stprfs.f man page

stprfs.f —

Synopsis

Functions/Subroutines

subroutine stprfs (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
STPRFS

Function/Subroutine Documentation

subroutine stprfs (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, real, dimension( * ) AP, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldx, * ) X, integer LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

STPRFS  

Purpose:

 STPRFS provides error bounds and backward error estimates for the
 solution to a system of linear equations with a triangular packed
 coefficient matrix.

 The solution matrix X must be computed by STPTRS or some other
 means before entering this routine.  STPRFS does not do iterative
 refinement because doing so cannot improve the backward error.
Parameters:

UPLO

          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

DIAG

          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

AP

          AP is REAL array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear 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.
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.

B

          B is REAL array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is REAL array, dimension (LDX,NRHS)
          The solution matrix X.

LDX

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

FERR

          FERR is 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 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

          BERR is REAL array, dimension (NRHS)
          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

          WORK is REAL array, dimension (3*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 177 of file stprfs.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page stprfs(3) is an alias of stprfs.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK