366 lines
9.5 KiB
Python
366 lines
9.5 KiB
Python
|
from __future__ import division, absolute_import, print_function
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from numpy.matrixlib.defmatrix import matrix, asmatrix
|
||
|
|
# need * as we're copying the numpy namespace (FIXME: this makes little sense)
|
||
|
|
from numpy import *
|
||
|
|
|
||
|
|
__version__ = np.__version__
|
||
|
|
|
||
|
|
__all__ = np.__all__[:] # copy numpy namespace
|
||
|
|
__all__ += ['rand', 'randn', 'repmat']
|
||
|
|
|
||
|
|
def empty(shape, dtype=None, order='C'):
|
||
|
|
"""Return a new matrix of given shape and type, without initializing entries.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
shape : int or tuple of int
|
||
|
|
Shape of the empty matrix.
|
||
|
|
dtype : data-type, optional
|
||
|
|
Desired output data-type.
|
||
|
|
order : {'C', 'F'}, optional
|
||
|
|
Whether to store multi-dimensional data in row-major
|
||
|
|
(C-style) or column-major (Fortran-style) order in
|
||
|
|
memory.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
empty_like, zeros
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
`empty`, unlike `zeros`, does not set the matrix values to zero,
|
||
|
|
and may therefore be marginally faster. On the other hand, it requires
|
||
|
|
the user to manually set all the values in the array, and should be
|
||
|
|
used with caution.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> np.matlib.empty((2, 2)) # filled with random data
|
||
|
|
matrix([[ 6.76425276e-320, 9.79033856e-307], # random
|
||
|
|
[ 7.39337286e-309, 3.22135945e-309]])
|
||
|
|
>>> np.matlib.empty((2, 2), dtype=int)
|
||
|
|
matrix([[ 6600475, 0], # random
|
||
|
|
[ 6586976, 22740995]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
return ndarray.__new__(matrix, shape, dtype, order=order)
|
||
|
|
|
||
|
|
def ones(shape, dtype=None, order='C'):
|
||
|
|
"""
|
||
|
|
Matrix of ones.
|
||
|
|
|
||
|
|
Return a matrix of given shape and type, filled with ones.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
shape : {sequence of ints, int}
|
||
|
|
Shape of the matrix
|
||
|
|
dtype : data-type, optional
|
||
|
|
The desired data-type for the matrix, default is np.float64.
|
||
|
|
order : {'C', 'F'}, optional
|
||
|
|
Whether to store matrix in C- or Fortran-contiguous order,
|
||
|
|
default is 'C'.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : matrix
|
||
|
|
Matrix of ones of given shape, dtype, and order.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
ones : Array of ones.
|
||
|
|
matlib.zeros : Zero matrix.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
|
||
|
|
`out` becomes a single row matrix of shape ``(1,N)``.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> np.matlib.ones((2,3))
|
||
|
|
matrix([[1., 1., 1.],
|
||
|
|
[1., 1., 1.]])
|
||
|
|
|
||
|
|
>>> np.matlib.ones(2)
|
||
|
|
matrix([[1., 1.]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
a = ndarray.__new__(matrix, shape, dtype, order=order)
|
||
|
|
a.fill(1)
|
||
|
|
return a
|
||
|
|
|
||
|
|
def zeros(shape, dtype=None, order='C'):
|
||
|
|
"""
|
||
|
|
Return a matrix of given shape and type, filled with zeros.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
shape : int or sequence of ints
|
||
|
|
Shape of the matrix
|
||
|
|
dtype : data-type, optional
|
||
|
|
The desired data-type for the matrix, default is float.
|
||
|
|
order : {'C', 'F'}, optional
|
||
|
|
Whether to store the result in C- or Fortran-contiguous order,
|
||
|
|
default is 'C'.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : matrix
|
||
|
|
Zero matrix of given shape, dtype, and order.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
numpy.zeros : Equivalent array function.
|
||
|
|
matlib.ones : Return a matrix of ones.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
|
||
|
|
`out` becomes a single row matrix of shape ``(1,N)``.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> np.matlib.zeros((2, 3))
|
||
|
|
matrix([[0., 0., 0.],
|
||
|
|
[0., 0., 0.]])
