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Interpret the input as a matrix.
Unlike `matrix`, `asmatrix` does not make a copy if the input is already
a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
Parameters
----------
data : array_like
Input data.
dtype : data-type
Data-type of the output matrix.
Returns
-------
mat : matrix
`data` interpreted as a matrix.
Examples
--------
>>> x = np.array([[1, 2], [3, 4]])
>>> m = np.asmatrix(x)
>>> x[0,0] = 5
>>> m
matrix([[5, 2],
[3, 4]])
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Raise a square matrix to the (integer) power `n`.
For positive integers `n`, the power is computed by repeated matrix
squarings and matrix multiplications. If ``n == 0``, the identity matrix
of the same shape as M is returned. If ``n < 0``, the inverse
is computed and then raised to the ``abs(n)``.
Parameters
----------
M : ndarray or matrix object
Matrix to be "powered." Must be square, i.e. ``M.shape == (m, m)``,
with `m` a positive integer.
n : int
The exponent can be any integer or long integer, positive,
negative, or zero.
Returns
-------
M**n : ndarray or matrix object
The return value is the same shape and type as `M`;
if the exponent is positive or zero then the type of the
elements is the same as those of `M`. If the exponent is
negative the elements are floating-point.
Raises
------
LinAlgError
If the matrix is not numerically invertible.
See Also
--------
matrix
Provides an equivalent function as the exponentiation operator
(``**``, not ``^``).
Examples
--------
>>> from numpy import linalg as LA
>>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit
>>> LA.matrix_power(i, 3) # should = -i
array([[ 0, -1],
[ 1, 0]])
>>> LA.matrix_power(np.matrix(i), 3) # matrix arg returns matrix
matrix([[ 0, -1],
[ 1, 0]])
>>> LA.matrix_power(i, 0)
array([[1, 0],
[0, 1]])
>>> LA.matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements
array([[ 0., 1.],
[-1., 0.]])
Somewhat more sophisticated example
>>> q = np.zeros((4, 4))
>>> q[0:2, 0:2] = -i
>>> q[2:4, 2:4] = i
>>> q # one of the three quarternion units not equal to 1
array([[ 0., -1., 0., 0.],
[ 1., 0., 0., 0.],
[ 0., 0., 0., 1.],
[ 0., 0., -1., 0.]])
>>> LA.matrix_power(q, 2) # = -np.eye(4)
array([[-1., 0., 0., 0.],
[ 0., -1., 0., 0.],
[ 0., 0., -1., 0.],
[ 0., 0., 0., -1.]])
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matrix(data, dtype=None, copy=True)
Returns a matrix from an array-like object, or from a string of data.
A matrix is a specialized 2-D array that retains its 2-D nature
through operations. It has certain special operators, such as ``*``
(matrix multiplication) and ``**`` (matrix power).
Parameters
----------
data : array_like or string
If `data` is a string, it is interpreted as a matrix with commas
or spaces separating columns, and semicolons separating rows.
dtype : data-type
Data-type of the output matrix.
copy : bool
If `data` is already an `ndarray`, then this flag determines
whether the data is copied (the default), or whether a view is
constructed.
See Also
--------
array
Examples
--------
>>> a = np.matrix('1 2; 3 4')
>>> print(a)
[[1 2]
[3 4]]
>>> np.matrix([[1, 2], [3, 4]])
matrix([[1, 2],
[3, 4]])
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splitlinesR< R$ t join( R t st lR ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyt __repr__m s
c C` s t | j � � S( N( RQ Rt ( R ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyt __str__w s c C` sJ | d k r | d S| d k r$ | S| d k r: | j � St d � � d S( s^ A convenience function for operations that need to preserve axis
orientation.
i i s unsupported axisN( i i ( R t transposeR% ( R t axis( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyt _alignz s
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to a scalar like _align, but are using keepdims=True
i N( i i ( R ( R R} ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyt _collapse� s c C` s | j � j � S( s�
Return the matrix as a (possibly nested) list.
See `ndarray.tolist` for full documentation.
See Also
--------
ndarray.tolist
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.tolist()
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
( Rt t tolist( R ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� � s c C` s( t j j | | | | d t �j | � S( s
Returns the sum of the matrix elements, along the given axis.
Refer to `numpy.sum` for full documentation.
