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1__all__ = ['matrix', 'bmat', 'mat', 'asmatrix']

3import sys

4import warnings

5import ast

6import numpy.core.numeric as N

7from numpy.core.numeric import concatenate, isscalar

8from numpy.core.overrides import set_module

9# While not in __all__, matrix_power used to be defined here, so we import

10# it for backward compatibility.

11from numpy.linalg import matrix_power

14def _convert_from_string(data):

15 for char in '[]':

16 data = data.replace(char, '')

18 rows = data.split(';')

19 newdata = []

20 count = 0

21 for row in rows:

22 trow = row.split(',')

23 newrow = []

24 for col in trow:

25 temp = col.split()

26 newrow.extend(map(ast.literal_eval, temp))

27 if count == 0:

28 Ncols = len(newrow)

29 elif len(newrow) != Ncols:

30 raise ValueError("Rows not the same size.")

31 count += 1

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 >>> x = np.array([[1, 2], [3, 4]])

60 >>> m = np.asmatrix(x)

62 >>> x[0,0] = 5

64 >>> m

65 matrix([[5, 2],

66 [3, 4]])

68 """

69 return matrix(data, dtype=dtype, copy=False)

72@set_module('numpy')

73class matrix(N.ndarray):

74 """

75 matrix(data, dtype=None, copy=True)

77 .. note:: It is no longer recommended to use this class, even for linear

78 algebra. Instead use regular arrays. The class may be removed

79 in the future.

81 Returns a matrix from an array-like object, or from a string of data.

82 A matrix is a specialized 2-D array that retains its 2-D nature

83 through operations. It has certain special operators, such as ``*``

84 (matrix multiplication) and ``**`` (matrix power).

86 Parameters

87 ----------

88 data : array_like or string

89 If `data` is a string, it is interpreted as a matrix with commas

90 or spaces separating columns, and semicolons separating rows.

91 dtype : data-type

92 Data-type of the output matrix.

93 copy : bool

94 If `data` is already an `ndarray`, then this flag determines

95 whether the data is copied (the default), or whether a view is

96 constructed.

98 See Also

99 --------

100 array

101

102 Examples

103 --------

104 >>> a = np.matrix('1 2; 3 4')

105 >>> a

106 matrix([[1, 2],

107 [3, 4]])

108

109 >>> np.matrix([[1, 2], [3, 4]])

110 matrix([[1, 2],

111 [3, 4]])

112

113 """

114 __array_priority__ = 10.0

115 def __new__(subtype, data, dtype=None, copy=True):

116 warnings.warn('the matrix subclass is not the recommended way to '

117 'represent matrices or deal with linear algebra (see '

118 'https://docs.scipy.org/doc/numpy/user/'

119 'numpy-for-matlab-users.html). '

120 'Please adjust your code to use regular ndarray.',

121 PendingDeprecationWarning, stacklevel=2)

122 if isinstance(data, matrix):

123 dtype2 = data.dtype

124 if (dtype is None):

125 dtype = dtype2

126 if (dtype2 == dtype) and (not copy):

127 return data

128 return data.astype(dtype)

129

130 if isinstance(data, N.ndarray):

131 if dtype is None:

132 intype = data.dtype

133 else:

134 intype = N.dtype(dtype)

135 new = data.view(subtype)

136 if intype != data.dtype:

137 return new.astype(intype)

138 if copy: return new.copy()

139 else: return new

140

141 if isinstance(data, str):

142 data = _convert_from_string(data)

143

144 # now convert data to an array

145 arr = N.array(data, dtype=dtype, copy=copy)

146 ndim = arr.ndim

147 shape = arr.shape

148 if (ndim > 2):

149 raise ValueError("matrix must be 2-dimensional")

150 elif ndim == 0:

151 shape = (1, 1)

152 elif ndim == 1:

153 shape = (1, shape[0])

154

155 order = 'C'

156 if (ndim == 2) and arr.flags.fortran:

157 order = 'F'

158

159 if not (order or arr.flags.contiguous):

160 arr = arr.copy()

161

162 ret = N.ndarray.__new__(subtype, shape, arr.dtype,

163 buffer=arr,

164 order=order)

165 return ret

166

167 def __array_finalize__(self, obj):

168 self._getitem = False

169 if (isinstance(obj, matrix) and obj._getitem): return

170 ndim = self.ndim

171 if (ndim == 2):

172 return

173 if (ndim > 2):

174 newshape = tuple([x for x in self.shape if x > 1])

175 ndim = len(newshape)

176 if ndim == 2:

177 self.shape = newshape

178 return

179 elif (ndim > 2):

180 raise ValueError("shape too large to be a matrix.")

