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SUBROUTINE DPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
$ RWORK, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER KD, LDA, LDB, LDX, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
$ X( LDX, * )
* ..
*
* Purpose
* =======
*
* DPBT02 computes the residual for a solution of a symmetric banded
* system of equations A*x = b:
* RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
* where EPS is the machine precision.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The number of rows and columns of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of super-diagonals of the matrix A if UPLO = 'U',
* or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* The original symmetric band matrix A. If UPLO = 'U', the
* upper triangular part of A is stored as a band matrix; if
* UPLO = 'L', the lower triangular part of A is stored. The
* columns of the appropriate triangle are stored in the columns
* of A and the diagonals of the triangle are stored in the rows
* of A. See DPBTRF for further details.
*
* LDA (input) INTEGER.
* The leading dimension of the array A. LDA >= max(1,KD+1).
*
* X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
* The computed solution vectors for the system of linear
* equations.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the right hand side vectors for the system of
* linear equations.
* On exit, B is overwritten with the difference B - A*X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RESID (output) DOUBLE PRECISION
* The maximum over the number of right hand sides of
* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J
DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DASUM, DLAMCH, DLANSB
EXTERNAL DASUM, DLAMCH, DLANSB
* ..
* .. External Subroutines ..
EXTERNAL DSBMV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0.
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = DLANSB( '1', UPLO, N, KD, A, LDA, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - A*X
*
DO 10 J = 1, NRHS
CALL DSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE,
$ B( 1, J ), 1 )
10 CONTINUE
*
* Compute the maximum over the number of right hand sides of
* norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
*
RESID = ZERO
DO 20 J = 1, NRHS
BNORM = DASUM( N, B( 1, J ), 1 )
XNORM = DASUM( N, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
20 CONTINUE
*
RETURN
*
* End of DPBT02
*
END
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