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SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
$ RWORK, RESID )
*
* -- LAPACK test routine (version 3.1.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* May 2007
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDA, LDB, LDX, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
* Purpose
* =======
*
* ZPOT06 computes the residual for a solution of a system of linear
* equations A*x = b :
* RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
* where EPS is the machine epsilon.
*
* 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.
*
* NRHS (input) INTEGER
* The number of columns of B, the matrix of right hand sides.
* NRHS >= 0.
*
* A (input) COMPLEX*16 array, dimension (LDA,N)
* The original M x N matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* X (input) COMPLEX*16 array, dimension (LDX,NRHS)
* The computed solution vectors for the system of linear
* equations.
*
* LDX (input) INTEGER
* The leading dimension of the array X. If TRANS = 'N',
* LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
*
* B (input/output) COMPLEX*16 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. IF TRANS = 'N',
* LDB >= max(1,M); if TRANS = 'T' or 'C', 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, NEGONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
PARAMETER ( NEGONE = -1.0D+0 )
COMPLEX*16 CONE, NEGCONE
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
PARAMETER ( NEGCONE = ( -1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER IFAIL, J
DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
COMPLEX*16 ZDUM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IZAMAX
DOUBLE PRECISION DLAMCH, ZLANSY
EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANSY
* ..
* .. External Subroutines ..
EXTERNAL ZHEMM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG, MAX
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0
*
IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANSY( 'I', UPLO, N, A, LDA, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - A*X and store in B.
IFAIL=0
*
CALL ZHEMM( 'Left', UPLO, N, NRHS, NEGCONE, A, LDA, X,
$ LDX, CONE, B, LDB )
*
* Compute the maximum over the number of right hand sides of
* norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
*
RESID = ZERO
DO 10 J = 1, NRHS
BNORM = CABS1(B(IZAMAX( N, B( 1, J ), 1 ),J))
XNORM = CABS1(X(IZAMAX( N, X( 1, J ), 1 ),J))
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
10 CONTINUE
*
RETURN
*
* End of ZPOT06
*
END
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