Chris@87: from __future__ import division, absolute_import, print_function
Chris@87: 
Chris@87: import numpy as np
Chris@87: from numpy.matrixlib.defmatrix import matrix, asmatrix
Chris@87: # need * as we're copying the numpy namespace
Chris@87: from numpy import *
Chris@87: 
Chris@87: __version__ = np.__version__
Chris@87: 
Chris@87: __all__ = np.__all__[:] # copy numpy namespace
Chris@87: __all__ += ['rand', 'randn', 'repmat']
Chris@87: 
Chris@87: def empty(shape, dtype=None, order='C'):
Chris@87:     """
Chris@87:     Return a new matrix of given shape and type, without initializing entries.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     shape : int or tuple of int
Chris@87:         Shape of the empty matrix.
Chris@87:     dtype : data-type, optional
Chris@87:         Desired output data-type.
Chris@87:     order : {'C', 'F'}, optional
Chris@87:         Whether to store multi-dimensional data in C (row-major) or
Chris@87:         Fortran (column-major) order in memory.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     empty_like, zeros
Chris@87: 
Chris@87:     Notes
Chris@87:     -----
Chris@87:     `empty`, unlike `zeros`, does not set the matrix values to zero,
Chris@87:     and may therefore be marginally faster.  On the other hand, it requires
Chris@87:     the user to manually set all the values in the array, and should be
Chris@87:     used with caution.
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> np.matlib.empty((2, 2))    # filled with random data
Chris@87:     matrix([[  6.76425276e-320,   9.79033856e-307],
Chris@87:             [  7.39337286e-309,   3.22135945e-309]])        #random
Chris@87:     >>> np.matlib.empty((2, 2), dtype=int)
Chris@87:     matrix([[ 6600475,        0],
Chris@87:             [ 6586976, 22740995]])                          #random
Chris@87: 
Chris@87:     """
Chris@87:     return ndarray.__new__(matrix, shape, dtype, order=order)
Chris@87: 
Chris@87: def ones(shape, dtype=None, order='C'):
Chris@87:     """
Chris@87:     Matrix of ones.
Chris@87: 
Chris@87:     Return a matrix of given shape and type, filled with ones.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     shape : {sequence of ints, int}
Chris@87:         Shape of the matrix
Chris@87:     dtype : data-type, optional
Chris@87:         The desired data-type for the matrix, default is np.float64.
Chris@87:     order : {'C', 'F'}, optional
Chris@87:         Whether to store matrix in C- or Fortran-contiguous order,
Chris@87:         default is 'C'.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     out : matrix
Chris@87:         Matrix of ones of given shape, dtype, and order.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     ones : Array of ones.
Chris@87:     matlib.zeros : Zero matrix.
Chris@87: 
Chris@87:     Notes
Chris@87:     -----
Chris@87:     If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
Chris@87:     `out` becomes a single row matrix of shape ``(1,N)``.
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> np.matlib.ones((2,3))
Chris@87:     matrix([[ 1.,  1.,  1.],
Chris@87:             [ 1.,  1.,  1.]])
Chris@87: 
Chris@87:     >>> np.matlib.ones(2)
Chris@87:     matrix([[ 1.,  1.]])
Chris@87: 
Chris@87:     """
Chris@87:     a = ndarray.__new__(matrix, shape, dtype, order=order)
Chris@87:     a.fill(1)
Chris@87:     return a
Chris@87: 
Chris@87: def zeros(shape, dtype=None, order='C'):
Chris@87:     """
Chris@87:     Return a matrix of given shape and type, filled with zeros.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     shape : int or sequence of ints
Chris@87:         Shape of the matrix
Chris@87:     dtype : data-type, optional
Chris@87:         The desired data-type for the matrix, default is float.
Chris@87:     order : {'C', 'F'}, optional
Chris@87:         Whether to store the result in C- or Fortran-contiguous order,
Chris@87:         default is 'C'.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     out : matrix
Chris@87:         Zero matrix of given shape, dtype, and order.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     numpy.zeros : Equivalent array function.
Chris@87:     matlib.ones : Return a matrix of ones.
Chris@87: 
Chris@87:     Notes
Chris@87:     -----
Chris@87:     If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
Chris@87:     `out` becomes a single row matrix of shape ``(1,N)``.
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> np.matlib.zeros((2, 3))
Chris@87:     matrix([[ 0.,  0.,  0.],
Chris@87:             [ 0.,  0.,  0.]])
