Shortcuts on this page
r m x toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
1__all__ = ['matrix', 'bmat', 'asmatrix']
3import ast
4import sys
5import warnings
7import numpy._core.numeric as N
8from numpy._core.numeric import concatenate, isscalar
9from numpy._utils import set_module
11# While not in __all__, matrix_power used to be defined here, so we import
12# it for backward compatibility.
13from numpy.linalg import matrix_power
16def _convert_from_string(data):
17 for char in '[]':
18 data = data.replace(char, '')
20 rows = data.split(';')
21 newdata = []
22 for count, row in enumerate(rows):
23 trow = row.split(',')
24 newrow = []
25 for col in trow:
26 temp = col.split()
27 newrow.extend(map(ast.literal_eval, temp))
28 if count == 0:
29 Ncols = len(newrow)
30 elif len(newrow) != Ncols:
31 raise ValueError("Rows not the same size.")
32 newdata.append(newrow)
33 return newdata
36@set_module('numpy')
37def asmatrix(data, dtype=None):
38 """
39 Interpret the input as a matrix.
41 Unlike `matrix`, `asmatrix` does not make a copy if the input is already
42 a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
44 Parameters
45 ----------
46 data : array_like
47 Input data.
48 dtype : data-type
49 Data-type of the output matrix.
51 Returns
52 -------
53 mat : matrix
54 `data` interpreted as a matrix.
56 Examples
57 --------
58 >>> import numpy as np
59 >>> x = np.array([[1, 2], [3, 4]])
61 >>> m = np.asmatrix(x)
63 >>> x[0,0] = 5
65 >>> m
66 matrix([[5, 2],
67 [3, 4]])
69 """
70 return matrix(data, dtype=dtype, copy=False)
73@set_module('numpy')
74class matrix(N.ndarray):
75 """
76 matrix(data, dtype=None, copy=True)
78 Returns a matrix from an array-like object, or from a string of data.
80 A matrix is a specialized 2-D array that retains its 2-D nature
81 through operations. It has certain special operators, such as ``*``
82 (matrix multiplication) and ``**`` (matrix power).
84 .. note:: It is no longer recommended to use this class, even for linear
85 algebra. Instead use regular arrays. The class may be removed
86 in the future.
88 Parameters
89 ----------
90 data : array_like or string
91 If `data` is a string, it is interpreted as a matrix with commas
92 or spaces separating columns, and semicolons separating rows.
93 dtype : data-type
94 Data-type of the output matrix.
95 copy : bool
96 If `data` is already an `ndarray`, then this flag determines
97 whether the data is copied (the default), or whether a view is
98 constructed.
100 See Also
101 --------
102 array
104 Examples
105 --------
106 >>> import numpy as np
107 >>> a = np.matrix('1 2; 3 4')
108 >>> a
109 matrix([[1, 2],
110 [3, 4]])
112 >>> np.matrix([[1, 2], [3, 4]])
113 matrix([[1, 2],
114 [3, 4]])
116 """
117 __array_priority__ = 10.0
119 def __new__(subtype, data, dtype=None, copy=True):
120 warnings.warn('the matrix subclass is not the recommended way to '
121 'represent matrices or deal with linear algebra (see '
122 'https://docs.scipy.org/doc/numpy/user/'
123 'numpy-for-matlab-users.html). '
124 'Please adjust your code to use regular ndarray.',
125 PendingDeprecationWarning, stacklevel=2)
126 if isinstance(data, matrix):
127 dtype2 = data.dtype
128 if (dtype is None):
129 dtype = dtype2
130 if (dtype2 == dtype) and (not copy):
131 return data
132 return data.astype(dtype)
134 if isinstance(data, N.ndarray):
135 if dtype is None:
136 intype = data.dtype
137 else:
138 intype = N.dtype(dtype)
139 new = data.view(subtype)
140 if intype != data.dtype:
141 return new.astype(intype)
142 if copy:
143 return new.copy()
144 else:
145 return new
147 if isinstance(data, str):
148 data = _convert_from_string(data)
150 # now convert data to an array
151 copy = None if not copy else True
152 arr = N.array(data, dtype=dtype, copy=copy)
153 ndim = arr.ndim
154 shape = arr.shape
155 if (ndim > 2):
156 raise ValueError("matrix must be 2-dimensional")
157 elif ndim == 0:
158 shape = (1, 1)
159 elif ndim == 1:
160 shape = (1, shape[0])
162 order = 'C'
163 if (ndim == 2) and arr.flags.fortran:
164 order = 'F'
166 if not (order or arr.flags.contiguous):
167 arr = arr.copy()
169 ret = N.ndarray.__new__(subtype, shape, arr.dtype,
170 buffer=arr,
171 order=order)
172 return ret
174 def __array_finalize__(self, obj):
175 self._getitem = False
176 if (isinstance(obj, matrix) and obj._getitem):
177 return
178 ndim = self.ndim
179 if (ndim == 2):
180 return
181 if (ndim > 2):
182 newshape = tuple(x for x in self.shape if x > 1)
183 ndim = len(newshape)
184 if ndim == 2:
185 self.shape = newshape
186 return
187 elif (ndim > 2):
188 raise ValueError("shape too large to be a matrix.")
