ztbt03.f - Man Page

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

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.