1197 lines
32 KiB
Python
1197 lines
32 KiB
Python
from __future__ import division, absolute_import, print_function
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__all__ = ['matrix', 'bmat', 'mat', 'asmatrix']
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import sys
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import ast
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import numpy.core.numeric as N
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from numpy.core.numeric import concatenate, isscalar, binary_repr, identity, asanyarray
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from numpy.core.numerictypes import issubdtype
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def _convert_from_string(data):
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for char in '[]':
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data = data.replace(char, '')
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rows = data.split(';')
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newdata = []
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count = 0
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for row in rows:
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trow = row.split(',')
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newrow = []
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for col in trow:
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temp = col.split()
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newrow.extend(map(ast.literal_eval, temp))
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if count == 0:
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Ncols = len(newrow)
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elif len(newrow) != Ncols:
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raise ValueError("Rows not the same size.")
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count += 1
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newdata.append(newrow)
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return newdata
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def asmatrix(data, dtype=None):
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"""
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Interpret the input as a matrix.
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Unlike `matrix`, `asmatrix` does not make a copy if the input is already
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a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
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Parameters
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----------
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data : array_like
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Input data.
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dtype : data-type
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Data-type of the output matrix.
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Returns
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-------
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mat : matrix
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`data` interpreted as a matrix.
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Examples
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--------
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>>> x = np.array([[1, 2], [3, 4]])
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>>> m = np.asmatrix(x)
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>>> x[0,0] = 5
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>>> m
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matrix([[5, 2],
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[3, 4]])
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"""
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return matrix(data, dtype=dtype, copy=False)
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def matrix_power(M, n):
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"""
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Raise a square matrix to the (integer) power `n`.
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For positive integers `n`, the power is computed by repeated matrix
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squarings and matrix multiplications. If ``n == 0``, the identity matrix
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of the same shape as M is returned. If ``n < 0``, the inverse
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is computed and then raised to the ``abs(n)``.
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Parameters
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----------
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M : ndarray or matrix object
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Matrix to be "powered." Must be square, i.e. ``M.shape == (m, m)``,
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with `m` a positive integer.
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n : int
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The exponent can be any integer or long integer, positive,
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negative, or zero.
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Returns
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-------
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M**n : ndarray or matrix object
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The return value is the same shape and type as `M`;
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if the exponent is positive or zero then the type of the
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elements is the same as those of `M`. If the exponent is
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negative the elements are floating-point.
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Raises
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------
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LinAlgError
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If the matrix is not numerically invertible.
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See Also
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--------
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matrix
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Provides an equivalent function as the exponentiation operator
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(``**``, not ``^``).
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Examples
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--------
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>>> from numpy import linalg as LA
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>>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit
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>>> LA.matrix_power(i, 3) # should = -i
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array([[ 0, -1],
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[ 1, 0]])
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>>> LA.matrix_power(np.matrix(i), 3) # matrix arg returns matrix
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matrix([[ 0, -1],
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[ 1, 0]])
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>>> LA.matrix_power(i, 0)
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array([[1, 0],
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[0, 1]])
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>>> LA.matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements
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array([[ 0., 1.],
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[-1., 0.]])
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Somewhat more sophisticated example
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>>> q = np.zeros((4, 4))
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>>> q[0:2, 0:2] = -i
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>>> q[2:4, 2:4] = i
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>>> q # one of the three quaternion units not equal to 1
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array([[ 0., -1., 0., 0.],
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[ 1., 0., 0., 0.],
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[ 0., 0., 0., 1.],
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[ 0., 0., -1., 0.]])
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>>> LA.matrix_power(q, 2) # = -np.eye(4)
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array([[-1., 0., 0., 0.],
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[ 0., -1., 0., 0.],
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[ 0., 0., -1., 0.],
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[ 0., 0., 0., -1.]])
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"""
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M = asanyarray(M)
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if M.ndim != 2 or M.shape[0] != M.shape[1]:
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raise ValueError("input must be a square array")
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if not issubdtype(type(n), N.integer):
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raise TypeError("exponent must be an integer")
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from numpy.linalg import inv
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if n==0:
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M = M.copy()
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M[:] = identity(M.shape[0])
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return M
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elif n<0:
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M = inv(M)
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n *= -1
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result = M
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if n <= 3:
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for _ in range(n-1):
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result=N.dot(result, M)
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return result
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# binary decomposition to reduce the number of Matrix
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# multiplications for n > 3.
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beta = binary_repr(n)
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Z, q, t = M, 0, len(beta)
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while beta[t-q-1] == '0':
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Z = N.dot(Z, Z)
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q += 1
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result = Z
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for k in range(q+1, t):
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Z = N.dot(Z, Z)
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if beta[t-k-1] == '1':
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result = N.dot(result, Z)
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return result
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class matrix(N.ndarray):
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"""
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matrix(data, dtype=None, copy=True)
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Returns a matrix from an array-like object, or from a string of data.
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A matrix is a specialized 2-D array that retains its 2-D nature
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through operations. It has certain special operators, such as ``*``
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(matrix multiplication) and ``**`` (matrix power).
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Parameters
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----------
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data : array_like or string
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If `data` is a string, it is interpreted as a matrix with commas
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or spaces separating columns, and semicolons separating rows.
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dtype : data-type
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Data-type of the output matrix.
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copy : bool
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If `data` is already an `ndarray`, then this flag determines
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whether the data is copied (the default), or whether a view is
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constructed.
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See Also
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--------
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array
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Examples
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--------
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>>> a = np.matrix('1 2; 3 4')
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>>> print(a)
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[[1 2]
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[3 4]]
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>>> np.matrix([[1, 2], [3, 4]])
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matrix([[1, 2],
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[3, 4]])
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"""
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__array_priority__ = 10.0
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def __new__(subtype, data, dtype=None, copy=True):
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if isinstance(data, matrix):
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dtype2 = data.dtype
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if (dtype is None):
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dtype = dtype2
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if (dtype2 == dtype) and (not copy):
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return data
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return data.astype(dtype)
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if isinstance(data, N.ndarray):
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if dtype is None:
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intype = data.dtype
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else:
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intype = N.dtype(dtype)
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new = data.view(subtype)
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if intype != data.dtype:
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return new.astype(intype)
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if copy: return new.copy()
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else: return new
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if isinstance(data, str):
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data = _convert_from_string(data)
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# now convert data to an array
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arr = N.array(data, dtype=dtype, copy=copy)
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ndim = arr.ndim
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shape = arr.shape
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if (ndim > 2):
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raise ValueError("matrix must be 2-dimensional")
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elif ndim == 0:
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shape = (1, 1)
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elif ndim == 1:
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shape = (1, shape[0])
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order = 'C'
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if (ndim == 2) and arr.flags.fortran:
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order = 'F'
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if not (order or arr.flags.contiguous):
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arr = arr.copy()
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ret = N.ndarray.__new__(subtype, shape, arr.dtype,
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buffer=arr,
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order=order)
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return ret
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def __array_finalize__(self, obj):
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self._getitem = False
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if (isinstance(obj, matrix) and obj._getitem): return
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ndim = self.ndim
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if (ndim == 2):
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return
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if (ndim > 2):
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newshape = tuple([x for x in self.shape if x > 1])
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ndim = len(newshape)
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if ndim == 2:
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self.shape = newshape
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return
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elif (ndim > 2):
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raise ValueError("shape too large to be a matrix.")
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else:
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newshape = self.shape
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if ndim == 0:
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self.shape = (1, 1)
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elif ndim == 1:
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self.shape = (1, newshape[0])
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return
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def __getitem__(self, index):
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self._getitem = True
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try:
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out = N.ndarray.__getitem__(self, index)
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finally:
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self._getitem = False
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if not isinstance(out, N.ndarray):
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return out
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if out.ndim == 0:
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return out[()]
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if out.ndim == 1:
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sh = out.shape[0]
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# Determine when we should have a column array
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try:
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n = len(index)
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except Exception:
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n = 0
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if n > 1 and isscalar(index[1]):
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out.shape = (sh, 1)
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else:
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out.shape = (1, sh)
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return out
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def __mul__(self, other):
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if isinstance(other, (N.ndarray, list, tuple)) :
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# This promotes 1-D vectors to row vectors
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return N.dot(self, asmatrix(other))
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if isscalar(other) or not hasattr(other, '__rmul__') :
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return N.dot(self, other)
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return NotImplemented
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def __rmul__(self, other):
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return N.dot(other, self)
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def __imul__(self, other):
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self[:] = self * other
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return self
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def __pow__(self, other):
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return matrix_power(self, other)
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def __ipow__(self, other):
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self[:] = self ** other
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return self
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def __rpow__(self, other):
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return NotImplemented
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def _align(self, axis):
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"""A convenience function for operations that need to preserve axis
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orientation.
