numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/zrscl.f | 6357B | -rw-r--r-- |
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*> \brief \b ZDRSCL multiplies a vector by the reciprocal of a real scalar. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZDRSCL + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zdrscl.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zdrscl.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zdrscl.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZRSCL( N, A, X, INCX ) * * .. Scalar Arguments .. * INTEGER INCX, N * COMPLEX*16 A * .. * .. Array Arguments .. * COMPLEX*16 X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZRSCL multiplies an n-element complex vector x by the complex scalar *> 1/a. This is done without overflow or underflow as long as *> the final result x/a does not overflow or underflow. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of components of the vector x. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 *> The scalar a which is used to divide each component of x. *> A must not be 0, or the subroutine will divide by zero. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension *> (1+(N-1)*abs(INCX)) *> The n-element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of the vector SX. *> > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZRSCL( N, A, X, INCX ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INCX, N COMPLEX*16 A * .. * .. Array Arguments .. COMPLEX*16 X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. DOUBLE PRECISION SAFMAX, SAFMIN, OV, AR, AI, ABSR, ABSI, UR, UI * .. * .. External Functions .. DOUBLE PRECISION DLAMCH COMPLEX*16 ZLADIV EXTERNAL DLAMCH, ZLADIV * .. * .. External Subroutines .. EXTERNAL DSCAL, ZDSCAL, ZDRSCL * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) $ RETURN * * Get machine parameters * SAFMIN = DLAMCH( 'S' ) SAFMAX = ONE / SAFMIN OV = DLAMCH( 'O' ) * * Initialize constants related to A. * AR = DBLE( A ) AI = DIMAG( A ) ABSR = ABS( AR ) ABSI = ABS( AI ) * IF( AI.EQ.ZERO ) THEN * If alpha is real, then we can use csrscl CALL ZDRSCL( N, AR, X, INCX ) * ELSE IF( AR.EQ.ZERO ) THEN * If alpha has a zero real part, then we follow the same rules as if * alpha were real. IF( ABSI.GT.SAFMAX ) THEN CALL ZDSCAL( N, SAFMIN, X, INCX ) CALL ZSCAL( N, DCMPLX( ZERO, -SAFMAX / AI ), X, INCX ) ELSE IF( ABSI.LT.SAFMIN ) THEN CALL ZSCAL( N, DCMPLX( ZERO, -SAFMIN / AI ), X, INCX ) CALL ZDSCAL( N, SAFMAX, X, INCX ) ELSE CALL ZSCAL( N, DCMPLX( ZERO, -ONE / AI ), X, INCX ) END IF * ELSE * The following numbers can be computed. * They are the inverse of the real and imaginary parts of 1/alpha. * Note that a and b are always different from zero. * NaNs are only possible if either: * 1. alphaR or alphaI is NaN. * 2. alphaR and alphaI are both infinite, in which case it makes sense * to propagate a NaN. UR = AR + AI * ( AI / AR ) UI = AI + AR * ( AR / AI ) * IF( (ABS( UR ).LT.SAFMIN).OR.(ABS( UI ).LT.SAFMIN) ) THEN * This means that both alphaR and alphaI are very small. CALL ZSCAL( N, DCMPLX( SAFMIN / UR, -SAFMIN / UI ), X, $ INCX ) CALL ZDSCAL( N, SAFMAX, X, INCX ) ELSE IF( (ABS( UR ).GT.SAFMAX).OR.(ABS( UI ).GT.SAFMAX) ) THEN IF( (ABSR.GT.OV).OR.(ABSI.GT.OV) ) THEN * This means that a and b are both Inf. No need for scaling. CALL ZSCAL( N, DCMPLX( ONE / UR, -ONE / UI ), X, $ INCX ) ELSE CALL ZDSCAL( N, SAFMIN, X, INCX ) IF( (ABS( UR ).GT.OV).OR.(ABS( UI ).GT.OV) ) THEN * Infs were generated. We do proper scaling to avoid them. IF( ABSR.GE.ABSI ) THEN * ABS( UR ) <= ABS( UI ) UR = (SAFMIN * AR) + SAFMIN * (AI * ( AI / AR )) UI = (SAFMIN * AI) + AR * ( (SAFMIN * AR) / AI ) ELSE * ABS( UR ) > ABS( UI ) UR = (SAFMIN * AR) + AI * ( (SAFMIN * AI) / AR ) UI = (SAFMIN * AI) + SAFMIN * (AR * ( AR / AI )) END IF CALL ZSCAL( N, DCMPLX( ONE / UR, -ONE / UI ), X, $ INCX ) ELSE CALL ZSCAL( N, DCMPLX( SAFMAX / UR, -SAFMAX / UI ), $ X, INCX ) END IF END IF ELSE CALL ZSCAL( N, DCMPLX( ONE / UR, -ONE / UI ), X, INCX ) END IF END IF * RETURN * * End of ZRSCL * END