cptrfs (3p)

Name

cptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiag- onal, provide error bounds and backward error estimates for the solu- tion

Synopsis

SUBROUTINE CPTRFS(UPLO, N, NRHS, D, E, DF, EF, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER*1 UPLO
COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
REAL D(*), DF(*), FERR(*), BERR(*), WORK2(*)

SUBROUTINE CPTRFS_64(UPLO, N, NRHS, D, E, DF, EF, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER*1 UPLO
COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
REAL D(*), DF(*), FERR(*), BERR(*), WORK2(*)




F95 INTERFACE
SUBROUTINE PTRFS(UPLO, N, NRHS, D, E, DF, EF, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: E, EF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: D, DF, FERR, BERR, WORK2

SUBROUTINE PTRFS_64(UPLO, N, NRHS, D, E, DF, EF, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: E, EF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: D, DF, FERR, BERR, WORK2




C INTERFACE
#include <sunperf.h>

void cptrfs(char uplo, int n, int nrhs, float  *d,  complex  *e,  float
*df,  complex  *ef, complex *b, int ldb, complex *x, int ldx,
float *ferr, float *berr, int *info);

void cptrfs_64(char uplo, long n, long  nrhs,  float  *d,  complex  *e,
float  *df,  complex  *ef,  complex *b, long ldb, complex *x,
long ldx, float *ferr, float *berr, long *info);

Description

Oracle Solaris Studio Performance Library                           cptrfs(3P)



NAME
       cptrfs  - improve the computed solution to a system of linear equations
       when the coefficient matrix is Hermitian positive definite and tridiag-
       onal,  provide  error bounds and backward error estimates for the solu-
       tion


SYNOPSIS
       SUBROUTINE CPTRFS(UPLO, N, NRHS, D, E, DF, EF, B, LDB, X,
             LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER*1 UPLO
       COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
       INTEGER N, NRHS, LDB, LDX, INFO
       REAL D(*), DF(*), FERR(*), BERR(*), WORK2(*)

       SUBROUTINE CPTRFS_64(UPLO, N, NRHS, D, E, DF, EF, B, LDB,
             X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER*1 UPLO
       COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
       INTEGER*8 N, NRHS, LDB, LDX, INFO
       REAL D(*), DF(*), FERR(*), BERR(*), WORK2(*)




   F95 INTERFACE
       SUBROUTINE PTRFS(UPLO, N, NRHS, D, E, DF, EF, B, LDB,
              X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: E, EF, WORK
       COMPLEX, DIMENSION(:,:) :: B, X
       INTEGER :: N, NRHS, LDB, LDX, INFO
       REAL, DIMENSION(:) :: D, DF, FERR, BERR, WORK2

       SUBROUTINE PTRFS_64(UPLO, N, NRHS, D, E, DF, EF, B,
              LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: E, EF, WORK
       COMPLEX, DIMENSION(:,:) :: B, X
       INTEGER(8) :: N, NRHS, LDB, LDX, INFO
       REAL, DIMENSION(:) :: D, DF, FERR, BERR, WORK2




   C INTERFACE
       #include <sunperf.h>

       void cptrfs(char uplo, int n, int nrhs, float  *d,  complex  *e,  float
                 *df,  complex  *ef, complex *b, int ldb, complex *x, int ldx,
                 float *ferr, float *berr, int *info);

       void cptrfs_64(char uplo, long n, long  nrhs,  float  *d,  complex  *e,
                 float  *df,  complex  *ef,  complex *b, long ldb, complex *x,
                 long ldx, float *ferr, float *berr, long *info);



PURPOSE
       cptrfs improves the computed solution to a system of  linear  equations
       when the coefficient matrix is Hermitian positive definite and tridiag-
       onal, and provides error bounds and backward error  estimates  for  the
       solution.


ARGUMENTS
       UPLO (input)
                 Specifies whether the superdiagonal or the subdiagonal of the
                 tridiagonal matrix A is stored and the form of the factoriza-
                 tion:
                 = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
                 =  'L':   E  is the subdiagonal of A, and A = L*D*L**H.  (The
                 two forms are equivalent if A is real.)


       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 matrix B.  NRHS >= 0.


       D (input) The n real diagonal elements of the tridiagonal matrix A.


       E (input) The  (n-1)  off-diagonal elements of the tridiagonal matrix A
                 (see UPLO).


       DF (input)
                 The n diagonal elements of the diagonal  matrix  D  from  the
                 factorization computed by CPTTRF.


       EF (input)
                 The (n-1) off-diagonal elements of the unit bidiagonal factor
                 U or L from the factorization computed by CPTTRF (see  UPLO).


       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 CPTTRS.  On
                 exit, the improved solution matrix X.


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


       FERR (output)
                 The 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 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).


       BERR (output)
                 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)
                 dimension(N)

       WORK2 (workspace)
                 dimension(N)


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




                                  7 Nov 2015                        cptrfs(3P)