matlib.py

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
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],
            [  7.39337286e-309,   3.22135945e-309]])        #random
    >>> np.matlib.empty((2, 2), dtype=int)
    matrix([[ 6600475,        0],
            [ 6586976, 22740995]])                          #random

    """
    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):
    """
    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.

    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, k, dtype))

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.rand

    Examples
    --------
    >>> import numpy.matlib
    >>> np.matlib.rand(2, 3)
    matrix([[ 0.68340382,  0.67926887,  0.83271405],
            [ 0.00793551,  0.20468222,  0.95253525]])       #random
    >>> np.matlib.rand((2, 3))
    matrix([[ 0.84682055,  0.73626594,  0.11308016],
            [ 0.85429008,  0.3294825 ,  0.89139555]])       #random

    If the first argument is a tuple, other arguments are ignored:

    >>> np.matlib.rand((2, 3), 4)
    matrix([[ 0.46898646,  0.15163588,  0.95188261],
            [ 0.59208621,  0.09561818,  0.00583606]])       #random

    """
    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, random.randn

    Notes
    -----
    For random samples from :math:`N(\\mu, \\sigma^2)`, use:

    ``sigma * np.matlib.randn(...) + mu``

    Examples
    --------
    >>> import numpy.matlib
    >>> np.matlib.randn(1)
    matrix([[-0.09542833]])                                 #random
    >>> np.matlib.randn(1, 2, 3)
    matrix([[ 0.16198284,  0.0194571 ,  0.18312985],
            [-0.7509172 ,  1.61055   ,  0.45298599]])       #random

    Two-by-four matrix of samples from :math:`N(3, 6.25)`:

    >>> 2.5 * np.matlib.randn((2, 4)) + 3
    matrix([[ 4.74085004,  8.89381862,  4.09042411,  4.83721922],
            [ 7.52373709,  5.07933944, -2.64043543,  0.45610557]])  #random

    """
    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)