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"""
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if axis is None:
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return self[0, 0]
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elif axis==0:
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return self
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elif axis==1:
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return self.transpose()
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else:
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raise ValueError("unsupported axis")
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def _collapse(self, axis):
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"""A convenience function for operations that want to collapse
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to a scalar like _align, but are using keepdims=True
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"""
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if axis is None:
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return self[0, 0]
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else:
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return self
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# Necessary because base-class tolist expects dimension
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# reduction by x[0]
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def tolist(self):
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"""
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Return the matrix as a (possibly nested) list.
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See `ndarray.tolist` for full documentation.
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See Also
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--------
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ndarray.tolist
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Examples
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--------
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>>> x = np.matrix(np.arange(12).reshape((3,4))); x
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matrix([[ 0, 1, 2, 3],
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[ 4, 5, 6, 7],
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[ 8, 9, 10, 11]])
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>>> x.tolist()
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[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
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"""
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return self.__array__().tolist()
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# To preserve orientation of result...
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def sum(self, axis=None, dtype=None, out=None):
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"""
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Returns the sum of the matrix elements, along the given axis.
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Refer to `numpy.sum` for full documentation.
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See Also
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--------
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numpy.sum
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Notes
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-----
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This is the same as `ndarray.sum`, except that where an `ndarray` would
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be returned, a `matrix` object is returned instead.
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Examples
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--------
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>>> x = np.matrix([[1, 2], [4, 3]])
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>>> x.sum()
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10
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>>> x.sum(axis=1)
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matrix([[3],
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[7]])
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>>> x.sum(axis=1, dtype='float')
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matrix([[ 3.],
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[ 7.]])
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>>> out = np.zeros((1, 2), dtype='float')
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>>> x.sum(axis=1, dtype='float', out=out)
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matrix([[ 3.],
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[ 7.]])
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"""
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return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)
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# To update docstring from array to matrix...
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def squeeze(self, axis=None):
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"""
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Return a possibly reshaped matrix.
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Refer to `numpy.squeeze` for more documentation.
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Parameters
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----------
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axis : None or int or tuple of ints, optional
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Selects a subset of the single-dimensional entries in the shape.
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If an axis is selected with shape entry greater than one,
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an error is raised.
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Returns
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-------
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squeezed : matrix
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The matrix, but as a (1, N) matrix if it had shape (N, 1).
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See Also
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--------
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numpy.squeeze : related function
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Notes
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-----
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If `m` has a single column then that column is returned
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as the single row of a matrix. Otherwise `m` is returned.
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The returned matrix is always either `m` itself or a view into `m`.
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Supplying an axis keyword argument will not affect the returned matrix
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but it may cause an error to be raised.
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Examples
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--------
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>>> c = np.matrix([[1], [2]])
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>>> c
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matrix([[1],
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[2]])
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>>> c.squeeze()
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matrix([[1, 2]])
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>>> r = c.T
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>>> r
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matrix([[1, 2]])
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>>> r.squeeze()
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matrix([[1, 2]])
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>>> m = np.matrix([[1, 2], [3, 4]])
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>>> m.squeeze()
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matrix([[1, 2],
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[3, 4]])
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"""
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return N.ndarray.squeeze(self, axis=axis)
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# To update docstring from array to matrix...
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def flatten(self, order='C'):
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"""
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Return a flattened copy of the matrix.
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All `N` elements of the matrix are placed into a single row.
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Parameters
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----------
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order : {'C', 'F', 'A', 'K'}, optional
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'C' means to flatten in row-major (C-style) order. 'F' means to
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flatten in column-major (Fortran-style) order. 'A' means to
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flatten in column-major order if `m` is Fortran *contiguous* in
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memory, row-major order otherwise. 'K' means to flatten `m` in
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the order the elements occur in memory. The default is 'C'.
