defmatrix.py

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.

    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 quarternion 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 = False
        if (ndim == 2) and arr.flags.fortran:
            order = True

        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)

    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):
        """
        Indices of the maximum values along an axis.

        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):
        """
        Return the indices of the minimum values along an axis.

        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 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.

    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