def matrix_power(M, n):
"""Raise a square matrix to the (integer) power `n`.
Args:
M (~cupy.ndarray): Matrix to raise by power n.
n (~int): Power to raise matrix to.
Returns:
~cupy.ndarray: Output array.
.. note:: M must be of dtype `float32` or `float64`.
..seealso:: :func:`numpy.linalg.matrix_power`
"""
if M.ndim != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not isinstance(n, six.integer_types):
raise TypeError("exponent must be an integer")
if n == 0:
return cupy.identity(M.shape[0], dtype=M.dtype)
elif n < 0:
M = inv(M)
n *= -1
# short-cuts
if n <= 3:
if n == 1:
return M
elif n == 2:
return cupy.matmul(M, M)
else:
return cupy.matmul(cupy.matmul(M, M), M)
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
result, Z = None, None
for b in cupy.binary_repr(n)[::-1]:
Z = M if Z is None else cupy.matmul(Z, Z)
if b == '1':
result = Z if result is None else cupy.matmul(result, Z)
return result
def matrix_power(M, n):
"""Raise a square matrix to the (integer) power `n`.
Args:
M (~cupy.ndarray): Matrix to raise by power n.
n (~int): Power to raise matrix to.
Returns:
~cupy.ndarray: Output array.
..seealso:: :func:`numpy.linalg.matrix_power`
"""
_util._assert_cupy_array(M)
_util._assert_stacked_2d(M)
_util._assert_stacked_square(M)
if not isinstance(n, int):
raise TypeError('exponent must be an integer')
if n == 0:
return _util.stacked_identity_like(M)
elif n < 0:
M = _solve.inv(M)
n *= -1
# short-cuts
if n <= 3:
if n == 1:
return M
elif n == 2:
return cupy.matmul(M, M)
else:
return cupy.matmul(cupy.matmul(M, M), M)
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
result, Z = None, None
for b in cupy.binary_repr(n)[::-1]:
Z = M if Z is None else cupy.matmul(Z, Z)
if b == '1':
result = Z if result is None else cupy.matmul(result, Z)
return result
def int_to_bit_str(integer, N):
return array(list(binary_repr(integer, width=N)), dtype=int)