181 else:

182 newshape = self.shape

183 if ndim == 0:

184 self.shape = (1, 1)

185 elif ndim == 1:

186 self.shape = (1, newshape[0])

187 return

188

189 def __getitem__(self, index):

190 self._getitem = True

191

192 try:

193 out = N.ndarray.__getitem__(self, index)

194 finally:

195 self._getitem = False

196

197 if not isinstance(out, N.ndarray):

198 return out

199

200 if out.ndim == 0:

201 return out[()]

202 if out.ndim == 1:

203 sh = out.shape[0]

204 # Determine when we should have a column array

205 try:

206 n = len(index)

207 except Exception:

208 n = 0

209 if n > 1 and isscalar(index[1]):

210 out.shape = (sh, 1)

211 else:

212 out.shape = (1, sh)

213 return out

214

215 def __mul__(self, other):

216 if isinstance(other, (N.ndarray, list, tuple)) :

217 # This promotes 1-D vectors to row vectors

218 return N.dot(self, asmatrix(other))

219 if isscalar(other) or not hasattr(other, '__rmul__') :

220 return N.dot(self, other)

221 return NotImplemented

222

223 def __rmul__(self, other):

224 return N.dot(other, self)

225

226 def __imul__(self, other):

227 self[:] = self * other

228 return self

229

230 def __pow__(self, other):

231 return matrix_power(self, other)

232

233 def __ipow__(self, other):

234 self[:] = self ** other

235 return self

236

237 def __rpow__(self, other):

238 return NotImplemented

239

240 def _align(self, axis):

241 """A convenience function for operations that need to preserve axis

242 orientation.

243 """

244 if axis is None:

245 return self[0, 0]

246 elif axis==0:

247 return self

248 elif axis==1:

249 return self.transpose()

250 else:

251 raise ValueError("unsupported axis")

252

253 def _collapse(self, axis):

254 """A convenience function for operations that want to collapse

255 to a scalar like _align, but are using keepdims=True

256 """

257 if axis is None:

258 return self[0, 0]

259 else:

260 return self

261

262 # Necessary because base-class tolist expects dimension

263 # reduction by x[0]

264 def tolist(self):

265 """

266 Return the matrix as a (possibly nested) list.

267

268 See `ndarray.tolist` for full documentation.

269

270 See Also

271 --------

272 ndarray.tolist

273

274 Examples

275 --------

276 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

277 matrix([[ 0, 1, 2, 3],

278 [ 4, 5, 6, 7],

279 [ 8, 9, 10, 11]])

280 >>> x.tolist()

281 [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]

282

283 """

284 return self.__array__().tolist()

285

286 # To preserve orientation of result...

287 def sum(self, axis=None, dtype=None, out=None):

288 """

289 Returns the sum of the matrix elements, along the given axis.

290

291 Refer to `numpy.sum` for full documentation.

292

293 See Also

294 --------

295 numpy.sum

296

297 Notes

298 -----

299 This is the same as `ndarray.sum`, except that where an `ndarray` would

300 be returned, a `matrix` object is returned instead.

301

302 Examples

303 --------

304 >>> x = np.matrix([[1, 2], [4, 3]])

305 >>> x.sum()

306 10

307 >>> x.sum(axis=1)

308 matrix([[3],

309 [7]])

310 >>> x.sum(axis=1, dtype='float')

311 matrix([[3.],

312 [7.]])

313 >>> out = np.zeros((2, 1), dtype='float')

314 >>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))

315 matrix([[3.],

316 [7.]])

317

318 """

319 return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)

320

321

322 # To update docstring from array to matrix...

323 def squeeze(self, axis=None):

324 """

325 Return a possibly reshaped matrix.

326

327 Refer to `numpy.squeeze` for more documentation.

328

329 Parameters

330 ----------

331 axis : None or int or tuple of ints, optional

332 Selects a subset of the axes of length one in the shape.

333 If an axis is selected with shape entry greater than one,

334 an error is raised.

