing its data.

Arguments

• x: Input tensor.
• newshape: The new shape should be compatible with the original shape. One shape dimension can be -1 in which case the value is inferred from the length of the array and remaining dimensions.

Returns

The reshaped tensor.

[source]

### roll function

keras.ops.roll(x, shift, axis=None)

Roll tensor elements along a given axis.

Elements that roll beyond the last position are re-introduced at the first.

Arguments

• x: Input tensor.
• shift: The number of places by which elements are shifted.
• axis: The axis along which elements are shifted. By default, the array is flattened before shifting, after which the original shape is restored.

Returns

Output tensor.

[source]

### round function

keras.ops.round(x, decimals=0)

Evenly round to the given number of decimals.

Arguments

• x: Input tensor.
• decimals: Number of decimal places to round to. Defaults to 0.

Returns

Output tensor.

[source]

### sign function

keras.ops.sign(x)

Returns a tensor with the signs of the elements of x.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### sin function

keras.ops.sin(x)

Trigonometric sine, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### sinh function

keras.ops.sinh(x)

Hyperbolic sine, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### size function

keras.ops.size(x)

Return the number of elements in a tensor.

Arguments

• x: Input tensor.

Returns

Number of elements in x.

[source]

### sort function

keras.ops.sort(x, axis=-1)

Sorts the elements of x along a given axis in ascending order.

Arguments

• x: Input tensor.
• axis: Axis along which to sort. If None, the tensor is flattened before sorting. Defaults to -1; the last axis.

Returns

Sorted tensor.

[source]

### split function

keras.ops.split(x, indices_or_sections, axis=0)

Split a tensor into chunks.

Arguments

• x: Input tensor.
• indices_or_sections: If an integer, N, the tensor will be split into N equal sections along axis. If a 1-D array of sorted integers, the entries indicate indices at which the tensor will be split along axis.
• axis: Axis along which to split. Defaults to 0.

Note: A split does not have to result in equal division when using Torch backend.

Returns

A list of tensors.

[source]

### sqrt function

keras.ops.sqrt(x)

Return the non-negative square root of a tensor, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor, the non-negative square root of x.

[source]

### square function

keras.ops.square(x)

Return the element-wise square of the input.

Arguments

• x: Input tensor.

Returns

Output tensor, the square of x.

[source]

### squeeze function

keras.ops.squeeze(x, axis=None)

Remove axes of length one from x.

Arguments

• x: Input tensor.
• axis: Select a subset of the entries of length one in the shape.

Returns

The input tensor with all or a subset of the dimensions of length 1 removed.

[source]

### stack function

keras.ops.stack(x, axis=0)

Join a sequence of tensors along a new axis.

The axis parameter specifies the index of the new axis in the dimensions of the result.

Arguments

• x: A sequence of tensors.
• axis: Axis along which to stack. Defaults to 0.

Returns

The stacked tensor.

[source]

### std function

keras.ops.std(x, axis=None, keepdims=False)

Compute the standard deviation along the specified axis.

Arguments

• x: Input tensor.
• axis: Axis along which to compute standard deviation. Default is to compute the standard deviation of the flattened tensor.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

Output tensor containing the standard deviation values.

[source]

### subtract function

keras.ops.subtract(x1, x2)

Subtract arguments element-wise.

Arguments

• x1: First input tensor.
• x2: Second input tensor.

Returns

Output tensor, element-wise difference of x1 and x2.

[source]

### sum function

keras.ops.sum(x, axis=None, keepdims=False)

Sum of a tensor over the given axes.

Arguments

• x: Input tensor.
• axis: Axis or axes along which the sum is computed. The default is to compute the sum of the flattened tensor.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

Output tensor containing the sum.

[source]

### swapaxes function

keras.ops.swapaxes(x, axis1, axis2)

Interchange two axes of a tensor.

Arguments

• x: Input tensor.
• axis1: First axis.
• axis2: Second axis.

Returns

A tensor with the axes swapped.

[source]

### take function

keras.ops.take(x, indices, axis=None)

Take elements from a tensor along an axis.

Arguments

• x: Source tensor.
• indices: The indices of the values to extract.
• axis: The axis over which to select values. By default, the flattened input tensor is used.

Returns

The corresponding tensor of values.

[source]

### take_along_axis function

keras.ops.take_along_axis(x, indices, axis=None)

Select values from x at the 1-D indices along the given axis.

Arguments

• x: Source tensor.
• indices: The indices of the values to extract.
• axis: The axis over which to select values. By default, the flattened input tensor is used.

Returns

The corresponding tensor of values.

[source]

### tan function

keras.ops.tan(x)

Compute tangent, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### tanh function

keras.ops.tanh(x)

Hyperbolic tangent, element-wise.

Arguments

• x: Input tensor.

Returns

Output tensor of same shape as x.

[source]

### tensordot function

keras.ops.tensordot(x1, x2, axes=2)

Compute the tensor dot product along specified axes.

Arguments

• x1: First tensor.
• x2: Second tensor.
• axes: - If an integer, N, sum over the last N axes of x1 and the first N axes of x2 in order. The sizes of the corresponding axes must match. - Or, a list of axes to be summed over, first sequence applying to x1, second to x2. Both sequences must be of the same length.