189 else:
190 newshape = self.shape
191 if ndim == 0:
192 self.shape = (1, 1)
193 elif ndim == 1:
194 self.shape = (1, newshape[0])
195 return
197 def __getitem__(self, index):
198 self._getitem = True
200 try:
201 out = N.ndarray.__getitem__(self, index)
202 finally:
203 self._getitem = False
205 if not isinstance(out, N.ndarray):
206 return out
208 if out.ndim == 0:
209 return out[()]
210 if out.ndim == 1:
211 sh = out.shape[0]
212 # Determine when we should have a column array
213 try:
214 n = len(index)
215 except Exception:
216 n = 0
217 if n > 1 and isscalar(index[1]):
218 out.shape = (sh, 1)
219 else:
220 out.shape = (1, sh)
221 return out
223 def __mul__(self, other):
224 if isinstance(other, (N.ndarray, list, tuple)):
225 # This promotes 1-D vectors to row vectors
226 return N.dot(self, asmatrix(other))
227 if isscalar(other) or not hasattr(other, '__rmul__'):
228 return N.dot(self, other)
229 return NotImplemented
231 def __rmul__(self, other):
232 return N.dot(other, self)
234 def __imul__(self, other):
235 self[:] = self * other
236 return self
238 def __pow__(self, other):
239 return matrix_power(self, other)
241 def __ipow__(self, other):
242 self[:] = self ** other
243 return self
245 def __rpow__(self, other):
246 return NotImplemented
248 def _align(self, axis):
249 """A convenience function for operations that need to preserve axis
250 orientation.
251 """
252 if axis is None:
253 return self[0, 0]
254 elif axis == 0:
255 return self
256 elif axis == 1:
257 return self.transpose()
258 else:
259 raise ValueError("unsupported axis")
261 def _collapse(self, axis):
262 """A convenience function for operations that want to collapse
263 to a scalar like _align, but are using keepdims=True
264 """
265 if axis is None:
266 return self[0, 0]
267 else:
268 return self
270 # Necessary because base-class tolist expects dimension
271 # reduction by x[0]
272 def tolist(self):
273 """
274 Return the matrix as a (possibly nested) list.
276 See `ndarray.tolist` for full documentation.
278 See Also
279 --------
280 ndarray.tolist
282 Examples
283 --------
284 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
285 matrix([[ 0, 1, 2, 3],
286 [ 4, 5, 6, 7],
287 [ 8, 9, 10, 11]])
288 >>> x.tolist()
289 [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
291 """
292 return self.__array__().tolist()
294 # To preserve orientation of result...
295 def sum(self, axis=None, dtype=None, out=None):
296 """
297 Returns the sum of the matrix elements, along the given axis.
299 Refer to `numpy.sum` for full documentation.
301 See Also
302 --------
303 numpy.sum
305 Notes
306 -----
307 This is the same as `ndarray.sum`, except that where an `ndarray` would
308 be returned, a `matrix` object is returned instead.
310 Examples
311 --------
312 >>> x = np.matrix([[1, 2], [4, 3]])
313 >>> x.sum()
314 10
315 >>> x.sum(axis=1)
316 matrix([[3],
317 [7]])
318 >>> x.sum(axis=1, dtype='float')
319 matrix([[3.],
320 [7.]])
321 >>> out = np.zeros((2, 1), dtype='float')
322 >>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))
323 matrix([[3.],
324 [7.]])
326 """
327 return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)
329 # To update docstring from array to matrix...