Chris@87: 
Chris@87:     >>> np.matlib.zeros(2)
Chris@87:     matrix([[ 0.,  0.]])
Chris@87: 
Chris@87:     """
Chris@87:     a = ndarray.__new__(matrix, shape, dtype, order=order)
Chris@87:     a.fill(0)
Chris@87:     return a
Chris@87: 
Chris@87: def identity(n,dtype=None):
Chris@87:     """
Chris@87:     Returns the square identity matrix of given size.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     n : int
Chris@87:         Size of the returned identity matrix.
Chris@87:     dtype : data-type, optional
Chris@87:         Data-type of the output. Defaults to ``float``.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     out : matrix
Chris@87:         `n` x `n` matrix with its main diagonal set to one,
Chris@87:         and all other elements zero.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     numpy.identity : Equivalent array function.
Chris@87:     matlib.eye : More general matrix identity function.
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> np.matlib.identity(3, dtype=int)
Chris@87:     matrix([[1, 0, 0],
Chris@87:             [0, 1, 0],
Chris@87:             [0, 0, 1]])
Chris@87: 
Chris@87:     """
Chris@87:     a = array([1]+n*[0], dtype=dtype)
Chris@87:     b = empty((n, n), dtype=dtype)
Chris@87:     b.flat = a
Chris@87:     return b
Chris@87: 
Chris@87: def eye(n,M=None, k=0, dtype=float):
Chris@87:     """
Chris@87:     Return a matrix with ones on the diagonal and zeros elsewhere.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     n : int
Chris@87:         Number of rows in the output.
Chris@87:     M : int, optional
Chris@87:         Number of columns in the output, defaults to `n`.
Chris@87:     k : int, optional
Chris@87:         Index of the diagonal: 0 refers to the main diagonal,
Chris@87:         a positive value refers to an upper diagonal,
Chris@87:         and a negative value to a lower diagonal.
Chris@87:     dtype : dtype, optional
Chris@87:         Data-type of the returned matrix.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     I : matrix
Chris@87:         A `n` x `M` matrix where all elements are equal to zero,
Chris@87:         except for the `k`-th diagonal, whose values are equal to one.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     numpy.eye : Equivalent array function.
Chris@87:     identity : Square identity matrix.
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> np.matlib.eye(3, k=1, dtype=float)
Chris@87:     matrix([[ 0.,  1.,  0.],
Chris@87:             [ 0.,  0.,  1.],
Chris@87:             [ 0.,  0.,  0.]])
Chris@87: 
Chris@87:     """
Chris@87:     return asmatrix(np.eye(n, M, k, dtype))
Chris@87: 
Chris@87: def rand(*args):
Chris@87:     """
Chris@87:     Return a matrix of random values with given shape.
Chris@87: 
Chris@87:     Create a matrix of the given shape and propagate it with
Chris@87:     random samples from a uniform distribution over ``[0, 1)``.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     \\*args : Arguments
Chris@87:         Shape of the output.
Chris@87:         If given as N integers, each integer specifies the size of one
Chris@87:         dimension.
Chris@87:         If given as a tuple, this tuple gives the complete shape.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     out : ndarray
Chris@87:         The matrix of random values with shape given by `\\*args`.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     randn, numpy.random.rand
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> np.matlib.rand(2, 3)
Chris@87:     matrix([[ 0.68340382,  0.67926887,  0.83271405],
Chris@87:             [ 0.00793551,  0.20468222,  0.95253525]])       #random
Chris@87:     >>> np.matlib.rand((2, 3))
Chris@87:     matrix([[ 0.84682055,  0.73626594,  0.11308016],
Chris@87:             [ 0.85429008,  0.3294825 ,  0.89139555]])       #random
Chris@87: 
Chris@87:     If the first argument is a tuple, other arguments are ignored:
Chris@87: 
Chris@87:     >>> np.matlib.rand((2, 3), 4)
Chris@87:     matrix([[ 0.46898646,  0.15163588,  0.95188261],
Chris@87:             [ 0.59208621,  0.09561818,  0.00583606]])       #random
Chris@87: 
Chris@87:     """
Chris@87:     if isinstance(args[0], tuple):
Chris@87:         args = args[0]
Chris@87:     return asmatrix(np.random.rand(*args))
Chris@87: 
Chris@87: def randn(*args):
Chris@87:     """
Chris@87:     Return a random matrix with data from the "standard normal" distribution.
