dpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, provide error bounds and backward error estimates for the solution
SUBROUTINE DPPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER N, NRHS, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DPPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE PPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X SUBROUTINE PPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void dpprfs(char uplo, int n, int nrhs, double *a, double *af, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dpprfs_64(char uplo, long n, long nrhs, double *a, double *af, double *b, long ldb, double *x, long ldx, double *ferr, dou- ble *berr, long *info);
Oracle Solaris Studio Performance Library dpprfs(3P) NAME dpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, provide error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE DPPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER N, NRHS, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DPPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE PPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X SUBROUTINE PPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void dpprfs(char uplo, int n, int nrhs, double *a, double *af, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dpprfs_64(char uplo, long n, long nrhs, double *a, double *af, double *b, long ldb, double *x, long ldx, double *ferr, dou- ble *berr, long *info); PURPOSE dpprfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, 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. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. AF (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPPTRF/ZPPTRF, packed columnwise in a linear array in the same format as A (see A). B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B. LDB (input) The leading dimension of the array B. LDB >= max(1,N). X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by DPPTRS. On exit, the improved solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). FERR (output) DOUBLE PRECISION array, dimension (NRHS) 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) DOUBLE PRECISION array, dimension (NRHS) 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) DOUBLE PRECISION array, dimension(3*N) WORK2 (workspace) INTEGER array, dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 7 Nov 2015 dpprfs(3P)