335

336 Returns

337 -------

338 squeezed : matrix

339 The matrix, but as a (1, N) matrix if it had shape (N, 1).

340

341 See Also

342 --------

343 numpy.squeeze : related function

344

345 Notes

346 -----

347 If `m` has a single column then that column is returned

348 as the single row of a matrix. Otherwise `m` is returned.

349 The returned matrix is always either `m` itself or a view into `m`.

350 Supplying an axis keyword argument will not affect the returned matrix

351 but it may cause an error to be raised.

352

353 Examples

354 --------

355 >>> c = np.matrix([[1], [2]])

356 >>> c

357 matrix([[1],

358 [2]])

359 >>> c.squeeze()

360 matrix([[1, 2]])

361 >>> r = c.T

362 >>> r

363 matrix([[1, 2]])

364 >>> r.squeeze()

365 matrix([[1, 2]])

366 >>> m = np.matrix([[1, 2], [3, 4]])

367 >>> m.squeeze()

368 matrix([[1, 2],

369 [3, 4]])

370

371 """

372 return N.ndarray.squeeze(self, axis=axis)

373

374

375 # To update docstring from array to matrix...

376 def flatten(self, order='C'):

377 """

378 Return a flattened copy of the matrix.

379

380 All `N` elements of the matrix are placed into a single row.

381

382 Parameters

383 ----------

384 order : {'C', 'F', 'A', 'K'}, optional

385 'C' means to flatten in row-major (C-style) order. 'F' means to

386 flatten in column-major (Fortran-style) order. 'A' means to

387 flatten in column-major order if `m` is Fortran *contiguous* in

388 memory, row-major order otherwise. 'K' means to flatten `m` in

389 the order the elements occur in memory. The default is 'C'.

390

391 Returns

392 -------

393 y : matrix

394 A copy of the matrix, flattened to a `(1, N)` matrix where `N`

395 is the number of elements in the original matrix.

396

397 See Also

398 --------

399 ravel : Return a flattened array.

400 flat : A 1-D flat iterator over the matrix.

401

402 Examples

403 --------

404 >>> m = np.matrix([[1,2], [3,4]])

405 >>> m.flatten()

406 matrix([[1, 2, 3, 4]])

407 >>> m.flatten('F')

408 matrix([[1, 3, 2, 4]])

409

410 """

411 return N.ndarray.flatten(self, order=order)

412

413 def mean(self, axis=None, dtype=None, out=None):

414 """

415 Returns the average of the matrix elements along the given axis.

416

417 Refer to `numpy.mean` for full documentation.

418

419 See Also

420 --------

421 numpy.mean

422

423 Notes

424 -----

425 Same as `ndarray.mean` except that, where that returns an `ndarray`,

426 this returns a `matrix` object.

427

428 Examples

429 --------

430 >>> x = np.matrix(np.arange(12).reshape((3, 4)))

431 >>> x

432 matrix([[ 0, 1, 2, 3],

433 [ 4, 5, 6, 7],

434 [ 8, 9, 10, 11]])

435 >>> x.mean()

436 5.5

437 >>> x.mean(0)

438 matrix([[4., 5., 6., 7.]])

439 >>> x.mean(1)

440 matrix([[ 1.5],

441 [ 5.5],

442 [ 9.5]])

443

444 """

445 return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)

446

447 def std(self, axis=None, dtype=None, out=None, ddof=0):

448 """

449 Return the standard deviation of the array elements along the given axis.

450

451 Refer to `numpy.std` for full documentation.

452

453 See Also

454 --------

455 numpy.std

456

457 Notes

458 -----

459 This is the same as `ndarray.std`, except that where an `ndarray` would

460 be returned, a `matrix` object is returned instead.

461

462 Examples

463 --------

464 >>> x = np.matrix(np.arange(12).reshape((3, 4)))

465 >>> x

466 matrix([[ 0, 1, 2, 3],

467 [ 4, 5, 6, 7],

468 [ 8, 9, 10, 11]])

469 >>> x.std()

470 3.4520525295346629 # may vary

471 >>> x.std(0)

472 matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary

473 >>> x.std(1)

474 matrix([[ 1.11803399],

475 [ 1.11803399],

476 [ 1.11803399]])

477

478 """

479 return N.ndarray.std(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)

480

481 def var(self, axis=None, dtype=None, out=None, ddof=0):

482 """

483 Returns the variance of the matrix elements, along the given axis.

484

485 Refer to `numpy.var` for full documentation.

486

487 See Also

488 --------

489 numpy.var

490

491 Notes

492 -----

493 This is the same as `ndarray.var`, except that where an `ndarray` would

494 be returned, a `matrix` object is returned instead.

