SUBROUTINE SPBSVX( FACT, UPLO, N, NDIAG, NRHS, A, LDA, AF, LDAF, * EQUED, SCALE, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, * INFO) CHARACTER * 1 FACT, UPLO, EQUED INTEGER N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER WORK2(*) REAL RCOND REAL A(LDA,*), AF(LDAF,*), SCALE(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE SPBSVX_64( FACT, UPLO, N, NDIAG, NRHS, A, LDA, AF, LDAF, * EQUED, SCALE, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, * INFO) CHARACTER * 1 FACT, UPLO, EQUED INTEGER*8 N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 WORK2(*) REAL RCOND REAL A(LDA,*), AF(LDAF,*), SCALE(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE PBSVX( FACT, UPLO, [N], NDIAG, [NRHS], A, [LDA], AF, * [LDAF], EQUED, SCALE, B, [LDB], X, [LDX], RCOND, FERR, BERR, * [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: FACT, UPLO, EQUED INTEGER :: N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL :: RCOND REAL, DIMENSION(:) :: SCALE, FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X SUBROUTINE PBSVX_64( FACT, UPLO, [N], NDIAG, [NRHS], A, [LDA], AF, * [LDAF], EQUED, SCALE, B, [LDB], X, [LDX], RCOND, FERR, BERR, * [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: FACT, UPLO, EQUED INTEGER(8) :: N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL :: RCOND REAL, DIMENSION(:) :: SCALE, FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X
void spbsvx(char fact, char uplo, int n, int ndiag, int nrhs, float *a, int lda, float *af, int ldaf, char equed, float *scale, float *b, int ldb, float *x, int ldx, float *rcond, float *ferr, float *berr, int *info);
void spbsvx_64(char fact, char uplo, long n, long ndiag, long nrhs, float *a, long lda, float *af, long ldaf, char equed, float *scale, float *b, long ldb, float *x, long ldx, float *rcond, float *ferr, float *berr, long *info);
Error bounds on the solution and a condition estimate are also provided.
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B Whether or not the system will be equilibrated depends on the scaling of the matrix A, but if equilibration is used, A is overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to factor the matrix A (after equilibration if FACT = 'E') as A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L', where U is an upper triangular band matrix, and L is a lower triangular band matrix.
3. If the leading i-by-i principal minor is not positive definite, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form of A.
5. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.
6. If equilibration was used, the matrix X is premultiplied by diag(S) so that it solves the original system before
equilibration.
On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by diag(SCALE)*A*diag(SCALE).
If FACT = 'N', then AF is an output argument and on exit returns the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.
If FACT = 'E', then AF is an output argument and on exit returns the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the equilibrated matrix A (see the description of A for the form of the equilibrated matrix).