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Returns
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-------
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y : matrix
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A copy of the matrix, flattened to a `(1, N)` matrix where `N`
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is the number of elements in the original matrix.
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See Also
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--------
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ravel : Return a flattened array.
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flat : A 1-D flat iterator over the matrix.
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Examples
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--------
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>>> m = np.matrix([[1,2], [3,4]])
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>>> m.flatten()
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matrix([[1, 2, 3, 4]])
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>>> m.flatten('F')
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matrix([[1, 3, 2, 4]])
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"""
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return N.ndarray.flatten(self, order=order)
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def mean(self, axis=None, dtype=None, out=None):
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"""
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Returns the average of the matrix elements along the given axis.
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Refer to `numpy.mean` for full documentation.
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See Also
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--------
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numpy.mean
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Notes
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-----
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Same as `ndarray.mean` except that, where that returns an `ndarray`,
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this returns a `matrix` object.
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Examples
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--------
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>>> x = np.matrix(np.arange(12).reshape((3, 4)))
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>>> x
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matrix([[ 0, 1, 2, 3],
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[ 4, 5, 6, 7],
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[ 8, 9, 10, 11]])
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>>> x.mean()
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5.5
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>>> x.mean(0)
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matrix([[ 4., 5., 6., 7.]])
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>>> x.mean(1)
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matrix([[ 1.5],
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[ 5.5],
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[ 9.5]])
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"""
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return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)
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def std(self, axis=None, dtype=None, out=None, ddof=0):
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"""
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Return the standard deviation of the array elements along the given axis.
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Refer to `numpy.std` for full documentation.
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See Also
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--------
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numpy.std
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Notes
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-----
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This is the same as `ndarray.std`, except that where an `ndarray` would
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be returned, a `matrix` object is returned instead.
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Examples
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--------
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>>> x = np.matrix(np.arange(12).reshape((3, 4)))
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>>> x
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matrix([[ 0, 1, 2, 3],
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[ 4, 5, 6, 7],
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[ 8, 9, 10, 11]])
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>>> x.std()
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3.4520525295346629
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>>> x.std(0)
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matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]])
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>>> x.std(1)
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matrix([[ 1.11803399],
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[ 1.11803399],
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[ 1.11803399]])
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"""
|
|
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]])
|
|
>>> (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.ndarray.ptp(self, axis, out)._align(axis)
|
|
|
|
def getI(self):
|
|
"""
|
|
Returns the (multiplicative) inverse of invertible `self`.
|
|
|
|
Parameters
|
|
----------
|
|
None
|
|
|
|
Returns
|
|
-------
|
|
ret : matrix object
|
|
If `self` is non-singular, `ret` is such that ``ret * self`` ==
|
|
``self * ret`` == ``np.matrix(np.eye(self[0,:].size)`` all return
|
|
``True``.
|
|
|
|
Raises
|
|
------
|
|
numpy.linalg.LinAlgError: Singular matrix
|
|
If `self` is singular.
|
|
|
|
See Also
|
|
--------
|
|
linalg.inv
|
|
|
|
Examples
|
|
--------
|
|
>>> m = np.matrix('[1, 2; 3, 4]'); m
|
|
matrix([[1, 2],
|
|
[3, 4]])
|
|
>>> m.getI()
|
|
matrix([[-2. , 1. ],
|
|
[ 1.5, -0.5]])
|
|
>>> m.getI() * m
|
|
matrix([[ 1., 0.],
|
|
[ 0., 1.]])
|
|
|
|
"""
|
|
M, N = self.shape
|
|
if M == N:
|
|
from numpy.dual import inv as func
|
|
else:
|
|
from numpy.dual import pinv as func
|
|
return asmatrix(func(self))
|
|
|
|
def getA(self):
|
|
"""
|
|
Return `self` as an `ndarray` object.
|
|
|
|
Equivalent to ``np.asarray(self)``.
|
|
|
|
Parameters
|
|
----------
|
|
None
|
|
|
|
Returns
|
|
-------
|
|
ret : ndarray
|
|
`self` as an `ndarray`
|
|
|
|
Examples
|
|
--------
|
|
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
|
|
matrix([[ 0, 1, 2, 3],
|
|
[ 4, 5, 6, 7],
|
|
[ 8, 9, 10, 11]])
|
|
>>> x.getA()
|
|
array([[ 0, 1, 2, 3],
|
|
[ 4, 5, 6, 7],
|
|
[ 8, 9, 10, 11]])
|
|
|
|
"""
|
|
return self.__array__()
|
|
|
|
def getA1(self):
|
|
"""
|
|
Return `self` as a flattened `ndarray`.
