# Elementwise#

ivy.allclose(a, b, /, *, rtol=1e-05, atol=1e-08, equal_nan=False, out=None)[source]#

Return a True if the two arrays are element-wise equal within given tolerance; otherwise False.

The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(x2)) and the absolute difference atol are added together to compare against the absolute difference between x1 and x2. The default atol is not appropriate for comparing numbers that are much smaller than one

Parameters:
• x1 – First input array.

• x2 – Second input array.

• rtol (float, default: 1e-05) – The relative tolerance parameter.

• atol (float, default: 1e-08) – The absolute tolerance parameter.

• equal_nan (bool, default: False) – Whether to compare NaN’s as equal. If True, NaN’s in x1 will be considered equal to NaN’s in x2 in the output array.

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

bool

Returns:

ret – Returns True if the two arrays are equal within the given tolerance; False otherwise.

Examples

>>> x1 = ivy.array([1e10, 1e-7])
>>> x2 = ivy.array([1.00001e10, 1e-8])
>>> y = ivy.allclose(x1, x2)
>>> print(y)
ivy.array(False)

>>> x1 = ivy.array([1.0, ivy.nan])
>>> x2 = ivy.array([1.0, ivy.nan])
>>> y = ivy.allclose(x1, x2, equal_nan=True)
>>> print(y)
ivy.array(True)

>>> x1 = ivy.array([1e-10, 1e-10])
>>> x2 = ivy.array([1.00001e-10, 1e-10])
>>> y = ivy.allclose(x1, x2, rtol=0.005, atol=0.0)
>>> print(y)
ivy.array(True)

ivy.amax(x, /, *, axis=None, keepdims=False, out=None)[source]#

Calculate the maximum value of the input array x.

Note

amax is an alias of max and both function behaves similarly in every backend except PyTorch and PaddlePaddle (see PyTorch’s amax function documentation<https://pytorch.org/docs/stable/generated/torch.amax.html>_) (see PaddlePaddle’s amax function documentation<https://www.paddlepaddle.org.cn/ documentation/docs/zh/api/paddle/amax_cn.html>_)

Note

When the number of elements over which to compute the maximum value is zero, the maximum value is implementation-defined. Specification-compliant libraries may choose to raise an error, return a sentinel value (e.g., if x is a floating-point input array, return NaN), or return the minimum possible value for the input array x data type (e.g., if x is a floating-point array, return -infinity).

Special Cases

For floating-point operands,

• If x_i is NaN, the maximum value is NaN (i.e., NaN values propagate).

Parameters:
• x (Union[Array, NativeArray]) – input array. Should have a real-valued data type.

• axis (Optional[Union[int, Sequence[int]]], default: None) – axis or axes along which maximum values must be computed. By default, the maximum value must be computed over the entire array. If a tuple of integers, maximum values must be computed over multiple axes. Default: None.

• keepdims (bool, default: False) – optional boolean, if True, the reduced axes (dimensions) must be included in the result as singleton dimensions, and, accordingly, the result must be compatible with the input array (see broadcasting<https://data-apis.org/ array-api/latest/API_specification/broadcasting.html#broadcasting>_). Otherwise, if False, the reduced axes (dimensions) must not be included in the result. Default: False.

• out (Optional[Array], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – if the maximum value was computed over the entire array, a zero-dimensional array containing the maximum value; otherwise, a non-zero-dimensional array containing the maximum values. The returned array must have the same data type as x.

This function conforms to the Array API Standard. This docstring is an extension of the docstring in the standard.

Both the description and the type hints above assumes an array input for simplicity, but this function is nestable, and therefore also accepts ivy.Container instances in place of any of the arguments.

Examples

With ivy.Array input:

>>> x = ivy.array([1, 2, 3])
>>> y = ivy.amax(x)
>>> print(y)
ivy.array(3)

>>> x = ivy.array([0, 1, 2])
>>> z = ivy.array([0, 0, 0])
>>> y = ivy.amax(x, out=z)
>>> print(z)
ivy.array(2)

>>> x = ivy.array([[0, 1, 2], [4, 6, 10]])
>>> y = ivy.amax(x, axis=0, keepdims=True)
>>> print(y)
ivy.array([[4, 6, 10]])

>>> x = ivy.native_array([[0, 1, 2], [4, 6, 10]])
>>> y = ivy.amax(x)
>>> print(y)
ivy.array(10)


With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([1, 2, 3]), b=ivy.array([2, 3, 4]))
>>> y = ivy.amax(x)
>>> print(y)
{
a: ivy.array(3),
b: ivy.array(4)
}

ivy.amin(x, /, *, axis=None, keepdims=False, out=None)[source]#

Calculate the minimum value of the input array x.

