LAPACK 3.3.1
Linear Algebra PACKage

zget08.f

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00001       SUBROUTINE ZGET08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
00002      $                   RWORK, RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     June 2010
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          TRANS
00010       INTEGER            LDA, LDB, LDX, M, 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 *  ZGET08 computes the residual for a solution of a system of linear
00022 *  equations  A*x = b  or  A'*x = b:
00023 *     RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
00024 *  where EPS is the machine epsilon.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  TRANS   (input) CHARACTER*1
00030 *          Specifies the form of the system of equations:
00031 *          = 'N':  A *x = b
00032 *          = 'T':  A^T*x = b, where A^T is the transpose of A
00033 *          = 'C':  A^H*x = b, where A^H is the conjugate transpose of A
00034 *
00035 *  M       (input) INTEGER
00036 *          The number of rows of the matrix A.  M >= 0.
00037 *
00038 *  N       (input) INTEGER
00039 *          The number of columns of the matrix A.  N >= 0.
00040 *
00041 *  NRHS    (input) INTEGER
00042 *          The number of columns of B, the matrix of right hand sides.
00043 *          NRHS >= 0.
00044 *
00045 *  A       (input) COMPLEX*16 array, dimension (LDA,N)
00046 *          The original M x N matrix A.
00047 *
00048 *  LDA     (input) INTEGER
00049 *          The leading dimension of the array A.  LDA >= max(1,M).
00050 *
00051 *  X       (input) COMPLEX*16 array, dimension (LDX,NRHS)
00052 *          The computed solution vectors for the system of linear
00053 *          equations.
00054 *
00055 *  LDX     (input) INTEGER
00056 *          The leading dimension of the array X.  If TRANS = 'N',
00057 *          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
00058 *
00059 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00060 *          On entry, the right hand side vectors for the system of
00061 *          linear equations.
00062 *          On exit, B is overwritten with the difference B - A*X.
00063 *
00064 *  LDB     (input) INTEGER
00065 *          The leading dimension of the array B.  IF TRANS = 'N',
00066 *          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
00067 *
00068 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (M)
00069 *
00070 *  RESID   (output) DOUBLE PRECISION
00071 *          The maximum over the number of right hand sides of
00072 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00073 *
00074 *  =====================================================================
00075 *
00076 *     .. Parameters ..
00077       DOUBLE PRECISION   ZERO, ONE
00078       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00079       COMPLEX*16         CONE
00080       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
00081 *     ..
00082 *     .. Local Scalars ..
00083       INTEGER            J, N1, N2
00084       DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
00085       COMPLEX*16         ZDUM
00086 *     ..
00087 *     .. External Functions ..
00088       LOGICAL            LSAME
00089       INTEGER            IZAMAX
00090       DOUBLE PRECISION   DLAMCH, ZLANGE
00091       EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANGE
00092 *     ..
00093 *     .. External Subroutines ..
00094       EXTERNAL           ZGEMM
00095 *     ..
00096 *     .. Intrinsic Functions ..
00097       INTRINSIC          ABS, DBLE, DIMAG, MAX
00098 *     ..
00099 *     .. Statement Functions ..
00100       DOUBLE PRECISION   CABS1
00101 *     ..
00102 *     .. Statement Function definitions ..
00103       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00104 *     ..
00105 *     .. Executable Statements ..
00106 *
00107 *     Quick exit if M = 0 or N = 0 or NRHS = 0
00108 *
00109       IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
00110          RESID = ZERO
00111          RETURN
00112       END IF
00113 *
00114       IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
00115          N1 = N
00116          N2 = M
00117       ELSE
00118          N1 = M
00119          N2 = N
00120       END IF
00121 *
00122 *     Exit with RESID = 1/EPS if ANORM = 0.
00123 *
00124       EPS = DLAMCH( 'Epsilon' )
00125       ANORM = ZLANGE( 'I', N1, N2, A, LDA, RWORK )
00126       IF( ANORM.LE.ZERO ) THEN
00127          RESID = ONE / EPS
00128          RETURN
00129       END IF
00130 *
00131 *     Compute  B - A*X  (or  B - A'*X ) and store in B.
00132 *
00133       CALL ZGEMM( TRANS, 'No transpose', N1, NRHS, N2, -CONE, A, LDA, X,
00134      $            LDX, CONE, B, LDB )
00135 *
00136 *     Compute the maximum over the number of right hand sides of
00137 *        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
00138 *
00139       RESID = ZERO
00140       DO 10 J = 1, NRHS
00141          BNORM = CABS1( B( IZAMAX( N1, B( 1, J ), 1 ), J ) )
00142          XNORM = CABS1( X( IZAMAX( N2, X( 1, J ), 1 ), J ) )
00143          IF( XNORM.LE.ZERO ) THEN
00144             RESID = ONE / EPS
00145          ELSE
00146             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00147          END IF
00148    10 CONTINUE
00149 *
00150       RETURN
00151 *
00152 *     End of ZGET02
00153 *
00154       END
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