See Also
--------
numpy.sum
Notes
-----
This is the same as `ndarray.sum`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix([[1, 2], [4, 3]])
>>> x.sum()
10
>>> x.sum(axis=1)
matrix([[3],
[7]])
>>> x.sum(axis=1, dtype='float')
matrix([[ 3.],
[ 7.]])
>>> out = np.zeros((1, 2), dtype='float')
>>> x.sum(axis=1, dtype='float', out=out)
matrix([[ 3.],
[ 7.]])
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Return a possibly reshaped matrix.
Refer to `numpy.squeeze` for more documentation.
Parameters
----------
axis : None or int or tuple of ints, optional
Selects a subset of the single-dimensional entries in the shape.
If an axis is selected with shape entry greater than one,
an error is raised.
Returns
-------
squeezed : matrix
The matrix, but as a (1, N) matrix if it had shape (N, 1).
See Also
--------
numpy.squeeze : related function
Notes
-----
If `m` has a single column then that column is returned
as the single row of a matrix. Otherwise `m` is returned.
The returned matrix is always either `m` itself or a view into `m`.
Supplying an axis keyword argument will not affect the returned matrix
but it may cause an error to be raised.
Examples
--------
>>> c = np.matrix([[1], [2]])
>>> c
matrix([[1],
[2]])
>>> c.squeeze()
matrix([[1, 2]])
>>> r = c.T
>>> r
matrix([[1, 2]])
>>> r.squeeze()
matrix([[1, 2]])
>>> m = np.matrix([[1, 2], [3, 4]])
>>> m.squeeze()
matrix([[1, 2],
[3, 4]])
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Return a flattened copy of the matrix.
All `N` elements of the matrix are placed into a single row.
Parameters
----------
order : {'C', 'F', 'A', 'K'}, optional
'C' means to flatten in row-major (C-style) order. 'F' means to
flatten in column-major (Fortran-style) order. 'A' means to
flatten in column-major order if `m` is Fortran *contiguous* in
memory, row-major order otherwise. 'K' means to flatten `m` in
the order the elements occur in memory. The default is 'C'.
Returns
-------
y : matrix
A copy of the matrix, flattened to a `(1, N)` matrix where `N`
is the number of elements in the original matrix.
See Also
--------
ravel : Return a flattened array.
flat : A 1-D flat iterator over the matrix.
Examples
--------
>>> m = np.matrix([[1,2], [3,4]])
>>> m.flatten()
matrix([[1, 2, 3, 4]])
>>> m.flatten('F')
matrix([[1, 3, 2, 4]])
RL ( R= RO t flatten( R RL ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� s #c C` s( t j j | | | | d t �j | � S( s�
Returns the average of the matrix elements along the given axis.
Refer to `numpy.mean` for full documentation.
See Also
--------
numpy.mean
Notes
-----
Same as `ndarray.mean` except that, where that returns an `ndarray`,
this returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.mean()
5.5
>>> x.mean(0)
matrix([[ 4., 5., 6., 7.]])
>>> x.mean(1)
matrix([[ 1.5],
[ 5.5],
[ 9.5]])
R� ( R= RO t meanRd R ( R R} R2 Rf ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� ' s i c C` s+ t j j | | | | | d t �j | � S( s?
Return the standard deviation of the array elements along the given axis.
Refer to `numpy.std` for full documentation.
See Also
--------
numpy.std
Notes
-----
This is the same as `ndarray.std`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.std()
3.4520525295346629
>>> x.std(0)
matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]])
>>> x.std(1)
matrix([[ 1.11803399],
[ 1.11803399],
[ 1.11803399]])
R� ( R= RO t stdRd R ( R R} R2 Rf t ddof( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� I s c C` s+ t j j | | | | | d t �j | � S( s*
Returns the variance of the matrix elements, along the given axis.
Refer to `numpy.var` for full documentation.
See Also
--------
numpy.var
Notes
-----
This is the same as `ndarray.var`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.var()
11.916666666666666
>>> x.var(0)
matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]])
>>> x.var(1)
matrix([[ 1.25],
[ 1.25],
[ 1.25]])
R� ( R= RO t varRd R ( R R} R2 Rf R� ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� k s c C` s( t j j | | | | d t �j | � S( s�
Return the product of the array elements over the given axis.
Refer to `prod` for full documentation.
