TESTING/LIN/ztbt03.f(3)

NAME
TESTING/LIN/ztbt03.f

SYNOPSIS

  Functions/Subroutines
subroutine ztbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
ZTBT03

Function/Subroutine Documentation

  subroutine ztbt03 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, double precision scale, double precision, dimension( * ) cnorm, double precision tscal, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, double precision resid)

ZTBT03

Purpose:

     ZTBT03 computes the residual for the solution to a scaled triangular
     system of equations  A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b
     when A is a triangular band matrix.  Here A**T  denotes the transpose
     of A, A**H denotes the conjugate 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, A**T, or A**H, 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**T *x = s*b  (Transpose)
              = 'C':  A**H *x = s*b  (Conjugate 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 174 of file ztbt03.f.

Author

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