cpprfs man page on OpenIndiana

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cpprfs(3P)		    Sun Performance Library		    cpprfs(3P)

NAME
       cpprfs  - improve the computed solution to a system of linear equations
       when the coefficient matrix is Hermitian positive definite and  packed,
       and provides error bounds and backward error estimates for the solution

SYNOPSIS
       SUBROUTINE CPPRFS(UPLO, N, NRHS, A, AF, 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
       REAL FERR(*), BERR(*), WORK2(*)

       SUBROUTINE CPPRFS_64(UPLO, N, NRHS, A, AF, 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
       REAL FERR(*), BERR(*), WORK2(*)

   F95 INTERFACE
       SUBROUTINE PPRFS(UPLO, [N], [NRHS], A, AF, 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
       REAL, DIMENSION(:) :: FERR, BERR, WORK2

       SUBROUTINE PPRFS_64(UPLO, [N], [NRHS], A, AF, 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
       REAL, DIMENSION(:) :: FERR, BERR, WORK2

   C INTERFACE
       #include <sunperf.h>

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

       void  cpprfs_64(char  uplo, long n, long nrhs, complex *a, complex *af,
		 complex *b, long ldb, complex	*x,  long  ldx,	 float	*ferr,
		 float *berr, long *info);

PURPOSE
       cpprfs  improves	 the computed solution to a system of linear equations
       when the coefficient matrix is Hermitian 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) 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)*(2n-j)/2)  =
		 A(i,j) for j<=i<=n.

       AF (input) COMPLEX array, dimension (N*(N+1)/2)
		 The  triangular factor U or L from the Cholesky factorization
		 A = U**H*U or A  =  L*L**H,  as  computed  by	SPPTRF/CPPTRF,
		 packed	 columnwise  in a linear array in the same format as A
		 (see A).

       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  CPPTRS.   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

				  6 Mar 2009			    cpprfs(3P)
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