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from __future__ import division, absolute_import, print_function
__all__ = ['matrix', 'bmat', 'mat', 'asmatrix']
import sys
import ast
import numpy.core.numeric as N
from numpy.core.numeric import concatenate, isscalar, binary_repr, identity, asanyarray
from numpy.core.numerictypes import issubdtype
def _convert_from_string(data):
for char in '[]':
data = data.replace(char, '')
rows = data.split(';')
newdata = []
count = 0
for row in rows:
trow = row.split(',')
newrow = []
for col in trow:
temp = col.split()
newrow.extend(map(ast.literal_eval, temp))
if count == 0:
Ncols = len(newrow)
elif len(newrow) != Ncols:
raise ValueError("Rows not the same size.")
count += 1
newdata.append(newrow)
return newdata
def asmatrix(data, dtype=None):
"""
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]])
"""
return matrix(data, dtype=dtype, copy=False)
def matrix_power(M, n):
"""
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 quaternion 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.]])
"""
M = asanyarray(M)
if M.ndim != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not issubdtype(type(n), N.integer):
raise TypeError("exponent must be an integer")
from numpy.linalg import inv
if n==0:
M = M.copy()
M[:] = identity(M.shape[0])
return M
elif n<0:
M = inv(M)
n *= -1
result = M
if n <= 3:
for _ in range(n-1):
result=N.dot(result, M)
return result
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
beta = binary_repr(n)
Z, q, t = M, 0, len(beta)
while beta[t-q-1] == '0':
Z = N.dot(Z, Z)
q += 1
result = Z
for k in range(q+1, t):
Z = N.dot(Z, Z)
if beta[t-k-1] == '1':
result = N.dot(result, Z)
return result
class matrix(N.ndarray):
"""
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]])
"""
__array_priority__ = 10.0
def __new__(subtype, data, dtype=None, copy=True):
if isinstance(data, matrix):
dtype2 = data.dtype
if (dtype is None):
dtype = dtype2
if (dtype2 == dtype) and (not copy):
return data
return data.astype(dtype)
if isinstance(data, N.ndarray):
if dtype is None:
intype = data.dtype
else:
intype = N.dtype(dtype)
new = data.view(subtype)
if intype != data.dtype:
return new.astype(intype)
if copy: return new.copy()
else: return new
if isinstance(data, str):
data = _convert_from_string(data)
# now convert data to an array
arr = N.array(data, dtype=dtype, copy=copy)
ndim = arr.ndim
shape = arr.shape
if (ndim > 2):
raise ValueError("matrix must be 2-dimensional")
elif ndim == 0:
shape = (1, 1)
elif ndim == 1:
shape = (1, shape[0])
order = 'C'
if (ndim == 2) and arr.flags.fortran:
order = 'F'
if not (order or arr.flags.contiguous):
arr = arr.copy()
ret = N.ndarray.__new__(subtype, shape, arr.dtype,
buffer=arr,
order=order)
return ret
def __array_finalize__(self, obj):
self._getitem = False
if (isinstance(obj, matrix) and obj._getitem): return
ndim = self.ndim
if (ndim == 2):
return
if (ndim > 2):
newshape = tuple([x for x in self.shape if x > 1])
ndim = len(newshape)
if ndim == 2:
self.shape = newshape
return
elif (ndim > 2):
raise ValueError("shape too large to be a matrix.")
else:
newshape = self.shape
if ndim == 0:
self.shape = (1, 1)
elif ndim == 1:
self.shape = (1, newshape[0])
return
def __getitem__(self, index):
self._getitem = True
try:
out = N.ndarray.__getitem__(self, index)
finally:
self._getitem = False
if not isinstance(out, N.ndarray):
return out
if out.ndim == 0:
return out[()]
if out.ndim == 1:
sh = out.shape[0]
# Determine when we should have a column array
try:
n = len(index)
except Exception:
n = 0
if n > 1 and isscalar(index[1]):
out.shape = (sh, 1)
else:
out.shape = (1, sh)
return out
def __mul__(self, other):
if isinstance(other, (N.ndarray, list, tuple)) :
# This promotes 1-D vectors to row vectors
return N.dot(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__') :
return N.dot(self, other)
return NotImplemented
def __rmul__(self, other):
return N.dot(other, self)
def __imul__(self, other):
self[:] = self * other
return self
def __pow__(self, other):
return matrix_power(self, other)
def __ipow__(self, other):
self[:] = self ** other
return self
def __rpow__(self, other):
return NotImplemented
def __repr__(self):
s = repr(self.__array__()).replace('array', 'matrix')
# now, 'matrix' has 6 letters, and 'array' 5, so the columns don't
# line up anymore. We need to add a space.
l = s.splitlines()
for i in range(1, len(l)):
if l[i]:
l[i] = ' ' + l[i]
return '\n'.join(l)
def __str__(self):
return str(self.__array__())
def _align(self, axis):
"""A convenience function for operations that need to preserve axis
orientation.
