dpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, provide error bounds and backward error estimates for the solution
SUBROUTINE DPBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DPBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE PBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X SUBROUTINE PBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X C INTERFACE #include <sunperf.h> void dpbrfs(char uplo, int n, int kd, int nrhs, double *a, int lda, double *af, int ldaf, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dpbrfs_64(char uplo, long n, long kd, long nrhs, double *a, long lda, double *af, long ldaf, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library dpbrfs(3P) NAME dpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, provide error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE DPBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DPBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE PBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X SUBROUTINE PBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X C INTERFACE #include <sunperf.h> void dpbrfs(char uplo, int n, int kd, int nrhs, double *a, int lda, double *af, int ldaf, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dpbrfs_64(char uplo, long n, long kd, long nrhs, double *a, long lda, double *af, long ldaf, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info); PURPOSE dpbrfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solu- tion. ARGUMENTS UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The order of the matrix A. N >= 0. KD (input) The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 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 upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). LDA (input) The leading dimension of the array A. LDA >= KD+1. AF (input) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A as computed by DPBTRF, in the same storage format as A (see A). LDAF (input) The leading dimension of the array AF. LDAF >= KD+1. 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 DPBTRS. 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 dpbrfs(3P)