330 def squeeze(self, axis=None):
331 """
332 Return a possibly reshaped matrix.
334 Refer to `numpy.squeeze` for more documentation.
336 Parameters
337 ----------
338 axis : None or int or tuple of ints, optional
339 Selects a subset of the axes of length one in the shape.
340 If an axis is selected with shape entry greater than one,
341 an error is raised.
343 Returns
344 -------
345 squeezed : matrix
346 The matrix, but as a (1, N) matrix if it had shape (N, 1).
348 See Also
349 --------
350 numpy.squeeze : related function
352 Notes
353 -----
354 If `m` has a single column then that column is returned
355 as the single row of a matrix. Otherwise `m` is returned.
356 The returned matrix is always either `m` itself or a view into `m`.
357 Supplying an axis keyword argument will not affect the returned matrix
358 but it may cause an error to be raised.
360 Examples
361 --------
362 >>> c = np.matrix([[1], [2]])
363 >>> c
364 matrix([[1],
365 [2]])
366 >>> c.squeeze()
367 matrix([[1, 2]])
368 >>> r = c.T
369 >>> r
370 matrix([[1, 2]])
371 >>> r.squeeze()
372 matrix([[1, 2]])
373 >>> m = np.matrix([[1, 2], [3, 4]])
374 >>> m.squeeze()
375 matrix([[1, 2],
376 [3, 4]])
378 """
379 return N.ndarray.squeeze(self, axis=axis)
381 # To update docstring from array to matrix...
382 def flatten(self, order='C'):
383 """
384 Return a flattened copy of the matrix.
386 All `N` elements of the matrix are placed into a single row.
388 Parameters
389 ----------
390 order : {'C', 'F', 'A', 'K'}, optional
391 'C' means to flatten in row-major (C-style) order. 'F' means to
392 flatten in column-major (Fortran-style) order. 'A' means to
393 flatten in column-major order if `m` is Fortran *contiguous* in
394 memory, row-major order otherwise. 'K' means to flatten `m` in
395 the order the elements occur in memory. The default is 'C'.
397 Returns
398 -------
399 y : matrix
400 A copy of the matrix, flattened to a `(1, N)` matrix where `N`
401 is the number of elements in the original matrix.
403 See Also
404 --------
405 ravel : Return a flattened array.
406 flat : A 1-D flat iterator over the matrix.
408 Examples
409 --------
410 >>> m = np.matrix([[1,2], [3,4]])
411 >>> m.flatten()
412 matrix([[1, 2, 3, 4]])
413 >>> m.flatten('F')
414 matrix([[1, 3, 2, 4]])
416 """
417 return N.ndarray.flatten(self, order=order)
419 def mean(self, axis=None, dtype=None, out=None):
420 """
421 Returns the average of the matrix elements along the given axis.
423 Refer to `numpy.mean` for full documentation.
425 See Also
426 --------
427 numpy.mean
429 Notes
430 -----
431 Same as `ndarray.mean` except that, where that returns an `ndarray`,
432 this returns a `matrix` object.
434 Examples
435 --------
436 >>> x = np.matrix(np.arange(12).reshape((3, 4)))
437 >>> x
438 matrix([[ 0, 1, 2, 3],
439 [ 4, 5, 6, 7],
440 [ 8, 9, 10, 11]])
441 >>> x.mean()
442 5.5
443 >>> x.mean(0)
444 matrix([[4., 5., 6., 7.]])
445 >>> x.mean(1)
446 matrix([[ 1.5],
447 [ 5.5],
448 [ 9.5]])
450 """
451 return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)
453 def std(self, axis=None, dtype=None, out=None, ddof=0):
454 """
455 Return the standard deviation of the array elements along the given axis.
457 Refer to `numpy.std` for full documentation.
459 See Also
460 --------
461 numpy.std
463 Notes
464 -----
465 This is the same as `ndarray.std`, except that where an `ndarray` would
466 be returned, a `matrix` object is returned instead.