Note

amin is an alias of min and both function behaves similarly in every backend except PyTorch and PaddlePaddle (see PyTorch’s amin function documentation<https://pytorch.org/docs/stable/generated/torch.amin.html>_) (see PaddlePaddle’s amin function documentation<https://www.paddlepaddle.org.cn/ documentation/docs/zh/api/paddle/amin_cn.html>_)

Note

When the number of elements over which to compute the minimum value is zero, the minimum value is implementation-defined. Specification-compliant libraries may choose to raise an error, return a sentinel value (e.g., if x is a floating-point input array, return NaN), or return the maximum possible value for the input array x data type (e.g., if x is a floating-point array, return +infinity).

Special Cases

For floating-point operands,

• If x_i is NaN, the minimum value is NaN (i.e., NaN values propagate).

Parameters:
• x (Union[Array, NativeArray]) – input array. Should have a real-valued data type.

• axis (Optional[Union[int, Sequence[int]]], default: None) – axis or axes along which minimum values must be computed. By default, the minimum value must be computed over the entire array. If a tuple of integers, minimum values must be computed over multiple axes. Default: None.

• keepdims (bool, default: False) – optional boolean, if True, the reduced axes (dimensions) must be included in the result as singleton dimensions, and, accordingly, the result must be compatible with the input array (see broadcasting<https://data-apis.org/ array-api/latest/API_specification/broadcasting.html#broadcasting>_). Otherwise, if False, the reduced axes (dimensions) must not be included in the result. Default: False.

• out (Optional[Array], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – if the minimum value was computed over the entire array, a zero-dimensional array containing the minimum value; otherwise, a non-zero-dimensional array containing the minimum values. The returned array must have the same data type as x.

This function conforms to the Array API Standard. This docstring is an extension of the docstring in the standard.

Both the description and the type hints above assumes an array input for simplicity, but this function is nestable, and therefore also accepts ivy.Container instances in place of any of the arguments.

Examples

With ivy.Array input:

>>> x = ivy.array([1, 2, 3])
>>> y = ivy.amin(x)
>>> print(y)
ivy.array(1)

>>> x = ivy.array([0, 1, 2])
>>> z = ivy.array([0, 0, 0])
>>> y = ivy.amin(x, out=z)
>>> print(z)
ivy.array(0)

>>> x = ivy.array([[0, 1, 2], [4, 6, 10]])
>>> y = ivy.amin(x, axis=0, keepdims=True)
>>> print(y)
ivy.array([[0, 1, 2]])

>>> x = ivy.native_array([[0, 1, 2], [4, 6, 10]])
>>> y = ivy.amin(x)
>>> print(y)
ivy.array(0)


With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([1, 2, 3]), b=ivy.array([2, 3, 4]))
>>> y = ivy.amin(x)
>>> print(y)
{
a: ivy.array(1),
b: ivy.array(2)
}

ivy.binarizer(x, /, *, threshold=0, out=None)[source]#

Map the values of the input tensor to either 0 or 1, element-wise, based on the outcome of a comparison against a threshold value.

Parameters:
• x (Union[Array, NativeArray]) – Data to be binarized

• threshold (float, default: 0) – Values greater than this are mapped to 1, others to 0.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – Binarized output data

ivy.conj(x, /, *, out=None)[source]#

Return the complex conjugate for each element x_i of the input array x.

For complex number of the form

$a + bj$

the complex conjugate is defined as

$a - bj$

Hence, the returned conjugates must be computed by negating the imaginary component of each element x_i

This method conforms to the Array API Standard. This docstring is an extension of the docstring in the standard.

Both the description and the type hints above assumes an array input for simplicity, but this function is nestable, and therefore also accepts ivy.Container instances in place of any of the arguments.

Parameters:
• x (Union[Array, NativeArray]) – input array.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

• ret – an array of the same dtype as the input array with the complex conjugates of the complex values present in the input array. If x is a scalar then a scalar will be returned.

