LAPACK 3.3.1 Linear Algebra PACKage

zpot06.f

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```00001       SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
00002      \$                   RWORK, RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1.2) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     May 2007
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            LDA, LDB, LDX, N, NRHS
00011       DOUBLE PRECISION   RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   RWORK( * )
00015       COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZPOT06 computes the residual for a solution of a system of linear
00022 *  equations  A*x = b :
00023 *     RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
00024 *  where EPS is the machine epsilon.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  UPLO    (input) CHARACTER*1
00030 *          Specifies whether the upper or lower triangular part of the
00031 *          symmetric matrix A is stored:
00032 *          = 'U':  Upper triangular
00033 *          = 'L':  Lower triangular
00034 *
00035 *  N       (input) INTEGER
00036 *          The number of rows and columns of the matrix A.  N >= 0.
00037 *
00038 *  NRHS    (input) INTEGER
00039 *          The number of columns of B, the matrix of right hand sides.
00040 *          NRHS >= 0.
00041 *
00042 *  A       (input) COMPLEX*16 array, dimension (LDA,N)
00043 *          The original M x N matrix A.
00044 *
00045 *  LDA     (input) INTEGER
00046 *          The leading dimension of the array A.  LDA >= max(1,N).
00047 *
00048 *  X       (input) COMPLEX*16 array, dimension (LDX,NRHS)
00049 *          The computed solution vectors for the system of linear
00050 *          equations.
00051 *
00052 *  LDX     (input) INTEGER
00053 *          The leading dimension of the array X.  If TRANS = 'N',
00054 *          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
00055 *
00056 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00057 *          On entry, the right hand side vectors for the system of
00058 *          linear equations.
00059 *          On exit, B is overwritten with the difference B - A*X.
00060 *
00061 *  LDB     (input) INTEGER
00062 *          The leading dimension of the array B.  IF TRANS = 'N',
00063 *          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
00064 *
00065 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
00066 *
00067 *  RESID   (output) DOUBLE PRECISION
00068 *          The maximum over the number of right hand sides of
00069 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00070 *
00071 *  =====================================================================
00072 *
00073 *     .. Parameters ..
00074       DOUBLE PRECISION   ZERO, ONE, NEGONE
00075       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00076       PARAMETER          ( NEGONE = -1.0D+0 )
00077       COMPLEX*16         CONE, NEGCONE
00078       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
00079       PARAMETER          ( NEGCONE = ( -1.0D+0, 0.0D+0 ) )
00080 *     ..
00081 *     .. Local Scalars ..
00082       INTEGER            IFAIL, J
00083       DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
00084       COMPLEX*16         ZDUM
00085 *     ..
00086 *     .. External Functions ..
00087       LOGICAL            LSAME
00088       INTEGER            IZAMAX
00089       DOUBLE PRECISION   DLAMCH, ZLANSY
00090       EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANSY
00091 *     ..
00092 *     .. External Subroutines ..
00093       EXTERNAL           ZHEMM
00094 *     ..
00095 *     .. Intrinsic Functions ..
00096       INTRINSIC          ABS, DBLE, DIMAG, MAX
00097 *     ..
00098 *     .. Statement Functions ..
00099       DOUBLE PRECISION   CABS1
00100 *     ..
00101 *     .. Statement Function definitions ..
00102       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00103 *     ..
00104 *     ..
00105 *     .. Executable Statements ..
00106 *
00107 *     Quick exit if N = 0 or NRHS = 0
00108 *
00109       IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN
00110          RESID = ZERO
00111          RETURN
00112       END IF
00113 *
00114 *     Exit with RESID = 1/EPS if ANORM = 0.
00115 *
00116       EPS = DLAMCH( 'Epsilon' )
00117       ANORM = ZLANSY( 'I', UPLO, N, A, LDA, RWORK )
00118       IF( ANORM.LE.ZERO ) THEN
00119          RESID = ONE / EPS
00120          RETURN
00121       END IF
00122 *
00123 *     Compute  B - A*X  and store in B.
00124       IFAIL=0
00125 *
00126       CALL ZHEMM( 'Left', UPLO, N, NRHS, NEGCONE, A, LDA, X,
00127      \$            LDX, CONE, B, LDB )
00128 *
00129 *     Compute the maximum over the number of right hand sides of
00130 *        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
00131 *
00132       RESID = ZERO
00133       DO 10 J = 1, NRHS
00134          BNORM = CABS1(B(IZAMAX( N, B( 1, J ), 1 ),J))
00135          XNORM = CABS1(X(IZAMAX( N, X( 1, J ), 1 ),J))
00136          IF( XNORM.LE.ZERO ) THEN
00137             RESID = ONE / EPS
00138          ELSE
00139             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00140          END IF
00141    10 CONTINUE
00142 *
00143       RETURN
00144 *
00145 *     End of ZPOT06
00146 *
00147       END
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