468 Examples
469 --------
470 >>> x = np.matrix(np.arange(12).reshape((3, 4)))
471 >>> x
472 matrix([[ 0, 1, 2, 3],
473 [ 4, 5, 6, 7],
474 [ 8, 9, 10, 11]])
475 >>> x.std()
476 3.4520525295346629 # may vary
477 >>> x.std(0)
478 matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary
479 >>> x.std(1)
480 matrix([[ 1.11803399],
481 [ 1.11803399],
482 [ 1.11803399]])
484 """
485 return N.ndarray.std(self, axis, dtype, out, ddof,
486 keepdims=True)._collapse(axis)
488 def var(self, axis=None, dtype=None, out=None, ddof=0):
489 """
490 Returns the variance of the matrix elements, along the given axis.
492 Refer to `numpy.var` for full documentation.
494 See Also
495 --------
496 numpy.var
498 Notes
499 -----
500 This is the same as `ndarray.var`, except that where an `ndarray` would
501 be returned, a `matrix` object is returned instead.
503 Examples
504 --------
505 >>> x = np.matrix(np.arange(12).reshape((3, 4)))
506 >>> x
507 matrix([[ 0, 1, 2, 3],
508 [ 4, 5, 6, 7],
509 [ 8, 9, 10, 11]])
510 >>> x.var()
511 11.916666666666666
512 >>> x.var(0)
513 matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary
514 >>> x.var(1)
515 matrix([[1.25],
516 [1.25],
517 [1.25]])
519 """
520 return N.ndarray.var(self, axis, dtype, out, ddof,
521 keepdims=True)._collapse(axis)
523 def prod(self, axis=None, dtype=None, out=None):
524 """
525 Return the product of the array elements over the given axis.
527 Refer to `prod` for full documentation.
529 See Also
530 --------
531 prod, ndarray.prod
533 Notes
534 -----
535 Same as `ndarray.prod`, except, where that returns an `ndarray`, this
536 returns a `matrix` object instead.
538 Examples
539 --------
540 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
541 matrix([[ 0, 1, 2, 3],
542 [ 4, 5, 6, 7],
543 [ 8, 9, 10, 11]])
544 >>> x.prod()
545 0
546 >>> x.prod(0)
547 matrix([[ 0, 45, 120, 231]])
548 >>> x.prod(1)
549 matrix([[ 0],
550 [ 840],
551 [7920]])
553 """
554 return N.ndarray.prod(self, axis, dtype, out, keepdims=True)._collapse(axis)
556 def any(self, axis=None, out=None):
557 """
558 Test whether any array element along a given axis evaluates to True.
560 Refer to `numpy.any` for full documentation.
562 Parameters
563 ----------
564 axis : int, optional
565 Axis along which logical OR is performed
566 out : ndarray, optional
567 Output to existing array instead of creating new one, must have
568 same shape as expected output
570 Returns
571 -------
572 any : bool, ndarray
573 Returns a single bool if `axis` is ``None``; otherwise,
574 returns `ndarray`
576 """
577 return N.ndarray.any(self, axis, out, keepdims=True)._collapse(axis)
579 def all(self, axis=None, out=None):
580 """
581 Test whether all matrix elements along a given axis evaluate to True.
583 Parameters
584 ----------
585 See `numpy.all` for complete descriptions
587 See Also
588 --------
589 numpy.all
591 Notes
592 -----
593 This is the same as `ndarray.all`, but it returns a `matrix` object.
595 Examples
596 --------
597 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
598 matrix([[ 0, 1, 2, 3],
599 [ 4, 5, 6, 7],
600 [ 8, 9, 10, 11]])
601 >>> y = x[0]; y
602 matrix([[0, 1, 2, 3]])
603 >>> (x == y)
604 matrix([[ True, True, True, True],
605 [False, False, False, False],
606 [False, False, False, False]])
607 >>> (x == y).all()
608 False
609 >>> (x == y).all(0)
610 matrix([[False, False, False, False]])
611 >>> (x == y).all(1)
612 matrix([[ True],
613 [False],
614 [False]])
616 """
617 return N.ndarray.all(self, axis, out, keepdims=True)._collapse(axis)
619 def max(self, axis=None, out=None):
620 """
621 Return the maximum value along an axis.
623 Parameters
624 ----------
625 See `amax` for complete descriptions
627 See Also
628 --------
629 amax, ndarray.max
631 Notes
632 -----
633 This is the same as `ndarray.max`, but returns a `matrix` object
634 where `ndarray.max` would return an ndarray.