See Also
--------
prod, ndarray.prod
Notes
-----
Same as `ndarray.prod`, except, where that returns an `ndarray`, this
returns a `matrix` object instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.prod()
0
>>> x.prod(0)
matrix([[ 0, 45, 120, 231]])
>>> x.prod(1)
matrix([[ 0],
[ 840],
[7920]])
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Test whether any array element along a given axis evaluates to True.
Refer to `numpy.any` for full documentation.
Parameters
----------
axis : int, optional
Axis along which logical OR is performed
out : ndarray, optional
Output to existing array instead of creating new one, must have
same shape as expected output
Returns
-------
any : bool, ndarray
Returns a single bool if `axis` is ``None``; otherwise,
returns `ndarray`
R� ( R= RO t anyRd R ( R R} Rf ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� � s c C` s% t j j | | | d t �j | � S( s�
Test whether all matrix elements along a given axis evaluate to True.
Parameters
----------
See `numpy.all` for complete descriptions
See Also
--------
numpy.all
Notes
-----
This is the same as `ndarray.all`, but it returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> y = x[0]; y
matrix([[0, 1, 2, 3]])
>>> (x == y)
matrix([[ True, True, True, True],
[False, False, False, False],
[False, False, False, False]], dtype=bool)
>>> (x == y).all()
False
>>> (x == y).all(0)
matrix([[False, False, False, False]], dtype=bool)
>>> (x == y).all(1)
matrix([[ True],
[False],
[False]], dtype=bool)
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Return the maximum value along an axis.
Parameters
----------
See `amax` for complete descriptions
See Also
--------
amax, ndarray.max
Notes
-----
This is the same as `ndarray.max`, but returns a `matrix` object
where `ndarray.max` would return an ndarray.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.max()
11
>>> x.max(0)
matrix([[ 8, 9, 10, 11]])
>>> x.max(1)
matrix([[ 3],
[ 7],
[11]])
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Indexes of the maximum values along an axis.
Return the indexes of the first occurrences of the maximum values
along the specified axis. If axis is None, the index is for the
flattened matrix.
Parameters
----------
See `numpy.argmax` for complete descriptions
See Also
--------
numpy.argmax
Notes
-----
This is the same as `ndarray.argmax`, but returns a `matrix` object
where `ndarray.argmax` would return an `ndarray`.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.argmax()
11
>>> x.argmax(0)
matrix([[2, 2, 2, 2]])
>>> x.argmax(1)
matrix([[3],
[3],
[3]])
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Return the minimum value along an axis.
Parameters
----------
See `amin` for complete descriptions.
See Also
--------
amin, ndarray.min
Notes
-----
This is the same as `ndarray.min`, but returns a `matrix` object
where `ndarray.min` would return an ndarray.
Examples
--------
>>> x = -np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, -1, -2, -3],
[ -4, -5, -6, -7],
[ -8, -9, -10, -11]])
>>> x.min()
-11
>>> x.min(0)
matrix([[ -8, -9, -10, -11]])
>>> x.min(1)
matrix([[ -3],
[ -7],
[-11]])
R� ( R= RO t minRd R ( R R} Rf ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� 7 s !c C` s t j j | | | � j | � S( s�
Indexes of the minimum values along an axis.
Return the indexes of the first occurrences of the minimum values
along the specified axis. If axis is None, the index is for the
flattened matrix.
Parameters
----------
See `numpy.argmin` for complete descriptions.
See Also
--------
numpy.argmin
Notes
-----
This is the same as `ndarray.argmin`, but returns a `matrix` object
where `ndarray.argmin` would return an `ndarray`.
Examples
--------
>>> x = -np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, -1, -2, -3],
[ -4, -5, -6, -7],
[ -8, -9, -10, -11]])
>>> x.argmin()
11
>>> x.argmin(0)
matrix([[2, 2, 2, 2]])
>>> x.argmin(1)
matrix([[3],
[3],
[3]])
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Peak-to-peak (maximum - minimum) value along the given axis.
Refer to `numpy.ptp` for full documentation.
See Also
--------
numpy.ptp
Notes
-----
Same as `ndarray.ptp`, except, where that would return an `ndarray` object,
this returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.ptp()
11
>>> x.ptp(0)
matrix([[8, 8, 8, 8]])
>>> x.ptp(1)
matrix([[3],
[3],
[3]])
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Returns the (multiplicative) inverse of invertible `self`.
Parameters
----------
None
Returns
-------
ret : matrix object
If `self` is non-singular, `ret` is such that ``ret * self`` ==
``self * ret`` == ``np.matrix(np.eye(self[0,:].size)`` all return
``True``.