495

496 Examples

497 --------

498 >>> x = np.matrix(np.arange(12).reshape((3, 4)))

499 >>> x

500 matrix([[ 0, 1, 2, 3],

501 [ 4, 5, 6, 7],

502 [ 8, 9, 10, 11]])

503 >>> x.var()

504 11.916666666666666

505 >>> x.var(0)

506 matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary

507 >>> x.var(1)

508 matrix([[1.25],

509 [1.25],

510 [1.25]])

511

512 """

513 return N.ndarray.var(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)

514

515 def prod(self, axis=None, dtype=None, out=None):

516 """

517 Return the product of the array elements over the given axis.

518

519 Refer to `prod` for full documentation.

520

521 See Also

522 --------

523 prod, ndarray.prod

524

525 Notes

526 -----

527 Same as `ndarray.prod`, except, where that returns an `ndarray`, this

528 returns a `matrix` object instead.

529

530 Examples

531 --------

532 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

533 matrix([[ 0, 1, 2, 3],

534 [ 4, 5, 6, 7],

535 [ 8, 9, 10, 11]])

536 >>> x.prod()

537 0

538 >>> x.prod(0)

539 matrix([[ 0, 45, 120, 231]])

540 >>> x.prod(1)

541 matrix([[ 0],

542 [ 840],

543 [7920]])

544

545 """

546 return N.ndarray.prod(self, axis, dtype, out, keepdims=True)._collapse(axis)

547

548 def any(self, axis=None, out=None):

549 """

550 Test whether any array element along a given axis evaluates to True.

551

552 Refer to `numpy.any` for full documentation.

553

554 Parameters

555 ----------

556 axis : int, optional

557 Axis along which logical OR is performed

558 out : ndarray, optional

559 Output to existing array instead of creating new one, must have

560 same shape as expected output

561

562 Returns

563 -------

564 any : bool, ndarray

565 Returns a single bool if `axis` is ``None``; otherwise,

566 returns `ndarray`

567

568 """

569 return N.ndarray.any(self, axis, out, keepdims=True)._collapse(axis)

570

571 def all(self, axis=None, out=None):

572 """

573 Test whether all matrix elements along a given axis evaluate to True.

574

575 Parameters

576 ----------

577 See `numpy.all` for complete descriptions

578

579 See Also

580 --------

581 numpy.all

582

583 Notes

584 -----

585 This is the same as `ndarray.all`, but it returns a `matrix` object.

586

587 Examples

588 --------

589 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

590 matrix([[ 0, 1, 2, 3],

591 [ 4, 5, 6, 7],

592 [ 8, 9, 10, 11]])

593 >>> y = x[0]; y

594 matrix([[0, 1, 2, 3]])

595 >>> (x == y)

596 matrix([[ True, True, True, True],

597 [False, False, False, False],

598 [False, False, False, False]])

599 >>> (x == y).all()

600 False

601 >>> (x == y).all(0)

602 matrix([[False, False, False, False]])

603 >>> (x == y).all(1)

604 matrix([[ True],

605 [False],

606 [False]])

607

608 """

609 return N.ndarray.all(self, axis, out, keepdims=True)._collapse(axis)

610

611 def max(self, axis=None, out=None):

612 """

613 Return the maximum value along an axis.

614

615 Parameters

616 ----------

617 See `amax` for complete descriptions

618

619 See Also

620 --------

621 amax, ndarray.max

622

623 Notes

624 -----

625 This is the same as `ndarray.max`, but returns a `matrix` object

626 where `ndarray.max` would return an ndarray.

627

628 Examples

629 --------

630 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

631 matrix([[ 0, 1, 2, 3],

632 [ 4, 5, 6, 7],

633 [ 8, 9, 10, 11]])

634 >>> x.max()

635 11

636 >>> x.max(0)

637 matrix([[ 8, 9, 10, 11]])

638 >>> x.max(1)

639 matrix([[ 3],

640 [ 7],

641 [11]])

642

643 """

644 return N.ndarray.max(self, axis, out, keepdims=True)._collapse(axis)

645

646 def argmax(self, axis=None, out=None):

647 """

648 Indexes of the maximum values along an axis.

649

650 Return the indexes of the first occurrences of the maximum values

651 along the specified axis. If axis is None, the index is for the

652 flattened matrix.