|
||
|
|
|
||
|
|
>>> np.matlib.zeros(2)
|
||
|
|
matrix([[0., 0.]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
a = ndarray.__new__(matrix, shape, dtype, order=order)
|
||
|
|
a.fill(0)
|
||
|
|
return a
|
||
|
|
|
||
|
|
def identity(n,dtype=None):
|
||
|
|
"""
|
||
|
|
Returns the square identity matrix of given size.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
n : int
|
||
|
|
Size of the returned identity matrix.
|
||
|
|
dtype : data-type, optional
|
||
|
|
Data-type of the output. Defaults to ``float``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : matrix
|
||
|
|
`n` x `n` matrix with its main diagonal set to one,
|
||
|
|
and all other elements zero.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
numpy.identity : Equivalent array function.
|
||
|
|
matlib.eye : More general matrix identity function.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> np.matlib.identity(3, dtype=int)
|
||
|
|
matrix([[1, 0, 0],
|
||
|
|
[0, 1, 0],
|
||
|
|
[0, 0, 1]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
a = array([1]+n*[0], dtype=dtype)
|
||
|
|
b = empty((n, n), dtype=dtype)
|
||
|
|
b.flat = a
|
||
|
|
return b
|
||
|
|
|
||
|
|
def eye(n,M=None, k=0, dtype=float, order='C'):
|
||
|
|
"""
|
||
|
|
Return a matrix with ones on the diagonal and zeros elsewhere.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
n : int
|
||
|
|
Number of rows in the output.
|
||
|
|
M : int, optional
|
||
|
|
Number of columns in the output, defaults to `n`.
|
||
|
|
k : int, optional
|
||
|
|
Index of the diagonal: 0 refers to the main diagonal,
|
||
|
|
a positive value refers to an upper diagonal,
|
||
|
|
and a negative value to a lower diagonal.
|
||
|
|
dtype : dtype, optional
|
||
|
|
Data-type of the returned matrix.
|
||
|
|
order : {'C', 'F'}, optional
|
||
|
|
Whether the output should be stored in row-major (C-style) or
|
||
|
|
column-major (Fortran-style) order in memory.
|
||
|
|
|
||
|
|
.. versionadded:: 1.14.0
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
I : matrix
|
||
|
|
A `n` x `M` matrix where all elements are equal to zero,
|
||
|
|
except for the `k`-th diagonal, whose values are equal to one.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
numpy.eye : Equivalent array function.
|
||
|
|
identity : Square identity matrix.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> np.matlib.eye(3, k=1, dtype=float)
|
||
|
|
matrix([[0., 1., 0.],
|
||
|
|
[0., 0., 1.],
|
||
|
|
[0., 0., 0.]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
return asmatrix(np.eye(n, M=M, k=k, dtype=dtype, order=order))
|
||
|
|
|
||
|
|
def rand(*args):
|
||
|
|
"""
|
||
|
|
Return a matrix of random values with given shape.
|
||
|
|
|
||
|
|
Create a matrix of the given shape and propagate it with
|
||
|
|
random samples from a uniform distribution over ``[0, 1)``.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
\\*args : Arguments
|
||
|
|
Shape of the output.
|
||
|
|
If given as N integers, each integer specifies the size of one
|
||
|
|
dimension.
|
||
|
|
If given as a tuple, this tuple gives the complete shape.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : ndarray
|
||
|
|
The matrix of random values with shape given by `\\*args`.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
randn, numpy.random.RandomState.rand
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> np.random.seed(123)
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> np.matlib.rand(2, 3)
|
||
|
|
matrix([[0.69646919, 0.28613933, 0.22685145],
|
||
|
|
[0.55131477, 0.71946897, 0.42310646]])
|
||
|
|
>>> np.matlib.rand((2, 3))
|
||
|
|
matrix([[0.9807642 , 0.68482974, 0.4809319 ],
|
||
|
|
[0.39211752, 0.34317802, 0.72904971]])
|
||
|
|
|
||
|
|
If the first argument is a tuple, other arguments are ignored:
|
||
|
|
|
||
|
|
>>> np.matlib.rand((2, 3), 4)
|
||
|
|
matrix([[0.43857224, 0.0596779 , 0.39804426],
|
||
|
|
[0.73799541, 0.18249173, 0.17545176]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
if isinstance(args[0], tuple):
|
||
|
|
args = args[0]
|
||
|
|
return asmatrix(np.random.rand(*args))
|
||
|
|
|
||
|
|
def randn(*args):
|
||
|
|
"""
|
||
|
|
Return a random matrix with data from the "standard normal" distribution.