• The descriptions above assume an array input for simplicity, but

• the method also accepts ivy.Container instances

• in place of (class:ivy.Array or ivy.NativeArray)

• instances, as shown in the type hints and also the examples below.

Examples

With ivy.Array inputs: >>> x = ivy.array([4.2-0j, 3j, 7+5j]) >>> z = ivy.conj(x) >>> print(z) ivy.array([4.2-0.j, 0. -3.j, 7. -5.j])

With ivy.Container input: >>> x = ivy.Container(a=ivy.array([-6.7-7j, 0.314+0.355j, 1.23]), … b=ivy.array([5j, 5.32-6.55j, 3.001])) >>> z = ivy.conj(x) >>> print(z) {

a: ivy.array([-6.7+7.j, 0.314-0.355j, 1.23-0.j]), b: ivy.array([0.-5.j, 5.32+6.55j, 3.001-0.j])

}

ivy.copysign(x1, x2, /, *, out=None)[source]#

Change the signs of x1 to match x2 x1 and x2 must be broadcastable to a common shape.

Parameters:
• x1 (Union[Array, NativeArray, Number]) – Array or scalar to change the sign of

• x2 (Union[Array, NativeArray, Number]) – Array or scalar from which the new signs are applied Unsigned zeroes are considered positive.

• out (Optional[Union[Array, NativeArray]], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – x1 with the signs of x2. This is a scalar if both x1 and x2 are scalars.

Examples

>>> x1 = ivy.array([-1, 0, 23, 2])
>>> x2 = ivy.array([1, -1, -10, 44])
>>> ivy.copysign(x1, x2)
ivy.array([  1.,  -0., -23.,   2.])
>>> ivy.copysign(x1, -1)
ivy.array([ -1.,  -0., -23.,  -2.])
>>> ivy.copysign(-10, 1)
ivy.array(10.)

ivy.count_nonzero(a, /, *, axis=None, keepdims=False, dtype=None, out=None)[source]#

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

Parameters:
• a (Union[Array, NativeArray]) – array for which to count non-zeros.

• axis (Optional[Union[int, Tuple[int, ...]]], default: None) – 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 the input array.

• keepdims (bool, default: False) – optional, 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.

• dtype (Optional[Union[Dtype, NativeDtype]], default: None) – optional output dtype. Default is of type integer.

• out (Optional[Union[Array, NativeArray]], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – 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.

Examples

>>> a = ivy.array([[0, 1, 2, 3],[4, 5, 6, 7]])
>>> ivy.count_nonzero(a)
ivy.array(7)
>>> a = ivy.array([[0, 1, 2, 3],[4, 5, 6, 7]])
>>> ivy.count_nonzero(a, axis=0)
ivy.array([1, 2, 2, 2])
>>> a = ivy.array([[[0,1],[2,3]],[[4,5],[6,7]]])
>>> ivy.count_nonzero(a, axis=(0,1), keepdims=True)
ivy.array([[[3, 4]]])

ivy.diff(x, /, *, n=1, axis=-1, prepend=None, append=None, out=None)[source]#

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

Parameters:
• x (Union[Array, NativeArray, list, tuple]) – Array-like input.

• n (int, default: 1) – The number of times values are differenced. If zero, the input is returned as-is.

• axis (int, default: -1) – The axis along which the difference is taken, default is the last axis.

• prepend (Optional[Union[Array, NativeArray, int, list, tuple]], default: None) – Values to prepend/append to x along given 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 x except along axis.

• append (Optional[Union[Array, NativeArray, int, list, tuple]], default: None) – Values to prepend/append to x along given 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 x except along axis.

• out (Optional[Array], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

• ret – Returns the n-th discrete difference along the given axis.

• Both the description and the type hints above assumes an array input for simplicity,

• but this function is nestable, and therefore also accepts ivy.Container

• instances in place of any of the arguments.

Examples

>>> x = ivy.array([1, 2, 4, 7, 0])
>>> ivy.diff(x)
ivy.array([ 1,  2,  3, -7])

ivy.digamma(x, /, *, out=None)[source]#

Compute the logarithmic derivative of the gamma function at x.

Note

The Ivy version only accepts real-valued inputs.

Parameters:
• x (Union[Array, NativeArray]) – Input array.

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

Array

Returns:

ret – Array with values computed from digamma function from input arrays’ values, element-wise.

Examples

>>> x = ivy.array([.9, 3, 3.2])
>>> y = ivy.digamma(x)
ivy.array([-0.7549271   0.92278427  0.9988394])

ivy.erfc(x, /, *, out=None)[source]#

Complementary error function, 1 - erf(x)

Parameters:
• x (Union[Array, NativeArray]) – Input array of real or complex valued argument.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – Values of the complementary error function.

Examples

>>> x = ivy.array([2, -1., 0])
>>> ivy.erfc(x)
ivy.array([0.00467773, 1.84270084, 1.        ])

ivy.fix(x, /, *, out=None)[source]#

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

Parameters:
• x (Union[Array, NativeArray, float, int, list, tuple]) – Array input.

• out (Optional[Array], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – Array of floats with elements corresponding to input elements rounded to nearest integer towards zero, element-wise.

Examples

>>> x = ivy.array([2.1, 2.9, -2.1])
>>> ivy.fix(x)
ivy.array([ 2.,  2., -2.])

ivy.float_power(x1, x2, /, *, out=None)[source]#

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.

Parameters:
• x1 (Union[Array, float, list, tuple]) – Array-like with elements to raise in power.

• x2 (Union[Array, float, list, tuple]) – Array-like of exponents. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output).

• out (Optional[Array], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – The bases in x1 raised to the exponents in x2. This is a scalar if both x1 and x2 are scalars

Examples

>>> x1 = ivy.array([1, 2, 3, 4, 5])
>>> ivy.float_power(x1, 3)
ivy.array([1.,    8.,   27.,   64.,  125.])
>>> x1 = ivy.array([1, 2, 3, 4, 5])
>>> x2 = ivy.array([2, 3, 3, 2, 1])
>>> ivy.float_power(x1, x2)
ivy.array([1.,   8.,  27.,  16.,   5.])

ivy.fmax(x1, x2, /, *, out=None)[source]#

Compute the element-wise maximums of two arrays. Differs from ivy.maximum in the case where one of the elements is NaN. ivy.maximum returns the NaN element while ivy.fmax returns the non-NaN element.

Parameters:
• x1 (Union[Array, NativeArray]) – First input array.

• x2 (Union[Array, NativeArray]) – Second input array.

• out (Optional[Union[Array, NativeArray]], default: None) – optional output array, for writing the result to.

Return type:

Union[Array, NativeArray]

Returns:

ret – Array with element-wise maximums.

Examples

>>> x1 = ivy.array([2, 3, 4])
>>> x2 = ivy.array([1, 5, 2])
>>> ivy.fmax(x1, x2)
ivy.array([ 2.,  5.,  4.])

>>> x1 = ivy.array([ivy.nan, 0, ivy.nan])
>>> x2 = ivy.array([0, ivy.nan, ivy.nan])
>>> ivy.fmax(x1, x2)
ivy.array([ 0.,  0.,  nan])

ivy.frexp(x, /, *, out=None)[source]#

Decompose the elements of x into mantissa and twos exponent.

Parameters:
• x (Union[Array, NativeArray]) – Input array.

• out (Optional[Tuple[Array, Array]], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Tuple[Array, Array]

Returns:

ret – A tuple of two arrays, the mantissa and the twos exponent.

Examples

>>> x = ivy.array([1, 2, 3])
>>> ivy.frexp(x)
(ivy.array([0.5, 0.5, 0.75]), ivy.array([1, 2, 2]))

ivy.gradient(x, /, *, spacing=1, edge_order=1, axis=None)[source]#

Calculate gradient of x with respect to (w.r.t.) spacing.

Parameters:
• x (Union[Array, NativeArray]) – input array representing outcomes of the function

• spacing (Union[int, list, tuple], default: 1) – if not given, indices of x will be used if scalar indices of x will be scaled with this value if array gradient of x w.r.t. spacing

• edge_order (int, default: 1) – 1 or 2, for ‘frist order’ and ‘second order’ estimation of boundary values of gradient respectively. Note: jax supports edge_order=1 case only

• axis (Optional[Union[int, list, tuple]], default: None) – dimension(s) to approximate the gradient over by default partial gradient is computed in every dimension

Return type:

Union[Array, List[Array]]

Returns:

ret – Array with values computed from gradient function from inputs

Examples

>>> spacing = (ivy.array([-2., -1., 1., 4.]),)
>>> x = ivy.array([4., 1., 1., 16.], )
ivy.array([-3., -2.,  2.,  5.])

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
[ivy.array([[ 9., 18., 36., 72.],
[ 9., 18., 36., 72.]]), ivy.array([[ 1. ,  1.5,  3. ,  4. ],
[10. , 15. , 30. , 40. ]])]

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
[ivy.array([[ 4.5,  9. , 18. , 36. ],
[ 4.5,  9. , 18. , 36. ]]), ivy.array([[ 0.5 ,  0.75,  1.5 ,  2.  ],
[ 5.  ,  7.5 , 15.  , 20.  ]])]

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
ivy.array([[ 1. ,  1.5,  3. ,  4. ],
[10. , 15. , 30. , 40. ]])

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
[ivy.array([[ 3.,  6., 12., 24.],
[ 3.,  6., 12., 24.]]), ivy.array([[ 0.5 ,  0.75,  1.5 ,  2.  ],
[ 5.  ,  7.5 , 15.  , 20.  ]])]

>>> spacing = (ivy.array([0, 2]), ivy.array([0, 3, 6, 9]))
[ivy.array([[ 4.5,  9. , 18. , 36. ],
[ 4.5,  9. , 18. , 36. ]]), ivy.array([[ 0.33333333, 0.5,  1., 1.33333333],
[ 3.33333333,  5.        , 10.        , 13.33333333]])]

ivy.hypot(x1, x2, /, *, out=None)[source]#

Return the hypotenuse given the two sides of a right angle triangle.

Parameters:
• x1 (Union[Array, NativeArray]) – The first input array

• x2 (Union[Array, NativeArray]) – The second input array

Return type:

Union[Array, NativeArray]

Returns:

ret – An array with the hypotenuse

Examples

>>> a = ivy.array([3.0, 4.0, 5.0])
>>> b = ivy.array([4.0, 5.0, 6.0])
>>> ivy.hypot(a, b)
ivy.array([5.0, 6.4031, 7.8102])

ivy.isclose(a, b, /, *, rtol=1e-05, atol=1e-08, equal_nan=False, out=None)[source]#

Return a boolean array where two arrays are element-wise equal within a tolerance.

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. The default atol is not appropriate for comparing numbers that are much smaller than one

Parameters:
• a (Union[Array, NativeArray]) – First input array.

• b (Union[Array, NativeArray]) – Second input array.

• rtol (float, default: 1e-05) – The relative tolerance parameter.

• atol (float, default: 1e-08) – The absolute tolerance parameter.

• equal_nan (bool, default: False) – 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.

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

Array

Returns:

ret – 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.

Examples

>>> ivy.isclose([1e10,1e-7], [1.00001e10,1e-8])
ivy.array([True, False])
>>> ivy.isclose([1.0, ivy.nan], [1.0, ivy.nan], equal_nan=True)
ivy.array([True, True])
>>> ivy.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0)
ivy.array([False, False])
>>> ivy.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], rtol=0.005, atol=0.0)
ivy.array([False, True])

ivy.ldexp(x1, x2, /, *, out=None)[source]#

Return x1 * (2**x2), element-wise.

Parameters:
• x1 (Union[Array, NativeArray]) – Input array.

• x2 (Union[Array, NativeArray]) – Input array.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – The next representable values of x1 in the direction of x2.

Examples

>>> x1 = ivy.array([1, 2, 3])
>>> x2 = ivy.array([0, 1, 2])
>>> ivy.ldexp(x1, x2)
ivy.array([1, 4, 12])

ivy.lerp(input, end, weight, /, *, out=None)[source]#

Return a linear interpolation of two arrays start (given by input) and end.

based on a scalar or array weight.

input + weight * (end - input), element-wise.

Parameters:
• input (Union[Array, NativeArray]) – array of starting points

• end (Union[Array, NativeArray]) – array of ending points

• weight (Union[Array, NativeArray, float]) – the weight for the interpolation formula. Scalar or Array.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – The result of input + ((end - input) * weight)

Examples

With ivy.Array inputs: >>> input = ivy.array([1, 2, 3]) >>> end = ivy.array([10, 10, 10]) >>> weight = 0.5 >>> y = ivy.lerp(input, end, weight) >>> print(y) ivy.array([5.5, 6. , 6.5])