653

654 Parameters

655 ----------

656 See `numpy.argmax` for complete descriptions

657

658 See Also

659 --------

660 numpy.argmax

661

662 Notes

663 -----

664 This is the same as `ndarray.argmax`, but returns a `matrix` object

665 where `ndarray.argmax` would return an `ndarray`.

666

667 Examples

668 --------

669 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

670 matrix([[ 0, 1, 2, 3],

671 [ 4, 5, 6, 7],

672 [ 8, 9, 10, 11]])

673 >>> x.argmax()

674 11

675 >>> x.argmax(0)

676 matrix([[2, 2, 2, 2]])

677 >>> x.argmax(1)

678 matrix([[3],

679 [3],

680 [3]])

681

682 """

683 return N.ndarray.argmax(self, axis, out)._align(axis)

684

685 def min(self, axis=None, out=None):

686 """

687 Return the minimum value along an axis.

688

689 Parameters

690 ----------

691 See `amin` for complete descriptions.

692

693 See Also

694 --------

695 amin, ndarray.min

696

697 Notes

698 -----

699 This is the same as `ndarray.min`, but returns a `matrix` object

700 where `ndarray.min` would return an ndarray.

701

702 Examples

703 --------

704 >>> x = -np.matrix(np.arange(12).reshape((3,4))); x

705 matrix([[ 0, -1, -2, -3],

706 [ -4, -5, -6, -7],

707 [ -8, -9, -10, -11]])

708 >>> x.min()

709 -11

710 >>> x.min(0)

711 matrix([[ -8, -9, -10, -11]])

712 >>> x.min(1)

713 matrix([[ -3],

714 [ -7],

715 [-11]])

716

717 """

718 return N.ndarray.min(self, axis, out, keepdims=True)._collapse(axis)

719

720 def argmin(self, axis=None, out=None):

721 """

722 Indexes of the minimum values along an axis.

723

724 Return the indexes of the first occurrences of the minimum values

725 along the specified axis. If axis is None, the index is for the

726 flattened matrix.

727

728 Parameters

729 ----------

730 See `numpy.argmin` for complete descriptions.

731

732 See Also

733 --------

734 numpy.argmin

735

736 Notes

737 -----

738 This is the same as `ndarray.argmin`, but returns a `matrix` object

739 where `ndarray.argmin` would return an `ndarray`.

740

741 Examples

742 --------

743 >>> x = -np.matrix(np.arange(12).reshape((3,4))); x

744 matrix([[ 0, -1, -2, -3],

745 [ -4, -5, -6, -7],

746 [ -8, -9, -10, -11]])

747 >>> x.argmin()

748 11

749 >>> x.argmin(0)

750 matrix([[2, 2, 2, 2]])

751 >>> x.argmin(1)

752 matrix([[3],

753 [3],

754 [3]])

755

756 """

757 return N.ndarray.argmin(self, axis, out)._align(axis)

758

759 def ptp(self, axis=None, out=None):

760 """

761 Peak-to-peak (maximum - minimum) value along the given axis.

762

763 Refer to `numpy.ptp` for full documentation.

764

765 See Also

766 --------

767 numpy.ptp

768

769 Notes

770 -----

771 Same as `ndarray.ptp`, except, where that would return an `ndarray` object,

772 this returns a `matrix` object.

773

774 Examples

775 --------

776 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

777 matrix([[ 0, 1, 2, 3],

778 [ 4, 5, 6, 7],

779 [ 8, 9, 10, 11]])

780 >>> x.ptp()

781 11

782 >>> x.ptp(0)

783 matrix([[8, 8, 8, 8]])

784 >>> x.ptp(1)

785 matrix([[3],

786 [3],

787 [3]])

788

789 """

790 return N.ndarray.ptp(self, axis, out)._align(axis)

791

792 @property

793 def I(self):

794 """

795 Returns the (multiplicative) inverse of invertible `self`.

796

797 Parameters

798 ----------

799 None

800

801 Returns

802 -------

803 ret : matrix object

804 If `self` is non-singular, `ret` is such that ``ret * self`` ==

805 ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return

806 ``True``.