|
|
|
|
Equivalent to ``np.asarray(x).ravel()``
|
|
|
|
Parameters
|
|
----------
|
|
None
|
|
|
|
Returns
|
|
-------
|
|
ret : ndarray
|
|
`self`, 1-D, as an `ndarray`
|
|
|
|
Examples
|
|
--------
|
|
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
|
|
matrix([[ 0, 1, 2, 3],
|
|
[ 4, 5, 6, 7],
|
|
[ 8, 9, 10, 11]])
|
|
>>> x.getA1()
|
|
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
|
|
|
|
"""
|
|
return self.__array__().ravel()
|
|
|
|
|
|
def ravel(self, order='C'):
|
|
"""
|
|
Return a flattened matrix.
|
|
|
|
Refer to `numpy.ravel` for more documentation.
|
|
|
|
Parameters
|
|
----------
|
|
order : {'C', 'F', 'A', 'K'}, optional
|
|
The elements of `m` are read using this index order. 'C' means to
|
|
index the elements in C-like order, with the last axis index
|
|
changing fastest, back to the first axis index changing slowest.
|
|
'F' means to index the elements in Fortran-like index order, with
|
|
the first index changing fastest, and the last index changing
|
|
slowest. Note that the 'C' and 'F' options take no account of the
|
|
memory layout of the underlying array, and only refer to the order
|
|
of axis indexing. 'A' means to read the elements in Fortran-like
|
|
index order if `m` is Fortran *contiguous* in memory, C-like order
|
|
otherwise. 'K' means to read the elements in the order they occur
|
|
in memory, except for reversing the data when strides are negative.
|
|
By default, 'C' index order is used.
|
|
|
|
Returns
|
|
-------
|
|
ret : matrix
|
|
Return the matrix flattened to shape `(1, N)` where `N`
|
|
is the number of elements in the original matrix.
|
|
A copy is made only if necessary.
|
|
|
|
See Also
|
|
--------
|
|
matrix.flatten : returns a similar output matrix but always a copy
|
|
matrix.flat : a flat iterator on the array.
|
|
numpy.ravel : related function which returns an ndarray
|
|
|
|
"""
|
|
return N.ndarray.ravel(self, order=order)
|
|
|
|
|
|
def getT(self):
|
|
"""
|
|
Returns the transpose of the matrix.
|
|
|
|
Does *not* conjugate! For the complex conjugate transpose, use ``.H``.
|
|
|
|
Parameters
|
|
----------
|
|
None
|
|
|
|
Returns
|
|
-------
|
|
ret : matrix object
|
|
The (non-conjugated) transpose of the matrix.
|
|
|
|
See Also
|
|
--------
|
|
transpose, getH
|
|
|
|
Examples
|
|
--------
|
|
>>> m = np.matrix('[1, 2; 3, 4]')
|
|
>>> m
|
|
matrix([[1, 2],
|
|
[3, 4]])
|
|
>>> m.getT()
|
|
matrix([[1, 3],
|
|
[2, 4]])
|
|
|
|
"""
|
|
return self.transpose()
|
|
|
|
def getH(self):
|
|
"""
|
|
Returns the (complex) conjugate transpose of `self`.
|
|
|
|
Equivalent to ``np.transpose(self)`` if `self` is real-valued.
