1120 lines
30 KiB
Python
1120 lines
30 KiB
Python
|
__all__ = ['matrix', 'bmat', 'asmatrix']
|
||
|
|
|
||
|
|
import ast
|
||
|
|
import sys
|
||
|
|
import warnings
|
||
|
|
|
||
|
|
import numpy._core.numeric as N
|
||
|
|
from numpy._core.numeric import concatenate, isscalar
|
||
|
|
from numpy._utils import set_module
|
||
|
|
|
||
|
|
# While not in __all__, matrix_power used to be defined here, so we import
|
||
|
|
# it for backward compatibility.
|
||
|
|
from numpy.linalg import matrix_power
|
||
|
|
|
||
|
|
|
||
|
|
def _convert_from_string(data):
|
||
|
|
for char in '[]':
|
||
|
|
data = data.replace(char, '')
|
||
|
|
|
||
|
|
rows = data.split(';')
|
||
|
|
newdata = []
|
||
|
|
for count, row in enumerate(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.")
|
||
|
|
newdata.append(newrow)
|
||
|
|
return newdata
|
||
|
|
|
||
|
|
|
||
|
|
@set_module('numpy')
|
||
|
|
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
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> 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)
|
||
|
|
|
||
|
|
|
||
|
|
@set_module('numpy')
|
||
|
|
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).
|
||
|
|
|
||
|
|
.. note:: It is no longer recommended to use this class, even for linear
|
||
|
|
algebra. Instead use regular arrays. The class may be removed
|
||
|
|
in the future.
|
||
|
|
|
||
|
|
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
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> a = np.matrix('1 2; 3 4')
|
||
|
|
>>> a
|
||
|
|
matrix([[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):
|
||
|
|
warnings.warn('the matrix subclass is not the recommended way to '
|
||
|
|
'represent matrices or deal with linear algebra (see '
|
||
|
|
'https://docs.scipy.org/doc/numpy/user/'
|
||
|
|
'numpy-for-matlab-users.html). '
|
||
|
|
'Please adjust your code to use regular ndarray.',
|
||
|
|
PendingDeprecationWarning, stacklevel=2)
|
||
|
|
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
|
||
|
|
copy = None if not copy else True
|
||
|
|
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 _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((2, 1), dtype='float')
|
||
|
|
>>> x.sum(axis=1, dtype='float', out=np.asmatrix(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 axes of length one 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 # may vary
|
||
|
|
>>> x.std(0)
|
||
|
|
matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary
|
||
|
|
>>> 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]]) # may vary
|
||
|
|
>>> 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]])
|
||
|
|
>>> (x == y).all()
|
||
|
|
False
|
||
|
|
>>> (x == y).all(0)
|
||
|
|
matrix([[False, False, False, False]])
|
||
|
|
>>> (x == y).all(1)
|
||
|
|
matrix([[ True],
|
||
|
|
[False],
|
||
|
|
[False]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
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.ptp(self, axis, out)._align(axis)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def I(self): # noqa: E743
|
||
|
|
"""
|
||
|
|
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.], # may vary
|
||
|
|
[ 0., 1.]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
M, N = self.shape
|
||
|
|
if M == N:
|
||
|
|
from numpy.linalg import inv as func
|
||
|
|
else:
|
||
|
|
from numpy.linalg import pinv as func
|
||
|
|
return asmatrix(func(self))
|
||
|
|
|
||
|
|
@property
|
||
|
|
def A(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__()
|
||
|
|
|
||
|
|
@property
|
||
|
|
def A1(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, ..., 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)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def T(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()
|
||
|
|
|
||
|
|
@property
|
||
|
|
def H(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()
|
||
|
|
|
||
|
|
# kept for compatibility
|
||
|
|
getT = T.fget
|
||
|
|
getA = A.fget
|
||
|
|
getA1 = A1.fget
|
||
|
|
getH = H.fget
|
||
|
|
getI = I.fget
|
||
|
|
|
||
|
|
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 as e:
|
||
|
|
raise NameError(f"name {col!r} is not defined") from None
|
||
|
|
|
||
|
|
coltup.append(thismat)
|
||
|
|
rowtup.append(concatenate(coltup, axis=-1))
|
||
|
|
return concatenate(rowtup, axis=0)
|
||
|
|
|
||
|
|
|
||
|
|
@set_module('numpy')
|
||
|
|
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
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> A = np.asmatrix('1 1; 1 1')
|
||
|
|
>>> B = np.asmatrix('2 2; 2 2')
|
||
|
|
>>> C = np.asmatrix('3 4; 5 6')
|
||
|
|
>>> D = np.asmatrix('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)
|