807

808 Raises

809 ------

810 numpy.linalg.LinAlgError: Singular matrix

811 If `self` is singular.

812

813 See Also

814 --------

815 linalg.inv

816

817 Examples

818 --------

819 >>> m = np.matrix('[1, 2; 3, 4]'); m

820 matrix([[1, 2],

821 [3, 4]])

822 >>> m.getI()

823 matrix([[-2. , 1. ],

824 [ 1.5, -0.5]])

825 >>> m.getI() * m

826 matrix([[ 1., 0.], # may vary

827 [ 0., 1.]])

828

829 """

830 M, N = self.shape

831 if M == N:

832 from numpy.linalg import inv as func

833 else:

834 from numpy.linalg import pinv as func

835 return asmatrix(func(self))

836

837 @property

838 def A(self):

839 """

840 Return `self` as an `ndarray` object.

841

842 Equivalent to ``np.asarray(self)``.

843

844 Parameters

845 ----------

846 None

847

848 Returns

849 -------

850 ret : ndarray

851 `self` as an `ndarray`

852

853 Examples

854 --------

855 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

856 matrix([[ 0, 1, 2, 3],

857 [ 4, 5, 6, 7],

858 [ 8, 9, 10, 11]])

859 >>> x.getA()

860 array([[ 0, 1, 2, 3],

861 [ 4, 5, 6, 7],

862 [ 8, 9, 10, 11]])

863

864 """

865 return self.__array__()

866

867 @property

868 def A1(self):

869 """

870 Return `self` as a flattened `ndarray`.

871

872 Equivalent to ``np.asarray(x).ravel()``

873

874 Parameters

875 ----------

876 None

877

878 Returns

879 -------

880 ret : ndarray

881 `self`, 1-D, as an `ndarray`

882

883 Examples

884 --------

885 >>> x = np.matrix(np.arange(12).reshape((3,4))); x

886 matrix([[ 0, 1, 2, 3],

887 [ 4, 5, 6, 7],

888 [ 8, 9, 10, 11]])

889 >>> x.getA1()

890 array([ 0, 1, 2, ..., 9, 10, 11])

891

892

893 """

894 return self.__array__().ravel()

895

896

897 def ravel(self, order='C'):

898 """

899 Return a flattened matrix.

900

901 Refer to `numpy.ravel` for more documentation.

902

903 Parameters

904 ----------

905 order : {'C', 'F', 'A', 'K'}, optional

906 The elements of `m` are read using this index order. 'C' means to

907 index the elements in C-like order, with the last axis index

908 changing fastest, back to the first axis index changing slowest.

909 'F' means to index the elements in Fortran-like index order, with

910 the first index changing fastest, and the last index changing

911 slowest. Note that the 'C' and 'F' options take no account of the

912 memory layout of the underlying array, and only refer to the order

913 of axis indexing. 'A' means to read the elements in Fortran-like

914 index order if `m` is Fortran *contiguous* in memory, C-like order

915 otherwise. 'K' means to read the elements in the order they occur

916 in memory, except for reversing the data when strides are negative.

917 By default, 'C' index order is used.

918

919 Returns

920 -------

921 ret : matrix

922 Return the matrix flattened to shape `(1, N)` where `N`

923 is the number of elements in the original matrix.

924 A copy is made only if necessary.

925

926 See Also

927 --------

928 matrix.flatten : returns a similar output matrix but always a copy

929 matrix.flat : a flat iterator on the array.

930 numpy.ravel : related function which returns an ndarray

931

932 """

933 return N.ndarray.ravel(self, order=order)

934

935 @property

936 def T(self):

937 """

938 Returns the transpose of the matrix.

939

940 Does *not* conjugate! For the complex conjugate transpose, use ``.H``.

941

942 Parameters

943 ----------

944 None

945

946 Returns

947 -------

948 ret : matrix object

949 The (non-conjugated) transpose of the matrix.

950

951 See Also

952 --------

953 transpose, getH

954

955 Examples

956 --------

957 >>> m = np.matrix('[1, 2; 3, 4]')

958 >>> m

959 matrix([[1, 2],

960 [3, 4]])

961 >>> m.getT()

962 matrix([[1, 3],

963 [2, 4]])

964

965 """

966 return self.transpose()

967

968 @property

969 def H(self):

970 """

971 Returns the (complex) conjugate transpose of `self`.

972

973 Equivalent to ``np.transpose(self)`` if `self` is real-valued.

974

975 Parameters

976 ----------

977 None

978

979 Returns

980 -------

981 ret : matrix object

982 complex conjugate transpose of `self`

983

984 Examples

985 --------

986 >>> x = np.matrix(np.arange(12).reshape((3,4)))

