solve#
- scipy.linalg.solve(a, b, lower=False, overwrite_a=False, overwrite_b=False, check_finite=True, assume_a=None, transposed=False)[source]#
Solves the linear equation set
a @ x == b
for the unknownx
for square a matrix.If the data matrix is known to be a particular type then supplying the corresponding string to
assume_a
key chooses the dedicated solver. The available options arediagonal
‘diagonal’
tridiagonal
‘tridiagonal’
upper triangular
‘upper triangular’
lower triangular
‘lower triangular’
symmetric
‘symmetric’ (or ‘sym’)
hermitian
‘hermitian’ (or ‘her’)
positive definite
‘positive definite’ (or ‘pos’)
general
‘general’ (or ‘gen’)
- Parameters:
- a(N, N) array_like
Square input data
- b(N, NRHS) array_like
Input data for the right hand side.
- lowerbool, default: False
Ignored unless
assume_a
is one of'sym'
,'her'
, or'pos'
. If True, the calculation uses only the data in the lower triangle of a; entries above the diagonal are ignored. If False (default), the calculation uses only the data in the upper triangle of a; entries below the diagonal are ignored.- overwrite_abool, default: False
Allow overwriting data in a (may enhance performance).
- overwrite_bbool, default: False
Allow overwriting data in b (may enhance performance).
- check_finitebool, default: True
Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.
- assume_astr, optional
Valid entries are described above. If omitted or
None
, checks are performed to identify structure so the appropriate solver can be called.- transposedbool, default: False
If True, solve
a.T @ x == b
. Raises NotImplementedError for complex a.
- Returns:
- x(N, NRHS) ndarray
The solution array.
- Raises:
- ValueError
If size mismatches detected or input a is not square.
- LinAlgError
If the matrix is singular.
- LinAlgWarning
If an ill-conditioned input a is detected.
- NotImplementedError
If transposed is True and input a is a complex matrix.
Notes
If the input b matrix is a 1-D array with N elements, when supplied together with an NxN input a, it is assumed as a valid column vector despite the apparent size mismatch. This is compatible with the numpy.dot() behavior and the returned result is still 1-D array.
The general, symmetric, Hermitian and positive definite solutions are obtained via calling ?GESV, ?SYSV, ?HESV, and ?POSV routines of LAPACK respectively.
The datatype of the arrays define which solver is called regardless of the values. In other words, even when the complex array entries have precisely zero imaginary parts, the complex solver will be called based on the data type of the array.
Examples
Given a and b, solve for x:
>>> import numpy as np >>> a = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]]) >>> b = np.array([2, 4, -1]) >>> from scipy import linalg >>> x = linalg.solve(a, b) >>> x array([ 2., -2., 9.]) >>> np.dot(a, x) == b array([ True, True, True], dtype=bool)