"""
if axis is None:
return self[0, 0]
elif axis==0:
return self
elif axis==1:
return self.transpose()
else:
raise ValueError("unsupported axis")
def _collapse(self, axis):
"""A convenience function for operations that want to collapse
to a scalar like _align, but are using keepdims=True
"""
if axis is None:
return self[0, 0]
else:
return self
# Necessary because base-class tolist expects dimension
# reduction by x[0]
def tolist(self):
"""
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]]
"""
return self.__array__().tolist()
# To preserve orientation of result...
def sum(self, axis=None, dtype=None, out=None):
"""
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.]])
"""
return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)
# To update docstring from array to matrix...
def squeeze(self, axis=None):
"""
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]])
"""
return N.ndarray.squeeze(self, axis=axis)
# To update docstring from array to matrix...
def flatten(self, order='C'):
"""
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]])
"""
return N.ndarray.flatten(self, order=order)
def mean(self, axis=None, dtype=None, out=None):
"""
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]])
"""
return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)
def std(self, axis=None, dtype=None, out=None, ddof=0):
"""
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]])
"""
return N.ndarray.std(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
def var(self, axis=None, dtype=None, out=None, ddof=0):
"""
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]])
"""
return N.ndarray.var(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
def prod(self, axis=None, dtype=None, out=None):
"""
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]])
"""
return N.ndarray.prod(self, axis, dtype, out, keepdims=True)._collapse(axis)
def any(self, axis=None, out=None):
"""
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`
"""
return N.ndarray.any(self, axis, out, keepdims=True)._collapse(axis)
def all(self, axis=None, out=None):
"""
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)
"""
return N.ndarray.all(self, axis, out, keepdims=True)._collapse(axis)
def max(self, axis=None, out=None):
"""
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]])
"""
return N.ndarray.max(self, axis, out, keepdims=True)._collapse(axis)
def argmax(self, axis=None, out=None):
"""
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]])
"""
return N.ndarray.argmax(self, axis, out)._align(axis)
def min(self, axis=None, out=None):
"""
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]])
"""
return N.ndarray.min(self, axis, out, keepdims=True)._collapse(axis)
def argmin(self, axis=None, out=None):
"""
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]])
"""
return N.ndarray.argmin(self, axis, out)._align(axis)
def ptp(self, axis=None, out=None):
"""
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]])
"""
return N.ndarray.ptp(self, axis, out)._align(axis)
def getI(self):
"""
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.]])
"""
M, N = self.shape
if M == N:
from numpy.dual import inv as func
else:
from numpy.dual import pinv as func
return asmatrix(func(self))
def getA(self):
"""
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]])
"""
return self.__array__()
def getA1(self):
"""
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])
"""
return self.__array__().ravel()
def ravel(self, order='C'):
"""
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
"""
return N.ndarray.ravel(self, order=order)
def getT(self):
"""
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]])
"""
return self.transpose()
def getH(self):
"""
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]])
"""
if issubclass(self.dtype.type, N.complexfloating):
return self.transpose().conjugate()
else:
return self.transpose()
T = property(getT, None)
A = property(getA, None)
A1 = property(getA1, None)
H = property(getH, None)
I = property(getI, None)
def _from_string(str, gdict, ldict):
rows = str.split(';')
rowtup = []
for row in rows:
trow = row.split(',')
newrow = []
for x in trow:
newrow.extend(x.split())
trow = newrow
coltup = []
for col in trow:
col = col.strip()
try:
thismat = ldict[col]
except KeyError:
try:
thismat = gdict[col]
except KeyError:
raise KeyError("%s not found" % (col,))
coltup.append(thismat)
rowtup.append(concatenate(coltup, axis=-1))
return concatenate(rowtup, axis=0)
def bmat(obj, ldict=None, gdict=None):
"""
Build a matrix object from a string, nested sequence, or array.
Parameters
----------
obj : str or array_like
Input data. If a string, variables in the current scope may be
referenced by name.
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
--------
block :
A generalization of this function for N-d arrays, that returns normal
ndarrays.
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]])
"""
if isinstance(obj, str):
if gdict is None:
# get previous frame
frame = sys._getframe().f_back
glob_dict = frame.f_globals
loc_dict = frame.f_locals
else:
glob_dict = gdict
loc_dict = ldict
return matrix(_from_string(obj, glob_dict, loc_dict))
if isinstance(obj, (tuple, list)):
# [[A,B],[C,D]]
arr_rows = []
for row in obj:
if isinstance(row, N.ndarray): # not 2-d
return matrix(concatenate(obj, axis=-1))
else:
arr_rows.append(concatenate(row, axis=-1))
return matrix(concatenate(arr_rows, axis=0))
if isinstance(obj, N.ndarray):
return matrix(obj)
mat = asmatrix