TESTING/LIN/dtpt03.f(3)

NAME
TESTING/LIN/dtpt03.f

SYNOPSIS

  Functions/Subroutines
subroutine dtpt03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
DTPT03

Function/Subroutine Documentation

  subroutine dtpt03 (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( * ) ap, double precision scale, double precision, dimension( * ) cnorm, double precision tscal, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, double precision resid)

DTPT03

Purpose:

     DTPT03 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 DOUBLE PRECISION 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 DOUBLE PRECISION
              The scaling factor s used in solving the triangular system.

    CNORM

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

    TSCAL

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

    X

              X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)

    RESID

              RESID is DOUBLE PRECISION
              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 dtpt03.f.

Author

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