chprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provide error bounds and backward error estimates for the solution
SUBROUTINE CHPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CHPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE HPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: A, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE HPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: A, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void chprfs(char uplo, int n, int nrhs, complex *a, complex *af, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void chprfs_64(char uplo, long n, long nrhs, complex *a, complex *af, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library chprfs(3P) NAME chprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provide error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE CHPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CHPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE HPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: A, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE HPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: A, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void chprfs(char uplo, int n, int nrhs, complex *a, complex *af, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void chprfs_64(char uplo, long n, long nrhs, complex *a, complex *af, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info); PURPOSE chprfs improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution. 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) COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. AF (input) COMPLEX array, dimension (N*(N+1)/2) The factored form of the matrix A. AF contains the block diagonal matrix D and the multipliers used to obtain the fac- tor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by CHPTRF, stored as a packed triangular matrix. IPIVOT (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHPTRF. B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CHPTRS. On exit, the improved solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). FERR (output) REAL 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) REAL 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) COMPLEX array, dimension(2*N) WORK2 (workspace) REAL array, dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 7 Nov 2015 chprfs(3P)