stpt03.f - Man Page

TESTING/LIN/stpt03.f

Synopsis

Functions/Subroutines

subroutine stpt03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
STPT03

Function/Subroutine Documentation

subroutine stpt03 (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( * ) ap, real scale, real, dimension( * ) cnorm, real tscal, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real resid)

STPT03

Purpose:

 STPT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b  when the triangular
 matrix A is stored in packed format.  Here A' is the transpose of A,
 s is a scalar, and x and b are N by NRHS matrices.  The test ratio is
 the maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = s*b  (No transpose)
          = 'T':  A'*x = s*b  (Transpose)
          = 'C':  A'*x = s*b  (Conjugate transpose = Transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  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 X and B.  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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

SCALE

          SCALE is REAL
          The scaling factor s used in solving the triangular system.

CNORM

          CNORM is REAL array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.

TSCAL

          TSCAL is REAL
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.

X

          X is REAL array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

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

B

          B is REAL array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

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

WORK

          WORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 159 of file stpt03.f.

Author

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Referenced By

The man page stpt03(3) is an alias of stpt03.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK