Module: tfp.experimental.fastgp.fast_log_det

Functions for quickly computing approximate log det of a big PSD matrix.

It's recommended to use fast_log_det in float64 mode only.

Modules

mbcg module: Modified Batched Conjugate Gradients (mBCG) for JAX.

partial_lanczos module: Run Lanczos for m iterations to get a good preconditioner.

preconditioners module: Library of popular matrix preconditioners.

sample_halton_sequence_lib module: Quasi Monte Carlo support: Halton sequence.

Classes

class Array: Array base class for JAX

class ProbeVectorType: Enum where members are also (and must be) ints

Functions

batch_log00(...): Return the (0, 0)-th entries of the log of the tridiagonal matrices.

get_log_det_algorithm(...)

log00(...): Return the (0, 0)-th entry of the log of the tridiagonal matrix.

log_det_jvp(...): Jacobian-Vector product for log_det.

log_det_taylor_series_with_hutchinson(...): Return an approximation of log det M.

make_probe_vectors(...): Return num_probe_vectors n-dim random vectors with mean zero.

r1(...): Approximate log det using a 2nd order rational function.

r2(...): Approximate log det using a 2nd order rational function.

r3(...): Approximate log det using a 3rd order rational function.

r4(...): Approximate log det using a 4th order rational function.

r5(...): Approximate log det using a 5th order rational function.

r6(...): Approximate log det using a 6th order rational function.

stochastic_lanczos_quadrature_log_det(...): Fast log det using the alg. from https://arxiv.org/pdf/1809.11165.pdf .

LOG_DET_REGISTRY 

{
 'r1': <function r1>,
 'r2': <function r2>,
 'r3': <function r3>,
 'r4': <function r4>,
 'r5': <function r5>,
 'r6': <function r6>,
 'slq': <function stochastic_lanczos_quadrature_log_det>
}

R1_COEFFICIENTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R1_SHIFTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R2_COEFFICIENTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R2_SHIFTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R3_COEFFICIENTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R3_SHIFTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R4_COEFFICIENTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R4_SHIFTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R5_COEFFICIENTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R5_SHIFTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R6_COEFFICIENTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])

R6_SHIFTS Instance of numpy.ndarray

ndarray(shape, dtype=None, buffer=None, offset=0, strides=None, order=None)

ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)

An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)

Arrays should be constructed using array, zeros or empty (refer to the See Also section below). The parameters given here refer to a low-level method (ndarray(...)) for instantiating an array.

For more information, refer to the numpy module and examine the methods and attributes of an array.

Parameters

(for the new method; see Notes below)

shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. Default is numpy.float64. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order.

Attributes

T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., x.flat = 3 (See ndarray.flat for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., itemsize * size. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous (3, 4) array of type int16 in C-order has strides (8, 2). This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (2 * 4). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its base (unless that array is also a view). The base array is where the array data is actually stored.

See Also

array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. numpy.typing.NDArray : An ndarray alias :term:generic <generic type> w.r.t. its dtype.type <numpy.dtype.type>.

Notes

There are two modes of creating an array using __new__:

  1. If buffer is None, then only shape, dtype, and order are used.

  2. If buffer is an object exposing the buffer interface, then all keywords are interpreted.

No __init__ method is needed because the array is fully initialized after the __new__ method.

Examples

These examples illustrate the low-level ndarray constructor. Refer to the See Also section above for easier ways of constructing an ndarray.

First mode, buffer is None:

import numpy as np np.ndarray(shape=(2,2), dtype=float, order='F') array([[0.0e+000, 0.0e+000], # random [ nan, 2.5e-323]])

Second mode:

np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3])