>>> input = ivy.array([1.1, 1.2, 1.3])
>>> end = ivy.array()
>>> weight = ivy.array([0.4, 0.5, 0.6])
>>> y = ivy.zeros(3)
>>> ivy.lerp(input, end, weight, out=y)
>>> print(y)
ivy.array([ 8.65999985, 10.60000038, 12.52000046])

>>> input = ivy.array([[4, 5, 6],[4.1, 4.2, 4.3]])
>>> end = ivy.array()
>>> weight = ivy.array([0.5])
>>> ivy.lerp(input, end, weight, out=input)
>>> print(input)
ivy.array([[7.        , 7.5       , 8.        ],
[7.05000019, 7.0999999 , 7.1500001 ]])


With ivy.Container input: >>> input = ivy.Container(a=ivy.array([0., 1., 2.]), b=ivy.array([3., 4., 5.])) >>> end = ivy.array([10.]) >>> weight = 1.1 >>> y = input.lerp(end, weight) >>> print(y) {

a: ivy.array([11., 10.90000057, 10.80000019]), b: ivy.array([10.70000076, 10.60000038, 10.5])

}

>>> input = ivy.Container(a=ivy.array([10.1, 11.1]), b=ivy.array([10, 11]))
>>> end = ivy.Container(a=ivy.array(), b=ivy.array())
>>> weight = 0.5
>>> y = input.lerp(end, weight)
>>> print(y)
{
a: ivy.array([7.55000019, 8.05000019]),
b: ivy.array([5., 5.5])
}

ivy.lgamma(x, /, *, out=None)[source]#

Compute the natural logarithm of the absolute value of the gamma function on x.

Parameters:
• x (Union[Array, NativeArray]) – input array. Should have a floating-point data type.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – an array containing the natural log of Gamma(x) of each element in x. The returned array must have a floating-point data type determined by type-promotion.

Examples

>>> x = ivy.array([1.6, 2.6, 3.5])
>>> y = x.lgamma()
>>> print(y)
ivy.array([-0.11259177,  0.3574118 ,  1.20097363])

>>> x = ivy.array([1., 2., 3. ])
>>> y = x.lgamma()
>>> print(y)
ivy.array([0. ,0. ,0.69314718])

>>> x = ivy.array([4.5, -4, -5.6])
>>> x.lgamma(out = x)
>>> print(x)
ivy.array([2.45373654, inf, -4.6477685 ])

ivy.modf(x, /, *, out=None)[source]#

Decompose the elements of x into fractional and integral parts.

Parameters:
• x (Union[Array, NativeArray]) – Input array.

• out (Optional[Tuple[Array, Array]], default: None) – Optional output array for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Tuple[Array, Array]

Returns:

ret – A tuple of two arrays, the fractional and integral parts.

Examples

>>> x = ivy.array([1.5, 2.7, 3.9])
>>> ivy.modf(x)
(ivy.array([0.5, 0.7, 0.9]), ivy.array([1, 2, 3]))

ivy.nansum(x, /, *, axis=None, dtype=None, keepdims=False, out=None)[source]#

Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.

Parameters:
• x (Union[Array, NativeArray]) – Input array.

• axis (Optional[Union[int, Tuple[int, ...]]], default: None) – Axis or axes along which the sum is computed. The default is to compute the sum of the flattened array.

• dtype (Optional[Union[Dtype, NativeDtype]], default: None) – The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of input is used.

• keepdims (bool, default: False) – If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

Array

Returns:

ret – A new array holding the result is returned unless out is specified, in which it is returned.

Examples

>>> a = ivy.array([[ 2.1,  3.4,  ivy.nan], [ivy.nan, 2.4, 2.1]])
>>> ivy.nansum(a)
10.0
>>> ivy.nansum(a, axis=0)
ivy.array([2.1, 5.8, 2.1])
>>> ivy.nansum(a, axis=1)
ivy.array([5.5, 4.5])

ivy.nextafter(x1, x2, /, *, out=None)[source]#

Return the next floating-point value after x1 towards x2, element-wise.

Parameters:
• x1 (Union[Array, NativeArray]) – First input array.

• x2 (Union[Array, NativeArray]) – Second input array.

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

bool

Returns:

ret – The next representable values of x1 in the direction of x2.

Examples

>>> x1 = ivy.array([1.0e-50, 2.0e+50])
>>> x2 = ivy.array([2.0, 1.0])
>>> ivy.nextafter(x1, x2)
ivy.array([1.4013e-45., 3.4028e+38])

ivy.signbit(x, /, *, out=None)[source]#

Return element-wise True where signbit is set (less than zero).

