Contents


NAME

     cporfs - improve the computed solution to a system of linear
     equations  when the coefficient matrix is Hermitian positive
     definite,

SYNOPSIS

     SUBROUTINE CPORFS(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
           FERR, BERR, WORK, WORK2, INFO)

     CHARACTER * 1 UPLO
     COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
     INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
     REAL FERR(*), BERR(*), WORK2(*)

     SUBROUTINE CPORFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
           FERR, BERR, WORK, WORK2, INFO)

     CHARACTER * 1 UPLO
     COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
     INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
     REAL FERR(*), BERR(*), WORK2(*)

  F95 INTERFACE
     SUBROUTINE PORFS(UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], B, [LDB],
            X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:) :: WORK
     COMPLEX, DIMENSION(:,:) :: A, AF, B, X
     INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
     REAL, DIMENSION(:) :: FERR, BERR, WORK2

     SUBROUTINE PORFS_64(UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], B, [LDB],
            X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:) :: WORK
     COMPLEX, DIMENSION(:,:) :: A, AF, B, X
     INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
     REAL, DIMENSION(:) :: FERR, BERR, WORK2

  C INTERFACE
     #include <sunperf.h>

     void cporfs(char uplo, int n, int nrhs, complex *a, int lda,
               complex  *af,  int ldaf, complex *b, int ldb, com-
               plex *x, int ldx, float *ferr,  float  *berr,  int
               *info);

     void cporfs_64(char uplo, long n,  long  nrhs,  complex  *a,
               long lda, complex *af, long ldaf, complex *b, long
               ldb, complex *x,  long  ldx,  float  *ferr,  float
               *berr, long *info);

PURPOSE

     cporfs improves the computed solution to a system of  linear
     equations  when the coefficient matrix is Hermitian positive
     definite, and provides error bounds and backward error esti-
     mates 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) The Hermitian matrix A.  If UPLO = 'U', the  lead-
               ing N-by-N upper triangular part of A contains the
               upper triangular part of the  matrix  A,  and  the
               strictly  lower triangular part of A is not refer-
               enced.  If UPLO = 'L', the  leading  N-by-N  lower
               triangular part of A contains the lower triangular
               part of the matrix A, and the strictly upper  tri-
               angular part of A is not referenced.

     LDA (input)
               The leading dimension of  the  array  A.   LDA  >=
               max(1,N).

     AF (input)
               The triangular factor U or  L  from  the  Cholesky
               factorization  A  =  U**H*U or A = L*L**H, as com-
               puted by CPOTRF.

     LDAF (input)
               The leading dimension of the array  AF.   LDAF  >=
               max(1,N).

     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
               CPOTRS.  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  solu-
               tion  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 estimated
               upper bound for the magnitude of the largest  ele-
               ment 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)
               The componentwise relative backward 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)
               dimension(2*N)

     WORK2 (workspace)
               dimension(N)

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value