636 Examples
637 --------
638 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
639 matrix([[ 0, 1, 2, 3],
640 [ 4, 5, 6, 7],
641 [ 8, 9, 10, 11]])
642 >>> x.max()
643 11
644 >>> x.max(0)
645 matrix([[ 8, 9, 10, 11]])
646 >>> x.max(1)
647 matrix([[ 3],
648 [ 7],
649 [11]])
651 """
652 return N.ndarray.max(self, axis, out, keepdims=True)._collapse(axis)
654 def argmax(self, axis=None, out=None):
655 """
656 Indexes of the maximum values along an axis.
658 Return the indexes of the first occurrences of the maximum values
659 along the specified axis. If axis is None, the index is for the
660 flattened matrix.
662 Parameters
663 ----------
664 See `numpy.argmax` for complete descriptions
666 See Also
667 --------
668 numpy.argmax
670 Notes
671 -----
672 This is the same as `ndarray.argmax`, but returns a `matrix` object
673 where `ndarray.argmax` would return an `ndarray`.
675 Examples
676 --------
677 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
678 matrix([[ 0, 1, 2, 3],
679 [ 4, 5, 6, 7],
680 [ 8, 9, 10, 11]])
681 >>> x.argmax()
682 11
683 >>> x.argmax(0)
684 matrix([[2, 2, 2, 2]])
685 >>> x.argmax(1)
686 matrix([[3],
687 [3],
688 [3]])
690 """
691 return N.ndarray.argmax(self, axis, out)._align(axis)
693 def min(self, axis=None, out=None):
694 """
695 Return the minimum value along an axis.
697 Parameters
698 ----------
699 See `amin` for complete descriptions.
701 See Also
702 --------
703 amin, ndarray.min
705 Notes
706 -----
707 This is the same as `ndarray.min`, but returns a `matrix` object
708 where `ndarray.min` would return an ndarray.
710 Examples
711 --------
712 >>> x = -np.matrix(np.arange(12).reshape((3,4))); x
713 matrix([[ 0, -1, -2, -3],
714 [ -4, -5, -6, -7],
715 [ -8, -9, -10, -11]])
716 >>> x.min()
717 -11
718 >>> x.min(0)
719 matrix([[ -8, -9, -10, -11]])
720 >>> x.min(1)
721 matrix([[ -3],
722 [ -7],
723 [-11]])
725 """
726 return N.ndarray.min(self, axis, out, keepdims=True)._collapse(axis)
728 def argmin(self, axis=None, out=None):
729 """
730 Indexes of the minimum values along an axis.
732 Return the indexes of the first occurrences of the minimum values
733 along the specified axis. If axis is None, the index is for the
734 flattened matrix.
736 Parameters
737 ----------
738 See `numpy.argmin` for complete descriptions.
740 See Also
741 --------
742 numpy.argmin
744 Notes
745 -----
746 This is the same as `ndarray.argmin`, but returns a `matrix` object
747 where `ndarray.argmin` would return an `ndarray`.
749 Examples
750 --------
751 >>> x = -np.matrix(np.arange(12).reshape((3,4))); x
752 matrix([[ 0, -1, -2, -3],
753 [ -4, -5, -6, -7],
754 [ -8, -9, -10, -11]])
755 >>> x.argmin()
756 11
757 >>> x.argmin(0)
758 matrix([[2, 2, 2, 2]])
759 >>> x.argmin(1)
760 matrix([[3],
761 [3],
762 [3]])
764 """
765 return N.ndarray.argmin(self, axis, out)._align(axis)
767 def ptp(self, axis=None, out=None):
768 """
769 Peak-to-peak (maximum - minimum) value along the given axis.
771 Refer to `numpy.ptp` for full documentation.
773 See Also
774 --------
775 numpy.ptp
777 Notes
778 -----
779 Same as `ndarray.ptp`, except, where that would return an `ndarray` object,
780 this returns a `matrix` object.
782 Examples
783 --------
784 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
785 matrix([[ 0, 1, 2, 3],
786 [ 4, 5, 6, 7],
787 [ 8, 9, 10, 11]])
788 >>> x.ptp()
789 11
790 >>> x.ptp(0)
791 matrix([[8, 8, 8, 8]])
792 >>> x.ptp(1)
793 matrix([[3],
794 [3],
795 [3]])
797 """
798 return N.ptp(self, axis, out)._align(axis)
800 @property
801 def I(self): # noqa: E743
802 """
803 Returns the (multiplicative) inverse of invertible `self`.
805 Parameters
806 ----------
807 None
809 Returns
810 -------
811 ret : matrix object
812 If `self` is non-singular, `ret` is such that ``ret * self`` ==
813 ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return
814 ``True``.
