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g d Z x$ e d ƒ D] Z e e ƒ e e >> 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, the string 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, 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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t | | ƒ S( N( R; ( RS Ra ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt __pow__K s c C s | | | (| S( N( ( RS Ra ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt __ipow__N s c C s t S( N( R` ( RS Ra ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt __rpow__R s c C sx t | i ƒ ƒ i d d ƒ } | i ƒ } x> t d t | ƒ ƒ D]' } | | o d | | | | >> 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]]
( Ri t tolist( RS ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyRu q s c C s" t i i | | | | ƒ i | ƒ 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.]])
( R0 RA t sumRt ( RS Rs R$ R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyRv ˆ s c C s" t i i | | | | ƒ i | ƒ S( sà
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]])
( R0 RA t meanRt ( RS Rs R$ R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyRw ª s i c C s% t i i | | | | | ƒ i | ƒ 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]])
( R0 RA t stdRt ( RS Rs R$ R[ t ddof( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyRx Ì s c C s% t i i | | | | | ƒ i | ƒ 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]])
( R0 RA t varRt ( RS Rs R$ R[ Ry ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyRz î s c C s" t i i | | | | ƒ i | ƒ S( sÕ
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]])
( R0 RA t prodRt ( RS Rs R$ R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR{ s c C s t i i | | | ƒ i | ƒ S( sE
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`
( R0 RA t anyRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR| 1 s c C s t i i | | | ƒ i | ƒ S( sì
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)
( R0 RA t allRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR} H s &c C s t i i | | | ƒ i | ƒ S( sÙ
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.argmax(1)
matrix([[3],
[7],
[11]])
( R0 RA t maxRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR~ p s !c C s t i i | | | ƒ i | ƒ S( sì
Indices of the maximum values along an axis.
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]])
( R0 RA t argmaxRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR “ s !c C s t i i | | | ƒ i | ƒ S( sð
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]])
( R0 RA t minRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR€ ¶ s !c C s t i i | | | ƒ i | ƒ S( s
Return the indices of the minimum values along an axis.
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]])
( R0 RA t argminRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR Ù s !c C s t i i | | | ƒ i | ƒ S( sÀ
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]])
( R0 RA t ptpRt ( RS Rs R[ ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyR‚ ü s c C sP | i \ } } | | j o d d k l } n d d k l } t | | ƒ ƒ S( sD
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.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.]])
iÿÿÿÿ( R' ( t pinv( R* t
numpy.dualR' Rƒ R ( RS R2 R0 t func( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt getI s
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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]])
( Ri ( RS ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt getAI s c C s | i ƒ i ƒ 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])
( Ri t ravel( RS ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt getA1f s c C s
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Returns the transpose of the matrix.
Does *not* conjugate! For the complex conjugate transpose, use `getH`.
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]])
( Rr ( RS ( ( s? /usr/lib64/python2.6/site-packages/numpy/matrixlib/defmatrix.pyt getT s c C s8 t | i i t i ƒ o | i ƒ i ƒ S| i ƒ 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
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obj : string, sequence or array
Input data. Variables names in the current scope may
be referenced, even if `obj` is 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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