Parameters:
• x (Union[Array, NativeArray, float, int, list, tuple]) – Array-like input.

• out (Optional[Array], default: None) – optional output array, for writing the result to.

Return type:

Array

Returns:

ret – Output array, or reference to out if that was supplied. This is a scalar if x is a scalar.

Examples

>>> x = ivy.array([1, -2, 3])
>>> ivy.signbit(x)
ivy.array([False, True, False])

ivy.sinc(x, /, *, out=None)[source]#

Calculate an implementation-dependent approximation of the principal value of the normalized sinc function, having domain (-infinity, +infinity) and codomain [-0.217234, 1], for each element x_i of the input array x. Each element x_i is assumed to be expressed in radians.

Special cases

For floating-point operands,

• If x_i is NaN, the result is NaN.

• If x_i is 0, the result is 1.

• If x_i is either +infinity or -infinity, the result is NaN.

Parameters:
• x (Union[Array, NativeArray]) – input array. Should have a floating-point data type.

• out (Optional[Array], default: None) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – an array containing the normalized sinc function of each element in x. The returned array must have a floating-point data type determined by type-promotion.

Examples

With ivy.Array input:

>>> x = ivy.array([0.5, 1.5, 2.5, 3.5])
>>> y = x.sinc()
>>> print(y)
ivy.array([0.637,-0.212,0.127,-0.0909])

>>> x = ivy.array([1.5, 0.5, -1.5])
>>> y = ivy.zeros(3)
>>> ivy.sinc(x, out=y)
>>> print(y)
ivy.array([-0.212,0.637,-0.212])


With ivy.NativeArray input:

>>> x = ivy.array([0.5, 1.5, 2.5, 3.5])
>>> y = ivy.sinc(x)
>>> print(y)
ivy.array([0.637,-0.212,0.127,-0.0909])


With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([0.5, 1.5, 2.5]),
...                   b=ivy.array([3.5, 4.5, 5.5]))
>>> y = x.sinc()
>>> print(y)
{
a: ivy.array([0.637,-0.212,0.127]),
b: ivy.array([-0.0909,0.0707,-0.0579])
}

ivy.sparsify_tensor(x, card, /, *, out=None)[source]#

Zeros out all elements in the tensor except card elements with maximum absolute values.

Parameters:
• x (Union[Array, NativeArray]) – Tensor to be sparsified

• card (int) – Desired number of non-zero elements in the tensor

• out (Optional[Array], default: None) – Optional output array for writing the result to.

Return type:

Array

Returns:

ivy.array of shape tensor.shape

Examples

>>> x = ivy.arange(100)
>>> x = ivy.reshape(x, (10, 10))
>>> sparsify_tensor(x, 10)
ivy.array([[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[90, 91, 92, 93, 94, 95, 96, 97, 98, 99]])

ivy.xlogy(x, y, /, *, out=None)[source]#

Compute x*log(y) element-wise so that the result is 0 if x = 0.

Parameters:
• x (Union[Array, NativeArray]) – First input array.

• y (Union[Array, NativeArray]) – Second input array.

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

bool

Returns:

ret – The next representable values of x1 in the direction of x2.

Examples

>>> x = ivy.zeros(3)
>>> y = ivy.array([-1.0, 0.0, 1.0])
>>> ivy.xlogy(x, y)
ivy.array([0.0, 0.0, 0.0])

>>> x = ivy.array([1.0, 2.0, 3.0])
>>> y = ivy.array([3.0, 2.0, 1.0])
>>> ivy.xlogy(x, y)
ivy.array([1.0986, 1.3863, 0.0000])

ivy.zeta(x, q, /, *, out=None)[source]#

Compute the Hurwitz zeta function elementwisely with each pair of floats in two arrays.

Parameters:
• x (Union[Array, NativeArray]) – First input array.

• q (Union[Array, NativeArray]) – Second input array, must have the same shape as the first input array

• out (Optional[Array], default: None) – Alternate output array in which to place the result. The default is None.

Return type:

bool

Returns:

ret – Array with values computed from zeta function from input arrays’ values.

Examples

>>> x = ivy.array([5.0, 3.0])
>>> q = ivy.array([2.0, 2.0])
>>> ivy.zeta(x, q)
ivy.array([0.0369, 0.2021])