379 lines
10 KiB
Python
379 lines
10 KiB
Python
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import warnings
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# 2018-05-29, PendingDeprecationWarning added to matrix.__new__
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# 2020-01-23, numpy 1.19.0 PendingDeprecatonWarning
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warnings.warn("Importing from numpy.matlib is deprecated since 1.19.0. "
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"The matrix subclass is not the recommended way to represent "
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"matrices or deal with linear algebra (see "
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"https://docs.scipy.org/doc/numpy/user/numpy-for-matlab-users.html). "
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"Please adjust your code to use regular ndarray. ",
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PendingDeprecationWarning, stacklevel=2)
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import numpy as np
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from numpy.matrixlib.defmatrix import matrix, asmatrix
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# Matlib.py contains all functions in the numpy namespace with a few
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# replacements. See doc/source/reference/routines.matlib.rst for details.
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# Need * as we're copying the numpy namespace.
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from numpy import * # noqa: F403
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__version__ = np.__version__
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__all__ = np.__all__[:] # copy numpy namespace
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__all__ += ['rand', 'randn', 'repmat']
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def empty(shape, dtype=None, order='C'):
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"""Return a new matrix of given shape and type, without initializing entries.
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Parameters
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----------
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shape : int or tuple of int
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Shape of the empty matrix.
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dtype : data-type, optional
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Desired output data-type.
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order : {'C', 'F'}, optional
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Whether to store multi-dimensional data in row-major
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(C-style) or column-major (Fortran-style) order in
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memory.
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See Also
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--------
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empty_like, zeros
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Notes
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-----
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`empty`, unlike `zeros`, does not set the matrix values to zero,
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and may therefore be marginally faster. On the other hand, it requires
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the user to manually set all the values in the array, and should be
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used with caution.
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Examples
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--------
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>>> import numpy.matlib
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>>> np.matlib.empty((2, 2)) # filled with random data
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matrix([[ 6.76425276e-320, 9.79033856e-307], # random
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[ 7.39337286e-309, 3.22135945e-309]])
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>>> np.matlib.empty((2, 2), dtype=int)
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matrix([[ 6600475, 0], # random
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[ 6586976, 22740995]])
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"""
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return ndarray.__new__(matrix, shape, dtype, order=order)
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def ones(shape, dtype=None, order='C'):
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"""
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Matrix of ones.
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Return a matrix of given shape and type, filled with ones.
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Parameters
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----------
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shape : {sequence of ints, int}
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Shape of the matrix
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dtype : data-type, optional
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The desired data-type for the matrix, default is np.float64.
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order : {'C', 'F'}, optional
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Whether to store matrix in C- or Fortran-contiguous order,
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default is 'C'.
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Returns
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-------
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out : matrix
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Matrix of ones of given shape, dtype, and order.
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See Also
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--------
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ones : Array of ones.
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matlib.zeros : Zero matrix.
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Notes
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-----
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If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
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`out` becomes a single row matrix of shape ``(1,N)``.
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Examples
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--------
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>>> np.matlib.ones((2,3))
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matrix([[1., 1., 1.],
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[1., 1., 1.]])
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>>> np.matlib.ones(2)
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matrix([[1., 1.]])
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"""
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a = ndarray.__new__(matrix, shape, dtype, order=order)
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a.fill(1)
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return a
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def zeros(shape, dtype=None, order='C'):
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"""
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Return a matrix of given shape and type, filled with zeros.
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Parameters
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----------
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shape : int or sequence of ints
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Shape of the matrix
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dtype : data-type, optional
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The desired data-type for the matrix, default is float.
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order : {'C', 'F'}, optional
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Whether to store the result in C- or Fortran-contiguous order,
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default is 'C'.
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Returns
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-------
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out : matrix
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Zero matrix of given shape, dtype, and order.
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See Also
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--------
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numpy.zeros : Equivalent array function.
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matlib.ones : Return a matrix of ones.
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Notes
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-----
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If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
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`out` becomes a single row matrix of shape ``(1,N)``.
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Examples
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--------
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>>> import numpy.matlib
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>>> np.matlib.zeros((2, 3))
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matrix([[0., 0., 0.],
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[0., 0., 0.]])
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>>> np.matlib.zeros(2)
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matrix([[0., 0.]])
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"""
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a = ndarray.__new__(matrix, shape, dtype, order=order)
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a.fill(0)
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return a
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def identity(n,dtype=None):
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"""
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Returns the square identity matrix of given size.
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Parameters
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----------
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n : int
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Size of the returned identity matrix.
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dtype : data-type, optional
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Data-type of the output. Defaults to ``float``.
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Returns
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-------
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out : matrix
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`n` x `n` matrix with its main diagonal set to one,
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and all other elements zero.
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See Also
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--------
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numpy.identity : Equivalent array function.
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matlib.eye : More general matrix identity function.
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Examples
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--------
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>>> import numpy.matlib
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>>> np.matlib.identity(3, dtype=int)
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matrix([[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1]])
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"""
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a = array([1]+n*[0], dtype=dtype)
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b = empty((n, n), dtype=dtype)
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b.flat = a
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return b
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def eye(n,M=None, k=0, dtype=float, order='C'):
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"""
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Return a matrix with ones on the diagonal and zeros elsewhere.
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Parameters
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----------
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n : int
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Number of rows in the output.
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M : int, optional
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Number of columns in the output, defaults to `n`.
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k : int, optional
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Index of the diagonal: 0 refers to the main diagonal,
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a positive value refers to an upper diagonal,
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and a negative value to a lower diagonal.
