numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/sladiv.f | 5827B | -rw-r--r-- |
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*> \brief \b SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SLADIV + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sladiv.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sladiv.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sladiv.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SLADIV( A, B, C, D, P, Q ) * * .. Scalar Arguments .. * REAL A, B, C, D, P, Q * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLADIV performs complex division in real arithmetic *> *> a + i*b *> p + i*q = --------- *> c + i*d *> *> The algorithm is due to Michael Baudin and Robert L. Smith *> and can be found in the paper *> "A Robust Complex Division in Scilab" *> \endverbatim * * Arguments: * ========== * *> \param[in] A *> \verbatim *> A is REAL *> \endverbatim *> *> \param[in] B *> \verbatim *> B is REAL *> \endverbatim *> *> \param[in] C *> \verbatim *> C is REAL *> \endverbatim *> *> \param[in] D *> \verbatim *> D is REAL *> The scalars a, b, c, and d in the above expression. *> \endverbatim *> *> \param[out] P *> \verbatim *> P is REAL *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is REAL *> The scalars p and q in the above expression. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup ladiv * * ===================================================================== SUBROUTINE SLADIV( A, B, C, D, P, Q ) * * -- 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 .. REAL A, B, C, D, P, Q * .. * * ===================================================================== * * .. Parameters .. REAL BS PARAMETER ( BS = 2.0E0 ) REAL HALF PARAMETER ( HALF = 0.5E0 ) REAL TWO PARAMETER ( TWO = 2.0E0 ) * * .. Local Scalars .. REAL AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL SLADIV1 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * AA = A BB = B CC = C DD = D AB = MAX( ABS(A), ABS(B) ) CD = MAX( ABS(C), ABS(D) ) S = 1.0E0 OV = SLAMCH( 'Overflow threshold' ) UN = SLAMCH( 'Safe minimum' ) EPS = SLAMCH( 'Epsilon' ) BE = BS / (EPS*EPS) IF( AB >= HALF*OV ) THEN AA = HALF * AA BB = HALF * BB S = TWO * S END IF IF( CD >= HALF*OV ) THEN CC = HALF * CC DD = HALF * DD S = HALF * S END IF IF( AB <= UN*BS/EPS ) THEN AA = AA * BE BB = BB * BE S = S / BE END IF IF( CD <= UN*BS/EPS ) THEN CC = CC * BE DD = DD * BE S = S * BE END IF IF( ABS( D ).LE.ABS( C ) ) THEN CALL SLADIV1(AA, BB, CC, DD, P, Q) ELSE CALL SLADIV1(BB, AA, DD, CC, P, Q) Q = -Q END IF P = P * S Q = Q * S * RETURN * * End of SLADIV * END *> \ingroup ladiv SUBROUTINE SLADIV1( A, B, C, D, P, Q ) * * -- 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 .. REAL A, B, C, D, P, Q * .. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E0 ) * * .. Local Scalars .. REAL R, T * .. * .. External Functions .. REAL SLADIV2 EXTERNAL SLADIV2 * .. * .. Executable Statements .. * R = D / C T = ONE / (C + D * R) P = SLADIV2(A, B, C, D, R, T) A = -A Q = SLADIV2(B, A, C, D, R, T) * RETURN * * End of SLADIV1 * END *> \ingroup ladiv REAL FUNCTION SLADIV2( A, B, C, D, R, T ) * * -- 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 .. REAL A, B, C, D, R, T * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * * .. Local Scalars .. REAL BR * .. * .. Executable Statements .. * IF( R.NE.ZERO ) THEN BR = B * R if( BR.NE.ZERO ) THEN SLADIV2 = (A + BR) * T ELSE SLADIV2 = A * T + (B * T) * R END IF ELSE SLADIV2 = (A + D * (B / C)) * T END IF * RETURN * * End of SLADIV2 * END