csprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution
SUBROUTINE CSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: AP, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: AP, 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 csprfs(char uplo, int n, int nrhs, complex *ap, complex *af, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void csprfs_64(char uplo, long n, long nrhs, complex *ap, complex *af, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library csprfs(3P) NAME csprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE CSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: AP, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: AP, 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 csprfs(char uplo, int n, int nrhs, complex *ap, complex *af, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void csprfs_64(char uplo, long n, long nrhs, complex *ap, complex *af, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info); PURPOSE csprfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric 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. AP (input) Complex array, dimension (N*(N+1)/2) The upper or lower tri- angle of the symmetric matrix A, packed columnwise in a lin- ear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(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 factor U or L from the factor- ization A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, 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 CSPTRF. 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 CSPTRS. On exit, the improved solu- tion 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 corre- sponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element 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 back- ward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution). WORK (workspace) Complex array, dimension(2*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 csprfs(3P)