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dtype : dtype, optional
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Data-type of the returned matrix.
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order : {'C', 'F'}, optional
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Whether the output should be stored in row-major (C-style) or
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column-major (Fortran-style) order in memory.
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.. versionadded:: 1.14.0
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Returns
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-------
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I : matrix
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A `n` x `M` matrix where all elements are equal to zero,
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except for the `k`-th diagonal, whose values are equal to one.
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See Also
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--------
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numpy.eye : Equivalent array function.
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identity : Square identity matrix.
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Examples
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--------
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>>> import numpy.matlib
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>>> np.matlib.eye(3, k=1, dtype=float)
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matrix([[0., 1., 0.],
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[0., 0., 1.],
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[0., 0., 0.]])
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"""
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return asmatrix(np.eye(n, M=M, k=k, dtype=dtype, order=order))
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def rand(*args):
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"""
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Return a matrix of random values with given shape.
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Create a matrix of the given shape and propagate it with
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random samples from a uniform distribution over ``[0, 1)``.
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Parameters
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----------
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\\*args : Arguments
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Shape of the output.
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If given as N integers, each integer specifies the size of one
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dimension.
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If given as a tuple, this tuple gives the complete shape.
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Returns
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-------
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out : ndarray
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The matrix of random values with shape given by `\\*args`.
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See Also
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--------
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randn, numpy.random.RandomState.rand
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Examples
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--------
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>>> np.random.seed(123)
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>>> import numpy.matlib
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>>> np.matlib.rand(2, 3)
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matrix([[0.69646919, 0.28613933, 0.22685145],
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[0.55131477, 0.71946897, 0.42310646]])
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>>> np.matlib.rand((2, 3))
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matrix([[0.9807642 , 0.68482974, 0.4809319 ],
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[0.39211752, 0.34317802, 0.72904971]])
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If the first argument is a tuple, other arguments are ignored:
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>>> np.matlib.rand((2, 3), 4)
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matrix([[0.43857224, 0.0596779 , 0.39804426],
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[0.73799541, 0.18249173, 0.17545176]])
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"""
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if isinstance(args[0], tuple):
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args = args[0]
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return asmatrix(np.random.rand(*args))
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def randn(*args):
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"""
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Return a random matrix with data from the "standard normal" distribution.
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`randn` generates a matrix filled with random floats sampled from a
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univariate "normal" (Gaussian) distribution of mean 0 and variance 1.
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Parameters
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----------
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\\*args : Arguments
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Shape of the output.
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If given as N integers, each integer specifies the size of one
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dimension. If given as a tuple, this tuple gives the complete shape.
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Returns
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-------
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Z : matrix of floats
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A matrix of floating-point samples drawn from the standard normal
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distribution.
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See Also
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--------
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rand, numpy.random.RandomState.randn
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Notes
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-----
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For random samples from the normal distribution with mean ``mu`` and
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standard deviation ``sigma``, use::
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sigma * np.matlib.randn(...) + mu
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Examples
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--------
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>>> np.random.seed(123)
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>>> import numpy.matlib
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>>> np.matlib.randn(1)
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matrix([[-1.0856306]])
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>>> np.matlib.randn(1, 2, 3)
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matrix([[ 0.99734545, 0.2829785 , -1.50629471],
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[-0.57860025, 1.65143654, -2.42667924]])
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Two-by-four matrix of samples from the normal distribution with
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mean 3 and standard deviation 2.5:
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>>> 2.5 * np.matlib.randn((2, 4)) + 3
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matrix([[1.92771843, 6.16484065, 0.83314899, 1.30278462],
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[2.76322758, 6.72847407, 1.40274501, 1.8900451 ]])
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"""
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if isinstance(args[0], tuple):
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args = args[0]
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return asmatrix(np.random.randn(*args))
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def repmat(a, m, n):
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"""
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Repeat a 0-D to 2-D array or matrix MxN times.
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Parameters
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----------
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a : array_like
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The array or matrix to be repeated.
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m, n : int
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The number of times `a` is repeated along the first and second axes.
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Returns
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-------
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out : ndarray
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The result of repeating `a`.
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Examples
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--------
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>>> import numpy.matlib
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>>> a0 = np.array(1)
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>>> np.matlib.repmat(a0, 2, 3)
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array([[1, 1, 1],
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[1, 1, 1]])
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>>> a1 = np.arange(4)
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>>> np.matlib.repmat(a1, 2, 2)
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array([[0, 1, 2, 3, 0, 1, 2, 3],
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[0, 1, 2, 3, 0, 1, 2, 3]])
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>>> a2 = np.asmatrix(np.arange(6).reshape(2, 3))
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>>> np.matlib.repmat(a2, 2, 3)
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matrix([[0, 1, 2, 0, 1, 2, 0, 1, 2],
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[3, 4, 5, 3, 4, 5, 3, 4, 5],
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[0, 1, 2, 0, 1, 2, 0, 1, 2],
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[3, 4, 5, 3, 4, 5, 3, 4, 5]])
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"""
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a = asanyarray(a)
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ndim = a.ndim
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if ndim == 0:
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origrows, origcols = (1, 1)
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elif ndim == 1:
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origrows, origcols = (1, a.shape[0])
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else:
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origrows, origcols = a.shape
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rows = origrows * m
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cols = origcols * n
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c = a.reshape(1, a.size).repeat(m, 0).reshape(rows, origcols).repeat(n, 0)
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return c.reshape(rows, cols)
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