816 Raises
817 ------
818 numpy.linalg.LinAlgError: Singular matrix
819 If `self` is singular.
821 See Also
822 --------
823 linalg.inv
825 Examples
826 --------
827 >>> m = np.matrix('[1, 2; 3, 4]'); m
828 matrix([[1, 2],
829 [3, 4]])
830 >>> m.getI()
831 matrix([[-2. , 1. ],
832 [ 1.5, -0.5]])
833 >>> m.getI() * m
834 matrix([[ 1., 0.], # may vary
835 [ 0., 1.]])
837 """
838 M, N = self.shape
839 if M == N:
840 from numpy.linalg import inv as func
841 else:
842 from numpy.linalg import pinv as func
843 return asmatrix(func(self))
845 @property
846 def A(self):
847 """
848 Return `self` as an `ndarray` object.
850 Equivalent to ``np.asarray(self)``.
852 Parameters
853 ----------
854 None
856 Returns
857 -------
858 ret : ndarray
859 `self` as an `ndarray`
861 Examples
862 --------
863 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
864 matrix([[ 0, 1, 2, 3],
865 [ 4, 5, 6, 7],
866 [ 8, 9, 10, 11]])
867 >>> x.getA()
868 array([[ 0, 1, 2, 3],
869 [ 4, 5, 6, 7],
870 [ 8, 9, 10, 11]])
872 """
873 return self.__array__()
875 @property
876 def A1(self):
877 """
878 Return `self` as a flattened `ndarray`.
880 Equivalent to ``np.asarray(x).ravel()``
882 Parameters
883 ----------
884 None
886 Returns
887 -------
888 ret : ndarray
889 `self`, 1-D, as an `ndarray`
891 Examples
892 --------
893 >>> x = np.matrix(np.arange(12).reshape((3,4))); x
894 matrix([[ 0, 1, 2, 3],
895 [ 4, 5, 6, 7],
896 [ 8, 9, 10, 11]])
897 >>> x.getA1()
898 array([ 0, 1, 2, ..., 9, 10, 11])
901 """
902 return self.__array__().ravel()
904 def ravel(self, order='C'):
905 """
906 Return a flattened matrix.
908 Refer to `numpy.ravel` for more documentation.
910 Parameters
911 ----------
912 order : {'C', 'F', 'A', 'K'}, optional
913 The elements of `m` are read using this index order. 'C' means to
914 index the elements in C-like order, with the last axis index
915 changing fastest, back to the first axis index changing slowest.
916 'F' means to index the elements in Fortran-like index order, with
917 the first index changing fastest, and the last index changing
918 slowest. Note that the 'C' and 'F' options take no account of the
919 memory layout of the underlying array, and only refer to the order
920 of axis indexing. 'A' means to read the elements in Fortran-like
921 index order if `m` is Fortran *contiguous* in memory, C-like order
922 otherwise. 'K' means to read the elements in the order they occur
923 in memory, except for reversing the data when strides are negative.
924 By default, 'C' index order is used.
926 Returns
927 -------
928 ret : matrix
929 Return the matrix flattened to shape `(1, N)` where `N`
930 is the number of elements in the original matrix.
931 A copy is made only if necessary.
933 See Also
934 --------
935 matrix.flatten : returns a similar output matrix but always a copy
936 matrix.flat : a flat iterator on the array.
937 numpy.ravel : related function which returns an ndarray
939 """
940 return N.ndarray.ravel(self, order=order)
942 @property
943 def T(self):
944 """
945 Returns the transpose of the matrix.
947 Does *not* conjugate! For the complex conjugate transpose, use ``.H``.
949 Parameters
950 ----------
951 None
953 Returns
954 -------
955 ret : matrix object
956 The (non-conjugated) transpose of the matrix.
958 See Also
959 --------
960 transpose, getH
962 Examples
963 --------
964 >>> m = np.matrix('[1, 2; 3, 4]')
965 >>> m
966 matrix([[1, 2],
967 [3, 4]])
968 >>> m.getT()
969 matrix([[1, 3],
970 [2, 4]])
972 """
973 return self.transpose()
975 @property
976 def H(self):
977 """
