numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/BLAS/SRC/drotmg.f | 6715B | -rw-r--r-- |
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*> \brief \b DROTMG * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM) * * .. Scalar Arguments .. * DOUBLE PRECISION DD1,DD2,DX1,DY1 * .. * .. Array Arguments .. * DOUBLE PRECISION DPARAM(5) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS *> THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T. *> WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. *> *> DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 *> *> (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) *> H=( ) ( ) ( ) ( ) *> (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). *> LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 *> RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE *> VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) *> *> THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE *> INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE *> OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. *> *> \endverbatim * * Arguments: * ========== * *> \param[in,out] DD1 *> \verbatim *> DD1 is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] DD2 *> \verbatim *> DD2 is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] DX1 *> \verbatim *> DX1 is DOUBLE PRECISION *> \endverbatim *> *> \param[in] DY1 *> \verbatim *> DY1 is DOUBLE PRECISION *> \endverbatim *> *> \param[out] DPARAM *> \verbatim *> DPARAM is DOUBLE PRECISION array, dimension (5) *> DPARAM(1)=DFLAG *> DPARAM(2)=DH11 *> DPARAM(3)=DH21 *> DPARAM(4)=DH12 *> DPARAM(5)=DH22 *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup rotmg * * ===================================================================== SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM) * * -- Reference BLAS level1 routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. DOUBLE PRECISION DD1,DD2,DX1,DY1 * .. * .. Array Arguments .. DOUBLE PRECISION DPARAM(5) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION DFLAG,DH11,DH12,DH21,DH22,DP1,DP2,DQ1,DQ2,DTEMP, $ DU,GAM,GAMSQ,ONE,RGAMSQ,TWO,ZERO * .. * .. Intrinsic Functions .. INTRINSIC DABS * .. * .. Data statements .. * DATA ZERO,ONE,TWO/0.D0,1.D0,2.D0/ DATA GAM,GAMSQ,RGAMSQ/4096.D0,16777216.D0,5.9604645D-8/ * .. IF (DD1.LT.ZERO) THEN * GO ZERO-H-D-AND-DX1.. DFLAG = -ONE DH11 = ZERO DH12 = ZERO DH21 = ZERO DH22 = ZERO * DD1 = ZERO DD2 = ZERO DX1 = ZERO ELSE * CASE-DD1-NONNEGATIVE DP2 = DD2*DY1 IF (DP2.EQ.ZERO) THEN DFLAG = -TWO DPARAM(1) = DFLAG RETURN END IF * REGULAR-CASE.. DP1 = DD1*DX1 DQ2 = DP2*DY1 DQ1 = DP1*DX1 * IF (DABS(DQ1).GT.DABS(DQ2)) THEN DH21 = -DY1/DX1 DH12 = DP2/DP1 * DU = ONE - DH12*DH21 * IF (DU.GT.ZERO) THEN DFLAG = ZERO DD1 = DD1/DU DD2 = DD2/DU DX1 = DX1*DU ELSE * This code path if here for safety. We do not expect this * condition to ever hold except in edge cases with rounding * errors. See DOI: 10.1145/355841.355847 DFLAG = -ONE DH11 = ZERO DH12 = ZERO DH21 = ZERO DH22 = ZERO * DD1 = ZERO DD2 = ZERO DX1 = ZERO END IF ELSE IF (DQ2.LT.ZERO) THEN * GO ZERO-H-D-AND-DX1.. DFLAG = -ONE DH11 = ZERO DH12 = ZERO DH21 = ZERO DH22 = ZERO * DD1 = ZERO DD2 = ZERO DX1 = ZERO ELSE DFLAG = ONE DH11 = DP1/DP2 DH22 = DX1/DY1 DU = ONE + DH11*DH22 DTEMP = DD2/DU DD2 = DD1/DU DD1 = DTEMP DX1 = DY1*DU END IF END IF * PROCEDURE..SCALE-CHECK IF (DD1.NE.ZERO) THEN DO WHILE ((DD1.LE.RGAMSQ) .OR. (DD1.GE.GAMSQ)) IF (DFLAG.EQ.ZERO) THEN DH11 = ONE DH22 = ONE DFLAG = -ONE ELSE DH21 = -ONE DH12 = ONE DFLAG = -ONE END IF IF (DD1.LE.RGAMSQ) THEN DD1 = DD1*GAM**2 DX1 = DX1/GAM DH11 = DH11/GAM DH12 = DH12/GAM ELSE DD1 = DD1/GAM**2 DX1 = DX1*GAM DH11 = DH11*GAM DH12 = DH12*GAM END IF ENDDO END IF IF (DD2.NE.ZERO) THEN DO WHILE ( (DABS(DD2).LE.RGAMSQ) .OR. (DABS(DD2).GE.GAMSQ) ) IF (DFLAG.EQ.ZERO) THEN DH11 = ONE DH22 = ONE DFLAG = -ONE ELSE DH21 = -ONE DH12 = ONE DFLAG = -ONE END IF IF (DABS(DD2).LE.RGAMSQ) THEN DD2 = DD2*GAM**2 DH21 = DH21/GAM DH22 = DH22/GAM ELSE DD2 = DD2/GAM**2 DH21 = DH21*GAM DH22 = DH22*GAM END IF END DO END IF END IF IF (DFLAG.LT.ZERO) THEN DPARAM(2) = DH11 DPARAM(3) = DH21 DPARAM(4) = DH12 DPARAM(5) = DH22 ELSE IF (DFLAG.EQ.ZERO) THEN DPARAM(3) = DH21 DPARAM(4) = DH12 ELSE DPARAM(2) = DH11 DPARAM(5) = DH22 END IF DPARAM(1) = DFLAG RETURN * * End of DROTMG * END