TESTING/LIN/dtbt03.f(3)

NAME
TESTING/LIN/dtbt03.f

SYNOPSIS

  Functions/Subroutines
subroutine dtbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
DTBT03

Function/Subroutine Documentation

  subroutine dtbt03 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, 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)

DTBT03

Purpose:

    !>
    !> DTBT03 computes the residual for the solution to a scaled triangular
    !> system of equations  A*x = s*b  or  A'*x = s*b  when A is a
    !> triangular band matrix. 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 = b  (No transpose)
    !>          = 'T':  A'*x = b  (Transpose)
    !>          = 'C':  A'*x = 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals or subdiagonals of the
    !>          triangular band matrix A.  KD >= 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.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          The upper or lower triangular band matrix A, stored in the
    !>          first kd+1 rows of the array. The j-th column of A is stored
    !>          in the j-th column of the array AB as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    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 172 of file dtbt03.f.

Author

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