/usr/lib/python3/dist-packages/numpy/matrixlib/defmatrix.py is in python3-numpy 1:1.12.1-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 | from __future__ import division, absolute_import, print_function
__all__ = ['matrix', 'bmat', 'mat', 'asmatrix']
import sys
import numpy.core.numeric as N
from numpy.core.numeric import concatenate, isscalar, binary_repr, identity, asanyarray
from numpy.core.numerictypes import issubdtype
# make translation table
_numchars = '0123456789.-+jeEL'
if sys.version_info[0] >= 3:
class _NumCharTable:
def __getitem__(self, i):
if chr(i) in _numchars:
return chr(i)
else:
return None
_table = _NumCharTable()
def _eval(astr):
str_ = astr.translate(_table)
if not str_:
raise TypeError("Invalid data string supplied: " + astr)
else:
return eval(str_)
else:
_table = [None]*256
for k in range(256):
_table[k] = chr(k)
_table = ''.join(_table)
_todelete = []
for k in _table:
if k not in _numchars:
_todelete.append(k)
_todelete = ''.join(_todelete)
del k
def _eval(astr):
str_ = astr.translate(_table, _todelete)
if not str_:
raise TypeError("Invalid data string supplied: " + astr)
else:
return eval(str_)
def _convert_from_string(data):
rows = data.split(';')
newdata = []
count = 0
for row in rows:
trow = row.split(',')
newrow = []
for col in trow:
temp = col.split()
newrow.extend(map(_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 len(M.shape) != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not issubdtype(type(n), int):
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:
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. Names of variables in the current scope may be
referenced, even if `obj` is a string.
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
--------
matrix
Examples
--------
>>> A = np.mat('1 1; 1 1')
>>> B = np.mat('2 2; 2 2')
>>> C = np.mat('3 4; 5 6')
>>> D = np.mat('7 8; 9 0')
All the following expressions construct the same block matrix:
>>> np.bmat([[A, B], [C, D]])
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
>>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
>>> np.bmat('A,B; C,D')
matrix([[1, 1, 2, 2],
[1, 1, 2, 2],
[3, 4, 7, 8],
[5, 6, 9, 0]])
"""
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
|