978 Returns the (complex) conjugate transpose of `self`.
980 Equivalent to ``np.transpose(self)`` if `self` is real-valued.
982 Parameters
983 ----------
984 None
986 Returns
987 -------
988 ret : matrix object
989 complex conjugate transpose of `self`
991 Examples
992 --------
993 >>> x = np.matrix(np.arange(12).reshape((3,4)))
994 >>> z = x - 1j*x; z
995 matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],
996 [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],
997 [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])
998 >>> z.getH()
999 matrix([[ 0. -0.j, 4. +4.j, 8. +8.j],
1000 [ 1. +1.j, 5. +5.j, 9. +9.j],
1001 [ 2. +2.j, 6. +6.j, 10.+10.j],
1002 [ 3. +3.j, 7. +7.j, 11.+11.j]])
1004 """
1005 if issubclass(self.dtype.type, N.complexfloating):
1006 return self.transpose().conjugate()
1007 else:
1008 return self.transpose()
1010 # kept for compatibility
1011 getT = T.fget
1012 getA = A.fget
1013 getA1 = A1.fget
1014 getH = H.fget
1015 getI = I.fget
1017def _from_string(str, gdict, ldict):
1018 rows = str.split(';')
1019 rowtup = []
1020 for row in rows:
1021 trow = row.split(',')
1022 newrow = []
1023 for x in trow:
1024 newrow.extend(x.split())
1025 trow = newrow
1026 coltup = []
1027 for col in trow:
1028 col = col.strip()
1029 try:
1030 thismat = ldict[col]
1031 except KeyError:
1032 try:
1033 thismat = gdict[col]
1034 except KeyError as e:
1035 raise NameError(f"name {col!r} is not defined") from None
1037 coltup.append(thismat)
1038 rowtup.append(concatenate(coltup, axis=-1))
1039 return concatenate(rowtup, axis=0)
1042@set_module('numpy')
1043def bmat(obj, ldict=None, gdict=None):
1044 """
1045 Build a matrix object from a string, nested sequence, or array.
1047 Parameters
1048 ----------
1049 obj : str or array_like
1050 Input data. If a string, variables in the current scope may be
1051 referenced by name.
1052 ldict : dict, optional
1053 A dictionary that replaces local operands in current frame.
1054 Ignored if `obj` is not a string or `gdict` is None.
1055 gdict : dict, optional
1056 A dictionary that replaces global operands in current frame.
1057 Ignored if `obj` is not a string.
1059 Returns
1060 -------
1061 out : matrix
1062 Returns a matrix object, which is a specialized 2-D array.
1064 See Also
1065 --------
1066 block :
1067 A generalization of this function for N-d arrays, that returns normal
1068 ndarrays.
1070 Examples
1071 --------
1072 >>> import numpy as np
1073 >>> A = np.asmatrix('1 1; 1 1')
1074 >>> B = np.asmatrix('2 2; 2 2')
1075 >>> C = np.asmatrix('3 4; 5 6')
1076 >>> D = np.asmatrix('7 8; 9 0')
1078 All the following expressions construct the same block matrix:
1080 >>> np.bmat([[A, B], [C, D]])
1081 matrix([[1, 1, 2, 2],
1082 [1, 1, 2, 2],
1083 [3, 4, 7, 8],
1084 [5, 6, 9, 0]])
1085 >>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])
1086 matrix([[1, 1, 2, 2],
1087 [1, 1, 2, 2],
1088 [3, 4, 7, 8],
1089 [5, 6, 9, 0]])
1090 >>> np.bmat('A,B; C,D')
1091 matrix([[1, 1, 2, 2],
1092 [1, 1, 2, 2],
1093 [3, 4, 7, 8],
1094 [5, 6, 9, 0]])
1096 """
1097 if isinstance(obj, str):
1098 if gdict is None:
1099 # get previous frame
1100 frame = sys._getframe().f_back
1101 glob_dict = frame.f_globals
1102 loc_dict = frame.f_locals
1103 else:
1104 glob_dict = gdict
1105 loc_dict = ldict
1107 return matrix(_from_string(obj, glob_dict, loc_dict))
1109 if isinstance(obj, (tuple, list)):
1110 # [[A,B],[C,D]]
1111 arr_rows = []
1112 for row in obj:
1113 if isinstance(row, N.ndarray): # not 2-d
1114 return matrix(concatenate(obj, axis=-1))
1115 else:
1116 arr_rows.append(concatenate(row, axis=-1))
1117 return matrix(concatenate(arr_rows, axis=0))
1118 if isinstance(obj, N.ndarray):
1119 return matrix(obj)