HP MLIB User's Guide Vol. 2 7th Ed.

1100 HP MLIB User’s Guide
DGESL Solve linear equations
Name DGESL
Solve linear equations
Purpose Given the triangular factorization of a general dense n-by-n coefficient matrix
A, and a right-hand-side n-vector b, this subprogram solves the system of linear
equations Ax = b. Specifically, given an n-by-n permutation matrix P, an
n-by-n unit lower-triangular matrix L, and a nonsingular n-by-n
upper-triangular matrix U, such that
and an n-vector b, to find x satisfying Ax = b, the subprograms compute
then successively solve
and
To solve A*x = b, the subprograms successively solve
and
and then compute
The triangular factors of the coefficient matrix may be computed by the
companion subprogram DGEFA. This computes only the factorization, using an
elementary test for singularity of the coefficient matrix. Refer to “DGEFA” on
page 1098 for more information.
Usage VECLIB:
INTEGER*4 lda, n, ipvt(n), job
REAL*8 a(lda, n), b(n)
CALL DGESL(a, lda, n, ipvt, b, job)
PA LU,=
vPb,=
Lw v=
Ux w.=
U*vb=
L*wv,=
xP*w.=