sgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution
SUBROUTINE SGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*), WORK2(*) REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE SGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*), WORK2(*) REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE GERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT, WORK2 REAL, DIMENSION(:) :: FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X SUBROUTINE GERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2 REAL, DIMENSION(:) :: FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X C INTERFACE #include <sunperf.h> void sgerfs(char transa, int n, int nrhs, float *a, int lda, float *af, int ldaf, int *ipivot, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info); void sgerfs_64(char transa, long n, long nrhs, float *a, long lda, float *af, long ldaf, long *ipivot, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library sgerfs(3P) NAME sgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE SGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*), WORK2(*) REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE SGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*), WORK2(*) REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE GERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT, WORK2 REAL, DIMENSION(:) :: FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X SUBROUTINE GERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2 REAL, DIMENSION(:) :: FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X C INTERFACE #include <sunperf.h> void sgerfs(char transa, int n, int nrhs, float *a, int lda, float *af, int ldaf, int *ipivot, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info); void sgerfs_64(char transa, long n, long nrhs, float *a, long lda, float *af, long ldaf, long *ipivot, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info); PURPOSE sgerfs improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solu- tion. ARGUMENTS TRANSA (input) Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose) N (input) The order of the matrix A. N >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. A (input) The original N-by-N matrix A. LDA (input) The leading dimension of the array A. LDA >= max(1,N). AF (input) The factors L and U from the factorization A = P*L*U as com- puted by SGETRF. LDAF (input) The leading dimension of the array AF. LDAF >= max(1,N). IPIVOT (input) The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIVOT(i). B (input) The right hand side matrix B. LDB (input) The leading dimension of the array B. LDB >= max(1,N). X (input/output) On entry, the solution matrix X, as computed by SGETRS. On exit, the improved solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). FERR (output) The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an esti- mated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest ele- ment in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error. BERR (output) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any ele- ment of A or B that makes X(j) an exact solution). WORK (workspace) dimension(3*N) WORK2 (workspace) dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 7 Nov 2015 sgerfs(3P)