Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: B = A.change_ring(CDF)
sage: B.solve_left(b)
(0.5 - 1.5*I, 0.5 + 0.5*I)
solve_left_LU(b)
Solve the equation Ax = b using LU decomposition.
Warning: This function is broken. See trac 4932.
INPUT:
•self – an invertible matrix
•b – a vector
Note: This method precomputes and stores the LU decomposition before solving. If many equations of
the form Ax=b need to be solved for a singe matrix A, then this method should be used instead of solve.
The first time this method is called it will compute the LU decomposition. If the matrix has not changed
then subsequent calls will be very fast as the precomputed LU decomposition will be reused.
EXAMPLES:
sage: A = matrix(RDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]); A
[ 1.0 2.0 5.0]
[ 7.6 2.3 1.0]
[ 1.0 2.0 -1.0]
sage: b = vector(RDF,[1,2,3])
sage: x = A.solve_left_LU(b); x
Traceback (most recent call last):
...
NotImplementedError: this function is not finished (see trac 4932)
TESTS:
We test two degenerate cases:
sage: A = matrix(RDF, 0, 3, [])
sage: A.solve_left_LU(vector(RDF,[]))
(0.0, 0.0, 0.0)
sage: A = matrix(RDF, 3, 0, [])
sage: A.solve_left_LU(vector(RDF,3, [1,2,3]))
()
solve_right(b)
Solve the vector equation A*x = b for a nonsingular A.
INPUT:
•self - a square matrix that is nonsigular (of full rank).
•b - a vector of the correct size. Elements of the vector must coerce into the base ring of the coefficient
matrix. In particular, if b has entries from CDF then self must have CDF as its base ring.
OUTPUT:
The unique solution x to the matrix equation A*x = b, as a vector over the same base ring as self.
ALGORITHM:
Uses the solve() routine from the SciPy scipy.linalg module.
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