numpy.matrixlib.defmatrix.matrix

class documentation

class matrix(N.ndarray):

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

Note

It is no longer recommended to use this class, even for linear algebra. Instead use regular arrays. The class may be removed in the future.

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.

Examples

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

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

Method	`__array_finalize__`	Undocumented
Method	`__getitem__`	Undocumented
Method	`__imul__`	Undocumented
Method	`__ipow__`	Undocumented
Method	`__mul__`	Undocumented
Method	`__new__`	Undocumented
Method	`__pow__`	Undocumented
Method	`__rmul__`	Undocumented
Method	`__rpow__`	Undocumented
Method	`_align`	A convenience function for operations that need to preserve axis orientation.
Method	`_collapse`	A convenience function for operations that want to collapse to a scalar like _align, but are using keepdims=True
Method	`all`	Test whether all matrix elements along a given axis evaluate to True.
Method	`any`	Test whether any array element along a given axis evaluates to True.
Method	`argmax`	Indexes of the maximum values along an axis.
Method	`argmin`	Indexes of the minimum values along an axis.
Method	`flatten`	Return a flattened copy of the matrix.
Method	`max`	Return the maximum value along an axis.
Method	`mean`	Returns the average of the matrix elements along the given axis.
Method	`min`	Return the minimum value along an axis.
Method	`prod`	Return the product of the array elements over the given axis.
Method	`ptp`	Peak-to-peak (maximum - minimum) value along the given axis.
Method	`ravel`	Return a flattened matrix.
Method	`squeeze`	Return a possibly reshaped matrix.
Method	`std`	Return the standard deviation of the array elements along the given axis.
Method	`sum`	Returns the sum of the matrix elements, along the given axis.
Method	`tolist`	Return the matrix as a (possibly nested) list.
Method	`var`	Returns the variance of the matrix elements, along the given axis.
Class Variable	`__array_priority__`	Undocumented
Instance Variable	`_getitem`	Undocumented
Instance Variable	`shape`	Undocumented
Property	`A`	Return `self` as an `ndarray` object.
Property	`A1`	Return `self` as a flattened `ndarray`.
Property	`H`	Returns the (complex) conjugate transpose of `self`.
Property	`I`	Returns the (multiplicative) inverse of invertible `self`.
Property	`T`	Returns the transpose of the matrix.

def __array_finalize__(self, obj):

Undocumented

def __getitem__(self, index):

Undocumented

def __imul__(self, other):

Undocumented

def __ipow__(self, other):

Undocumented

def __mul__(self, other):

Undocumented

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

Undocumented

def __pow__(self, other):

Undocumented

def __rmul__(self, other):

Undocumented

def __rpow__(self, other):

Undocumented

def _align(self, axis):

A convenience function for operations that need to preserve axis orientation.

def _collapse(self, axis):

A convenience function for operations that want to collapse to a scalar like _align, but are using keepdims=True

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

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]])

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

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

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]])

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.

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]])

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.

Examples

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

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

Return the maximum value along an axis.

Parameters

See amax for complete descriptions

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]])

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.

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]])

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

Return the minimum value along an axis.

Parameters

See amin for complete descriptions.

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]])

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.

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]])

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

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

Refer to numpy.ptp for full documentation.

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]])

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.

Parameters

axis : None or int or tuple of ints, optional: Selects a subset of the axes of length one in the shape. If an axis is selected with shape entry greater than one, an error is raised.

Returns

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

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]])

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.

Notes

This is the same as ndarray.std, except that where an ndarray would be returned, a matrix object is returned instead.

Examples

>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]])
>>> x.std()
3.4520525295346629 # may vary
>>> x.std(0)
matrix([[ 3.26598632,  3.26598632,  3.26598632,  3.26598632]]) # may vary
>>> x.std(1)
matrix([[ 1.11803399],
        [ 1.11803399],
        [ 1.11803399]])

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.

Notes

This is the same as ndarray.sum, except that where an ndarray would be returned, a matrix object is returned instead.

Examples

>>> x = np.matrix([[1, 2], [4, 3]])
>>> x.sum()
10
>>> x.sum(axis=1)
matrix([[3],
        [7]])
>>> x.sum(axis=1, dtype='float')
matrix([[3.],
        [7.]])
>>> out = np.zeros((2, 1), dtype='float')
>>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))
matrix([[3.],
        [7.]])

def tolist(self):

Return the matrix as a (possibly nested) list.

See ndarray.tolist for full documentation.

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]]

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.

Notes

This is the same as ndarray.var, except that where an ndarray would be returned, a matrix object is returned instead.

Examples

>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]])
>>> x.var()
11.916666666666666
>>> x.var(0)
matrix([[ 10.66666667,  10.66666667,  10.66666667,  10.66666667]]) # may vary
>>> x.var(1)
matrix([[1.25],
        [1.25],
        [1.25]])

__array_priority__: float =

Undocumented

_getitem: bool =

Undocumented

shape: tuple[int, ...] =

Undocumented

@property
A =

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]])

@property
A1 =

Return self as a flattened ndarray.

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

Parameters

None

Returns

ret : ndarray: self, 1-D, as an ndarray

Examples

>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]])
>>> x.getA1()
array([ 0,  1,  2, ...,  9, 10, 11])

@property
H =

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]])

@property
I =

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.

Examples

>>> m = np.matrix('[1, 2; 3, 4]'); m
matrix([[1, 2],
        [3, 4]])
>>> m.getI()
matrix([[-2. ,  1. ],
        [ 1.5, -0.5]])
>>> m.getI() * m
matrix([[ 1.,  0.], # may vary
        [ 0.,  1.]])

@property
T =

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.

Examples

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

numpy.matrixlib.defmatrix.matrix

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`numpy.matrixlib.defmatrix.matrix`