|
|
|
|
Parameters
|
|
----------
|
|
None
|
|
|
|
Returns
|
|
-------
|
|
ret : matrix object
|
|
complex conjugate transpose of `self`
|
|
|
|
Examples
|
|
--------
|
|
>>> x = np.matrix(np.arange(12).reshape((3,4)))
|
|
>>> z = x - 1j*x; z
|
|
matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],
|
|
[ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],
|
|
[ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])
|
|
>>> z.getH()
|
|
matrix([[ 0. +0.j, 4. +4.j, 8. +8.j],
|
|
[ 1. +1.j, 5. +5.j, 9. +9.j],
|
|
[ 2. +2.j, 6. +6.j, 10.+10.j],
|
|
[ 3. +3.j, 7. +7.j, 11.+11.j]])
|
|
|
|
"""
|
|
if issubclass(self.dtype.type, N.complexfloating):
|
|
return self.transpose().conjugate()
|
|
else:
|
|
return self.transpose()
|
|
|
|
T = property(getT, None)
|
|
A = property(getA, None)
|
|
A1 = property(getA1, None)
|
|
H = property(getH, None)
|
|
I = property(getI, None)
|
|
|
|
def _from_string(str, gdict, ldict):
|
|
rows = str.split(';')
|
|
rowtup = []
|
|
for row in rows:
|
|
trow = row.split(',')
|
|
newrow = []
|
|
for x in trow:
|
|
newrow.extend(x.split())
|
|
trow = newrow
|
|
coltup = []
|
|
for col in trow:
|
|
col = col.strip()
|
|
try:
|
|
thismat = ldict[col]
|
|
except KeyError:
|
|
try:
|
|
thismat = gdict[col]
|
|
except KeyError:
|
|
raise KeyError("%s not found" % (col,))
|
|
|
|
coltup.append(thismat)
|
|
rowtup.append(concatenate(coltup, axis=-1))
|
|
return concatenate(rowtup, axis=0)
|
|
|
|
|
|
def bmat(obj, ldict=None, gdict=None):
|
|
"""
|
|
Build a matrix object from a string, nested sequence, or array.
|
|
|
|
Parameters
|
|
----------
|
|
obj : str or array_like
|
|
Input data. If a string, variables in the current scope may be
|
|
referenced by name.
|
|
ldict : dict, optional
|
|
A dictionary that replaces local operands in current frame.
|
|
Ignored if `obj` is not a string or `gdict` is `None`.
|
|
gdict : dict, optional
|
|
A dictionary that replaces global operands in current frame.
|
|
Ignored if `obj` is not a string.
|
|
|
|
Returns
|
|
-------
|
|
out : matrix
|
|
Returns a matrix object, which is a specialized 2-D array.
|
|
|
|
See Also
|
|
--------
|
|
block :
|
|
A generalization of this function for N-d arrays, that returns normal
|
|
ndarrays.
|
|
|
|
Examples
|
|
--------
|
|
>>> A = np.mat('1 1; 1 1')
|
|
>>> B = np.mat('2 2; 2 2')
|
|
>>> C = np.mat('3 4; 5 6')
|
|
>>> D = np.mat('7 8; 9 0')
|
|
|
|
All the following expressions construct the same block matrix:
|
|
|
|
>>> np.bmat([[A, B], [C, D]])
|
|
matrix([[1, 1, 2, 2],
|
|
[1, 1, 2, 2],
|
|
[3, 4, 7, 8],
|
|
[5, 6, 9, 0]])
|
|
>>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])
|
|
matrix([[1, 1, 2, 2],
|
|
[1, 1, 2, 2],
|
|
[3, 4, 7, 8],
|
|
[5, 6, 9, 0]])
|
|
>>> np.bmat('A,B; C,D')
|
|
matrix([[1, 1, 2, 2],
|
|
[1, 1, 2, 2],
|
|
[3, 4, 7, 8],
|
|
[5, 6, 9, 0]])
|
|
|
|
"""
|
|
if isinstance(obj, str):
|
|
if gdict is None:
|
|
# get previous frame
|
|
frame = sys._getframe().f_back
|
|
glob_dict = frame.f_globals
|
|
loc_dict = frame.f_locals
|
|
else:
|
|
glob_dict = gdict
|
|
loc_dict = ldict
|
|
|
|
return matrix(_from_string(obj, glob_dict, loc_dict))
|
|
|
|
if isinstance(obj, (tuple, list)):
|
|
# [[A,B],[C,D]]
|
|
arr_rows = []
|
|
for row in obj:
|
|
if isinstance(row, N.ndarray): # not 2-d
|
|
return matrix(concatenate(obj, axis=-1))
|
|
else:
|
|
arr_rows.append(concatenate(row, axis=-1))
|
|
return matrix(concatenate(arr_rows, axis=0))
|
|
if isinstance(obj, N.ndarray):
|
|
return matrix(obj)
|
|
|
|
mat = asmatrix
|