Chris@87: 
Chris@87:     `randn` generates a matrix filled with random floats sampled from a
Chris@87:     univariate "normal" (Gaussian) distribution of mean 0 and variance 1.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     \\*args : Arguments
Chris@87:         Shape of the output.
Chris@87:         If given as N integers, each integer specifies the size of one
Chris@87:         dimension. If given as a tuple, this tuple gives the complete shape.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     Z : matrix of floats
Chris@87:         A matrix of floating-point samples drawn from the standard normal
Chris@87:         distribution.
Chris@87: 
Chris@87:     See Also
Chris@87:     --------
Chris@87:     rand, random.randn
Chris@87: 
Chris@87:     Notes
Chris@87:     -----
Chris@87:     For random samples from :math:`N(\\mu, \\sigma^2)`, use:
Chris@87: 
Chris@87:     ``sigma * np.matlib.randn(...) + mu``
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> np.matlib.randn(1)
Chris@87:     matrix([[-0.09542833]])                                 #random
Chris@87:     >>> np.matlib.randn(1, 2, 3)
Chris@87:     matrix([[ 0.16198284,  0.0194571 ,  0.18312985],
Chris@87:             [-0.7509172 ,  1.61055   ,  0.45298599]])       #random
Chris@87: 
Chris@87:     Two-by-four matrix of samples from :math:`N(3, 6.25)`:
Chris@87: 
Chris@87:     >>> 2.5 * np.matlib.randn((2, 4)) + 3
Chris@87:     matrix([[ 4.74085004,  8.89381862,  4.09042411,  4.83721922],
Chris@87:             [ 7.52373709,  5.07933944, -2.64043543,  0.45610557]])  #random
Chris@87: 
Chris@87:     """
Chris@87:     if isinstance(args[0], tuple):
Chris@87:         args = args[0]
Chris@87:     return asmatrix(np.random.randn(*args))
Chris@87: 
Chris@87: def repmat(a, m, n):
Chris@87:     """
Chris@87:     Repeat a 0-D to 2-D array or matrix MxN times.
Chris@87: 
Chris@87:     Parameters
Chris@87:     ----------
Chris@87:     a : array_like
Chris@87:         The array or matrix to be repeated.
Chris@87:     m, n : int
Chris@87:         The number of times `a` is repeated along the first and second axes.
Chris@87: 
Chris@87:     Returns
Chris@87:     -------
Chris@87:     out : ndarray
Chris@87:         The result of repeating `a`.
Chris@87: 
Chris@87:     Examples
Chris@87:     --------
Chris@87:     >>> import numpy.matlib
Chris@87:     >>> a0 = np.array(1)
Chris@87:     >>> np.matlib.repmat(a0, 2, 3)
Chris@87:     array([[1, 1, 1],
Chris@87:            [1, 1, 1]])
Chris@87: 
Chris@87:     >>> a1 = np.arange(4)
Chris@87:     >>> np.matlib.repmat(a1, 2, 2)
Chris@87:     array([[0, 1, 2, 3, 0, 1, 2, 3],
Chris@87:            [0, 1, 2, 3, 0, 1, 2, 3]])
Chris@87: 
Chris@87:     >>> a2 = np.asmatrix(np.arange(6).reshape(2, 3))
Chris@87:     >>> np.matlib.repmat(a2, 2, 3)
Chris@87:     matrix([[0, 1, 2, 0, 1, 2, 0, 1, 2],
Chris@87:             [3, 4, 5, 3, 4, 5, 3, 4, 5],
Chris@87:             [0, 1, 2, 0, 1, 2, 0, 1, 2],
Chris@87:             [3, 4, 5, 3, 4, 5, 3, 4, 5]])
Chris@87: 
Chris@87:     """
Chris@87:     a = asanyarray(a)
Chris@87:     ndim = a.ndim
Chris@87:     if ndim == 0:
Chris@87:         origrows, origcols = (1, 1)
Chris@87:     elif ndim == 1:
Chris@87:         origrows, origcols = (1, a.shape[0])
Chris@87:     else:
Chris@87:         origrows, origcols = a.shape
Chris@87:     rows = origrows * m
Chris@87:     cols = origcols * n
Chris@87:     c = a.reshape(1, a.size).repeat(m, 0).reshape(rows, origcols).repeat(n, 0)
Chris@87:     return c.reshape(rows, cols)