Raises
------
numpy.linalg.LinAlgError: Singular matrix
If `self` is singular.
See Also
--------
linalg.inv
Examples
--------
>>> m = np.matrix('[1, 2; 3, 4]'); m
matrix([[1, 2],
[3, 4]])
>>> m.getI()
matrix([[-2. , 1. ],
[ 1.5, -0.5]])
>>> m.getI() * m
matrix([[ 1., 0.],
[ 0., 1.]])
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Return `self` as an `ndarray` object.
Equivalent to ``np.asarray(self)``.
Parameters
----------
None
Returns
-------
ret : ndarray
`self` as an `ndarray`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.getA()
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
( Rt ( R ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyt getA� s c C` s | j � j � S( s
Return `self` as a flattened `ndarray`.
Equivalent to ``np.asarray(x).ravel()``
Parameters
----------
None
Returns
-------
ret : ndarray
`self`, 1-D, as an `ndarray`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.getA1()
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
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Return a flattened matrix.
Refer to `numpy.ravel` for more documentation.
Parameters
----------
order : {'C', 'F', 'A', 'K'}, optional
The elements of `m` are read using this index order. 'C' means to
index the elements in C-like order, with the last axis index
changing fastest, back to the first axis index changing slowest.
'F' means to index the elements in Fortran-like index order, with
the first index changing fastest, and the last index changing
slowest. Note that the 'C' and 'F' options take no account of the
memory layout of the underlying array, and only refer to the order
of axis indexing. 'A' means to read the elements in Fortran-like
index order if `m` is Fortran *contiguous* in memory, C-like order
otherwise. 'K' means to read the elements in the order they occur
in memory, except for reversing the data when strides are negative.
By default, 'C' index order is used.
Returns
-------
ret : matrix
Return the matrix flattened to shape `(1, N)` where `N`
is the number of elements in the original matrix.
A copy is made only if necessary.
See Also
--------
matrix.flatten : returns a similar output matrix but always a copy
matrix.flat : a flat iterator on the array.
numpy.ravel : related function which returns an ndarray
RL ( R= RO R� ( R RL ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyR� s $c C` s
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Returns the transpose of the matrix.
Does *not* conjugate! For the complex conjugate transpose, use ``.H``.
Parameters
----------
None
Returns
-------
ret : matrix object
The (non-conjugated) transpose of the matrix.
See Also
--------
transpose, getH
Examples
--------
>>> m = np.matrix('[1, 2; 3, 4]')
>>> m
matrix([[1, 2],
[3, 4]])
>>> m.getT()
matrix([[1, 3],
[2, 4]])
( R| ( R ( ( sL /opt/alt/python27/lib64/python2.7/site-packages/numpy/matrixlib/defmatrix.pyt getT. s c C` s6 t | j j t j � r( | j � j � S| j � Sd S( sF
Returns the (complex) conjugate transpose of `self`.
Equivalent to ``np.transpose(self)`` if `self` is real-valued.
Parameters
----------
None
Returns
-------
ret : matrix object
complex conjugate transpose of `self`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4)))
>>> z = x - 1j*x; z
matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],
[ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],
[ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])
>>> z.getH()
matrix([[ 0. +0.j, 4. +4.j, 8. +8.j],
[ 1. +1.j, 5. +5.j, 9. +9.j],
[ 2. +2.j, 6. +6.j, 10.+10.j],
[ 3. +3.j, 7. +7.j, 11.+11.j]])
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Build a matrix object from a string, nested sequence, or array.
Parameters
----------
obj : str or array_like
Input data. Names of variables in the current scope may be
referenced, even if `obj` is a string.
ldict : dict, optional
A dictionary that replaces local operands in current frame.
Ignored if `obj` is not a string or `gdict` is `None`.
gdict : dict, optional
A dictionary that replaces global operands in current frame.
Ignored if `obj` is not a string.
Returns
-------
out : matrix
Returns a matrix object, which is a specialized 2-D array.
See Also
--------
matrix
Examples
--------
>>> A = np.mat('1 1; 1 1')
>>> B = np.mat('2 2; 2 2')
>>> C = np.mat('3 4; 5 6')
>>> D = np.mat('7 8; 9 0')
All the following expressions construct the same block matrix:
>>> np.bmat([[A, B], [C, D]])
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
>>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
>>> np.bmat('A,B; C,D')
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
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