987 >>> z = x - 1j*x; z

988 matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],

989 [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],

990 [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])

991 >>> z.getH()

992 matrix([[ 0. -0.j, 4. +4.j, 8. +8.j],

993 [ 1. +1.j, 5. +5.j, 9. +9.j],

994 [ 2. +2.j, 6. +6.j, 10.+10.j],

995 [ 3. +3.j, 7. +7.j, 11.+11.j]])

996

997 """

998 if issubclass(self.dtype.type, N.complexfloating):

999 return self.transpose().conjugate()

1000 else:

1001 return self.transpose()

1002

1003 # kept for compatibility

1004 getT = T.fget

1005 getA = A.fget

1006 getA1 = A1.fget

1007 getH = H.fget

1008 getI = I.fget

1009

1010def _from_string(str, gdict, ldict):

1011 rows = str.split(';')

1012 rowtup = []

1013 for row in rows:

1014 trow = row.split(',')

1015 newrow = []

1016 for x in trow:

1017 newrow.extend(x.split())

1018 trow = newrow

1019 coltup = []

1020 for col in trow:

1021 col = col.strip()

1022 try:

1023 thismat = ldict[col]

1024 except KeyError:

1025 try:

1026 thismat = gdict[col]

1027 except KeyError as e:

1028 raise NameError(f"name {col!r} is not defined") from None

1029

1030 coltup.append(thismat)

1031 rowtup.append(concatenate(coltup, axis=-1))

1032 return concatenate(rowtup, axis=0)

1033

1034

1035@set_module('numpy')

1036def bmat(obj, ldict=None, gdict=None):

1037 """

1038 Build a matrix object from a string, nested sequence, or array.

1039

1040 Parameters

1041 ----------

1042 obj : str or array_like

1043 Input data. If a string, variables in the current scope may be

1044 referenced by name.

1045 ldict : dict, optional

1046 A dictionary that replaces local operands in current frame.

1047 Ignored if `obj` is not a string or `gdict` is None.

1048 gdict : dict, optional

1049 A dictionary that replaces global operands in current frame.

1050 Ignored if `obj` is not a string.

1051

1052 Returns

1053 -------

1054 out : matrix

1055 Returns a matrix object, which is a specialized 2-D array.

1056

1057 See Also

1058 --------

1059 block :

1060 A generalization of this function for N-d arrays, that returns normal

1061 ndarrays.

1062

1063 Examples

1064 --------

1065 >>> A = np.mat('1 1; 1 1')

1066 >>> B = np.mat('2 2; 2 2')

1067 >>> C = np.mat('3 4; 5 6')

1068 >>> D = np.mat('7 8; 9 0')

1069

1070 All the following expressions construct the same block matrix:

1071

1072 >>> np.bmat([[A, B], [C, D]])

1073 matrix([[1, 1, 2, 2],

1074 [1, 1, 2, 2],

1075 [3, 4, 7, 8],

1076 [5, 6, 9, 0]])

1077 >>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])

1078 matrix([[1, 1, 2, 2],

1079 [1, 1, 2, 2],

1080 [3, 4, 7, 8],

1081 [5, 6, 9, 0]])

1082 >>> np.bmat('A,B; C,D')

1083 matrix([[1, 1, 2, 2],

1084 [1, 1, 2, 2],

1085 [3, 4, 7, 8],

1086 [5, 6, 9, 0]])

1087

1088 """

1089 if isinstance(obj, str):

1090 if gdict is None:

1091 # get previous frame

1092 frame = sys._getframe().f_back

1093 glob_dict = frame.f_globals

1094 loc_dict = frame.f_locals

1095 else:

1096 glob_dict = gdict

1097 loc_dict = ldict

1098

1099 return matrix(_from_string(obj, glob_dict, loc_dict))

1100

1101 if isinstance(obj, (tuple, list)):

1102 # [[A,B],[C,D]]

1103 arr_rows = []

1104 for row in obj:

1105 if isinstance(row, N.ndarray): # not 2-d

1106 return matrix(concatenate(obj, axis=-1))

1107 else:

1108 arr_rows.append(concatenate(row, axis=-1))

1109 return matrix(concatenate(arr_rows, axis=0))

1110 if isinstance(obj, N.ndarray):

1111 return matrix(obj)

1112

1113mat = asmatrix