TESTING/LIN/ztbt03.f(3)    Library Functions Manual    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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/LIN/ztbt03.f(3)