SSYSV - compute the solution to a real system of linear
equations A * X = B,
SYNOPSIS
SUBROUTINE SSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
WORK, LWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
INTEGER IPIV( * )
REAL A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
SSYSV computes the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric matrix
and X and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper
(lower) triangular matrices, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks. The fac
tored form of A is then used to solve the system of equa
tions A * X = B.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of
the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number
of columns of the matrix B. NRHS >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U',
the leading N-by-N upper triangular part of A con
tains the upper triangular part of the matrix A,
and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading N-by-N
lower triangular part of A contains the lower tri
angular part of the matrix A, and the strictly
upper triangular part of A is not referenced.
and the multipliers used to obtain the factor U or
L from the factorization A = U*D*U**T or A =
L*D*L**T as computed by SSYTRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block struc
ture of D, as determined by SSYTRF. If IPIV(k) >
0, then rows and columns k and IPIV(k) were inter
changed, and D(k,k) is a 1-by-1 diagonal block.
If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then
rows and columns k-1 and -IPIV(k) were inter
changed and D(k-1:k,k-1:k) is a 2-by-2 diagonal
block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0,
then rows and columns k+1 and -IPIV(k) were inter
changed and D(k:k+1,k:k+1) is a 2-by-2 diagonal
block.
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution
matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input) INTEGER
The length of WORK. LWORK >= 1, and for best per
formance LWORK >= N*NB, where NB is the optimal
blocksize for SSYTRF.
If LWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
> 0: if INFO = i, D(i,i) is exactly zero. The
factorization has been completed, but the block
diagonal matrix D is exactly singular, so the
solution could not be computed.
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