Returns

The tensor dot product of the inputs.

[source]

### tile function

keras.ops.tile(x, repeats)

Repeat x the number of times given by repeats.

If repeats has length d, the result will have dimension of max(d, x.ndim).

If x.ndim < d, x is promoted to be d-dimensional by prepending new axes.

If x.ndim > d, repeats is promoted to x.ndim by prepending 1's to it.

Arguments

• x: Input tensor.
• repeats: The number of repetitions of x along each axis.

Returns

The tiled output tensor.

[source]

### trace function

keras.ops.trace(x, offset=0, axis1=0, axis2=1)

Return the sum along diagonals of the tensor.

If x is 2-D, the sum along its diagonal with the given offset is returned, i.e., the sum of elements x[i, i+offset] for all i.

If a has more than two dimensions, then the axes specified by axis1 and axis2 are used to determine the 2-D sub-arrays whose traces are returned.

The shape of the resulting tensor is the same as that of x with axis1 and axis2 removed.

Arguments

• x: Input tensor.
• offset: Offset of the diagonal from the main diagonal. Can be both positive and negative. Defaults to 0.
• axis1: Axis to be used as the first axis of the 2-D sub-arrays. Defaults to 0.(first axis).
• axis2: Axis to be used as the second axis of the 2-D sub-arrays. Defaults to 1 (second axis).

Returns

If x is 2-D, the sum of the diagonal is returned. If x has larger dimensions, then a tensor of sums along diagonals is returned.

[source]

### transpose function

keras.ops.transpose(x, axes=None)

Returns a tensor with axes transposed.

Arguments

• x: Input tensor.
• axes: Sequence of integers. Permutation of the dimensions of x. By default, the order of the axes are reversed.

Returns

x with its axes permuted.

[source]

### tri function

keras.ops.tri(N, M=None, k=0, dtype=None)

Return a tensor with ones at and below a diagonal and zeros elsewhere.

Arguments

• N: Number of rows in the tensor.
• M: Number of columns in the tensor.
• k: The sub-diagonal at and below which the array is filled. k = 0 is the main diagonal, while k < 0 is below it, and k > 0 is above. The default is 0.
• dtype: Data type of the returned tensor. The default is "float32".

Returns

Tensor with its lower triangle filled with ones and zeros elsewhere. T[i, j] == 1 for j <= i + k, 0 otherwise.

[source]

### tril function

keras.ops.tril(x, k=0)

Return lower triangle of a tensor.

For tensors with ndim exceeding 2, tril will apply to the final two axes.

Arguments

• x: Input tensor.
• k: Diagonal above which to zero elements. Defaults to 0. the main diagonal. k < 0 is below it, and k > 0 is above it.

Returns

Lower triangle of x, of same shape and data type as x.

[source]

### triu function

keras.ops.triu(x, k=0)

Return upper triangle of a tensor.

For tensors with ndim exceeding 2, triu will apply to the final two axes.

Arguments

• x: Input tensor.
• k: Diagonal below which to zero elements. Defaults to 0. the main diagonal. k < 0 is below it, and k > 0 is above it.

Returns

Upper triangle of x, of same shape and data type as x.

[source]

### true_divide function

keras.ops.true_divide(x1, x2)

Alias for keras.ops.divide.

[source]

### var function

keras.ops.var(x, axis=None, keepdims=False)

Compute the variance along the specified axes.

Arguments

• x: Input tensor.
• axis: Axis or axes along which the variance is computed. The default is to compute the variance of the flattened tensor.
• keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

Output tensor containing the variance.

[source]

### vdot function

keras.ops.vdot(x1, x2)

Return the dot product of two vectors.

If the first argument is complex, the complex conjugate of the first argument is used for the calculation of the dot product.

Multidimensional tensors are flattened before the dot product is taken.

Arguments

• x1: First input tensor. If complex, its complex conjugate is taken before calculation of the dot product.
• x2: Second input tensor.

Returns

Output tensor.

[source]

### vstack function

keras.ops.vstack(xs)

Stack tensors in sequence vertically (row wise).

Arguments

• xs: Sequence of tensors.

Returns

Tensor formed by stacking the given tensors.

[source]

### where function

keras.ops.where(condition, x1=None, x2=None)

Return elements chosen from x1 or x2 depending on condition.

Arguments

• condition: Where True, yield x1, otherwise yield x2.
• x1: Values from which to choose when condition is True.
• x2: Values from which to choose when condition is False.

Returns

A tensor with elements from x1 where condition is True, and elements from x2 where condition is False.

[source]

### zeros function

keras.ops.zeros(shape, dtype=None)

Return a new tensor of given shape and type, filled with zeros.

Arguments

• shape: Shape of the new tensor.
• dtype: Desired data type of the tensor.

Returns

Tensor of zeros with the given shape and dtype.

[source]

### zeros_like function

keras.ops.zeros_like(x, dtype=None)

Return a tensor of zeros with the same shape and type as x.

Arguments

• x: Input tensor.
• dtype: Overrides the data type of the result.

Returns

A tensor of zeros with the same shape and type as x.