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defmatrix.py
__all__ = ['matrix', 'bmat', 'mat', 'asmatrix'] import sys import warnings import ast from .._utils import set_module import numpy.core.numeric as N from numpy.core.numeric import concatenate, isscalar # While not in __all__, matrix_power used to be defined here, so we import # it for backward compatibility. from numpy.linalg import matrix_power def _convert_from_string(data): for char in '[]': data = data.replace(char, '') rows = data.split(';') newdata = [] count = 0 for row in rows: trow = row.split(',') newrow = [] for col in trow: temp = col.split() newrow.extend(map(ast.literal_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 @set_module('numpy') def asmatrix(data, dtype=None): """ Interpret the input as a matrix. Unlike `matrix`, `asmatrix` does not make a copy if the input is already a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``. Parameters ---------- data : array_like Input data. dtype : data-type Data-type of the output matrix. Returns ------- mat : matrix `data` interpreted as a matrix. Examples -------- >>> x = np.array([[1, 2], [3, 4]]) >>> m = np.asmatrix(x) >>> x[0,0] = 5 >>> m matrix([[5, 2], [3, 4]]) """ return matrix(data, dtype=dtype, copy=False) @set_module('numpy') 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. See Also -------- array 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]]) """ __array_priority__ = 10.0 def __new__(subtype, data, dtype=None, copy=True): warnings.warn('the matrix subclass is not the recommended way to ' 'represent matrices or deal with linear algebra (see ' 'https://docs.scipy.org/doc/numpy/user/' 'numpy-for-matlab-users.html). ' 'Please adjust your code to use regular ndarray.', PendingDeprecationWarning, stacklevel=2) if isinstance(data, matrix): dtype2 = data.dtype if (dtype is None): dtype = dtype2 if (dtype2 == dtype) and (not copy): return data return data.astype(dtype) if isinstance(data, N.ndarray): if dtype is None: intype = data.dtype else: intype = N.dtype(dtype) new = data.view(subtype) if intype != data.dtype: return new.astype(intype) if copy: return new.copy() else: return new if isinstance(data, str): data = _convert_from_string(data) # now convert data to an array arr = N.array(data, dtype=dtype, copy=copy) ndim = arr.ndim shape = arr.shape if (ndim > 2): raise ValueError("matrix must be 2-dimensional") elif ndim == 0: shape = (1, 1) elif ndim == 1: shape = (1, shape[0]) order = 'C' if (ndim == 2) and arr.flags.fortran: order = 'F' if not (order or arr.flags.contiguous): arr = arr.copy() ret = N.ndarray.__new__(subtype, shape, arr.dtype, buffer=arr, order=order) return ret def __array_finalize__(self, obj): self._getitem = False if (isinstance(obj, matrix) and obj._getitem): return ndim = self.ndim if (ndim == 2): return if (ndim > 2): newshape = tuple([x for x in self.shape if x > 1]) ndim = len(newshape) if ndim == 2: self.shape = newshape return elif (ndim > 2): raise ValueError("shape too large to be a matrix.") else: newshape = self.shape if ndim == 0: self.shape = (1, 1) elif ndim == 1: self.shape = (1, newshape[0]) return def __getitem__(self, index): self._getitem = True try: out = N.ndarray.__getitem__(self, index) finally: self._getitem = False if not isinstance(out, N.ndarray): return out if out.ndim == 0: return out[()] if out.ndim == 1: sh = out.shape[0] # Determine when we should have a column array try: n = len(index) except Exception: 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 _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((2, 1), dtype='float') >>> x.sum(axis=1, dtype='float', out=np.asmatrix(out)) matrix([[3.], [7.]]) """ return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis) # To update docstring from array to matrix... def squeeze(self, axis=None): """ Return a possibly reshaped matrix. Refer to `numpy.squeeze` for more documentation. Parameters ---------- axis : None or int or tuple of ints, optional Selects a subset of the 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). See Also -------- numpy.squeeze : related function Notes ----- If `m` has a single column then that column is returned as the single row of a matrix. Otherwise `m` is returned. The returned matrix is always either `m` itself or a view into `m`. Supplying an axis keyword argument will not affect the returned matrix but it may cause an error to be raised. Examples -------- >>> c = np.matrix([[1], [2]]) >>> c matrix([[1], [2]]) >>> c.squeeze() matrix([[1, 2]]) >>> r = c.T >>> r matrix([[1, 2]]) >>> r.squeeze() matrix([[1, 2]]) >>> m = np.matrix([[1, 2], [3, 4]]) >>> m.squeeze() matrix([[1, 2], [3, 4]]) """ return N.ndarray.squeeze(self, axis=axis) # To update docstring from array to matrix... def flatten(self, order='C'): """ Return a flattened copy of the matrix. All `N` elements of the matrix are placed into a single row. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional 'C' means to flatten in row-major (C-style) order. 'F' means to flatten in column-major (Fortran-style) order. 'A' means to flatten in column-major order if `m` is Fortran *contiguous* in memory, row-major order otherwise. 'K' means to flatten `m` in the order the elements occur in memory. The default is 'C'. Returns ------- y : matrix A copy of the matrix, flattened to a `(1, N)` matrix where `N` is the number of elements in the original matrix. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the matrix. Examples -------- >>> m = np.matrix([[1,2], [3,4]]) >>> m.flatten() matrix([[1, 2, 3, 4]]) >>> m.flatten('F') matrix([[1, 3, 2, 4]]) """ return N.ndarray.flatten(self, order=order) def mean(self, axis=None, dtype=None, out=None): """ Returns the average of the matrix elements along the given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean Notes ----- Same as `ndarray.mean` except that, where that returns an `ndarray`, this returns a `matrix` object. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3, 4))) >>> x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.mean() 5.5 >>> x.mean(0) matrix([[4., 5., 6., 7.]]) >>> x.mean(1) matrix([[ 1.5], [ 5.5], [ 9.5]]) """ return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis) def std(self, axis=None, dtype=None, out=None, ddof=0): """ Return the standard deviation of the array elements along the given axis. Refer to `numpy.std` for full documentation. See Also -------- numpy.std Notes ----- This is the same as `ndarray.std`, except that where an `ndarray` would be returned, a `matrix` object is returned instead. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3, 4))) >>> x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.std() 3.4520525295346629 # 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]]) """ 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]]) # may vary >>> 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) @property def I(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.], # may vary [ 0., 1.]]) """ M, N = self.shape if M == N: from numpy.linalg import inv as func else: from numpy.linalg import pinv as func return asmatrix(func(self)) @property def A(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__() @property def A1(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, ..., 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) @property def T(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() @property def H(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() # kept for compatibility getT = T.fget getA = A.fget getA1 = A1.fget getH = H.fget getI = I.fget 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 as e: raise NameError(f"name {col!r} is not defined") from None coltup.append(thismat) rowtup.append(concatenate(coltup, axis=-1)) return concatenate(rowtup, axis=0) @set_module('numpy') 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
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