|
||
|
|
|
||
|
|
`randn` generates a matrix filled with random floats sampled from a
|
||
|
|
univariate "normal" (Gaussian) distribution of mean 0 and variance 1.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
\\*args : Arguments
|
||
|
|
Shape of the output.
|
||
|
|
If given as N integers, each integer specifies the size of one
|
||
|
|
dimension. If given as a tuple, this tuple gives the complete shape.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
Z : matrix of floats
|
||
|
|
A matrix of floating-point samples drawn from the standard normal
|
||
|
|
distribution.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
rand, numpy.random.RandomState.randn
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
For random samples from :math:`N(\\mu, \\sigma^2)`, use:
|
||
|
|
|
||
|
|
``sigma * np.matlib.randn(...) + mu``
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> np.random.seed(123)
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> np.matlib.randn(1)
|
||
|
|
matrix([[-1.0856306]])
|
||
|
|
>>> np.matlib.randn(1, 2, 3)
|
||
|
|
matrix([[ 0.99734545, 0.2829785 , -1.50629471],
|
||
|
|
[-0.57860025, 1.65143654, -2.42667924]])
|
||
|
|
|
||
|
|
Two-by-four matrix of samples from :math:`N(3, 6.25)`:
|
||
|
|
|
||
|
|
>>> 2.5 * np.matlib.randn((2, 4)) + 3
|
||
|
|
matrix([[1.92771843, 6.16484065, 0.83314899, 1.30278462],
|
||
|
|
[2.76322758, 6.72847407, 1.40274501, 1.8900451 ]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
if isinstance(args[0], tuple):
|
||
|
|
args = args[0]
|
||
|
|
return asmatrix(np.random.randn(*args))
|
||
|
|
|
||
|
|
def repmat(a, m, n):
|
||
|
|
"""
|
||
|
|
Repeat a 0-D to 2-D array or matrix MxN times.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
a : array_like
|
||
|
|
The array or matrix to be repeated.
|
||
|
|
m, n : int
|
||
|
|
The number of times `a` is repeated along the first and second axes.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : ndarray
|
||
|
|
The result of repeating `a`.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy.matlib
|
||
|
|
>>> a0 = np.array(1)
|
||
|
|
>>> np.matlib.repmat(a0, 2, 3)
|
||
|
|
array([[1, 1, 1],
|
||
|
|
[1, 1, 1]])
|
||
|
|
|
||
|
|
>>> a1 = np.arange(4)
|
||
|
|
>>> np.matlib.repmat(a1, 2, 2)
|
||
|
|
array([[0, 1, 2, 3, 0, 1, 2, 3],
|
||
|
|
[0, 1, 2, 3, 0, 1, 2, 3]])
|
||
|
|
|
||
|
|
>>> a2 = np.asmatrix(np.arange(6).reshape(2, 3))
|
||
|
|
>>> np.matlib.repmat(a2, 2, 3)
|
||
|
|
matrix([[0, 1, 2, 0, 1, 2, 0, 1, 2],
|
||
|
|
[3, 4, 5, 3, 4, 5, 3, 4, 5],
|
||
|
|
[0, 1, 2, 0, 1, 2, 0, 1, 2],
|
||
|
|
[3, 4, 5, 3, 4, 5, 3, 4, 5]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
a = asanyarray(a)
|
||
|
|
ndim = a.ndim
|
||
|
|
if ndim == 0:
|
||
|
|
origrows, origcols = (1, 1)
|
||
|
|
elif ndim == 1:
|
||
|
|
origrows, origcols = (1, a.shape[0])
|
||
|
|
else:
|
||
|
|
origrows, origcols = a.shape
|
||
|
|
rows = origrows * m
|
||
|
|
cols = origcols * n
|
||
|
|
c = a.reshape(1, a.size).repeat(m, 0).reshape(rows, origcols).repeat(n, 0)
|
||
|
|
return c.reshape(rows, cols)
|