numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/BLAS/SRC/srotmg.f | 6569B | -rw-r--r-- |
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*> \brief \b SROTMG * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM) * * .. Scalar Arguments .. * REAL SD1,SD2,SX1,SY1 * .. * .. Array Arguments .. * REAL SPARAM(5) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS *> THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T. *> WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. *> *> SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 *> *> (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) *> H=( ) ( ) ( ) ( ) *> (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). *> LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 *> RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE *> VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) *> *> 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 SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. *> *> \endverbatim * * Arguments: * ========== * *> \param[in,out] SD1 *> \verbatim *> SD1 is REAL *> \endverbatim *> *> \param[in,out] SD2 *> \verbatim *> SD2 is REAL *> \endverbatim *> *> \param[in,out] SX1 *> \verbatim *> SX1 is REAL *> \endverbatim *> *> \param[in] SY1 *> \verbatim *> SY1 is REAL *> \endverbatim *> *> \param[out] SPARAM *> \verbatim *> SPARAM is REAL array, dimension (5) *> SPARAM(1)=SFLAG *> SPARAM(2)=SH11 *> SPARAM(3)=SH21 *> SPARAM(4)=SH12 *> SPARAM(5)=SH22 *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup rotmg * * ===================================================================== SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM) * * -- 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 .. REAL SD1,SD2,SX1,SY1 * .. * .. Array Arguments .. REAL SPARAM(5) * .. * * ===================================================================== * * .. Local Scalars .. REAL GAM,GAMSQ,ONE,RGAMSQ,SFLAG,SH11,SH12,SH21,SH22,SP1,SP2,SQ1, $ SQ2,STEMP,SU,TWO,ZERO * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. Data statements .. * DATA ZERO,ONE,TWO/0.E0,1.E0,2.E0/ DATA GAM,GAMSQ,RGAMSQ/4096.E0,1.67772E7,5.96046E-8/ * .. IF (SD1.LT.ZERO) THEN * GO ZERO-H-D-AND-SX1.. SFLAG = -ONE SH11 = ZERO SH12 = ZERO SH21 = ZERO SH22 = ZERO * SD1 = ZERO SD2 = ZERO SX1 = ZERO ELSE * CASE-SD1-NONNEGATIVE SP2 = SD2*SY1 IF (SP2.EQ.ZERO) THEN SFLAG = -TWO SPARAM(1) = SFLAG RETURN END IF * REGULAR-CASE.. SP1 = SD1*SX1 SQ2 = SP2*SY1 SQ1 = SP1*SX1 * IF (ABS(SQ1).GT.ABS(SQ2)) THEN SH21 = -SY1/SX1 SH12 = SP2/SP1 * SU = ONE - SH12*SH21 * IF (SU.GT.ZERO) THEN SFLAG = ZERO SD1 = SD1/SU SD2 = SD2/SU SX1 = SX1*SU 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 SFLAG = -ONE SH11 = ZERO SH12 = ZERO SH21 = ZERO SH22 = ZERO * SD1 = ZERO SD2 = ZERO SX1 = ZERO END IF ELSE IF (SQ2.LT.ZERO) THEN * GO ZERO-H-D-AND-SX1.. SFLAG = -ONE SH11 = ZERO SH12 = ZERO SH21 = ZERO SH22 = ZERO * SD1 = ZERO SD2 = ZERO SX1 = ZERO ELSE SFLAG = ONE SH11 = SP1/SP2 SH22 = SX1/SY1 SU = ONE + SH11*SH22 STEMP = SD2/SU SD2 = SD1/SU SD1 = STEMP SX1 = SY1*SU END IF END IF * PROCEDURE..SCALE-CHECK IF (SD1.NE.ZERO) THEN DO WHILE ((SD1.LE.RGAMSQ) .OR. (SD1.GE.GAMSQ)) IF (SFLAG.EQ.ZERO) THEN SH11 = ONE SH22 = ONE SFLAG = -ONE ELSE SH21 = -ONE SH12 = ONE SFLAG = -ONE END IF IF (SD1.LE.RGAMSQ) THEN SD1 = SD1*GAM**2 SX1 = SX1/GAM SH11 = SH11/GAM SH12 = SH12/GAM ELSE SD1 = SD1/GAM**2 SX1 = SX1*GAM SH11 = SH11*GAM SH12 = SH12*GAM END IF ENDDO END IF IF (SD2.NE.ZERO) THEN DO WHILE ( (ABS(SD2).LE.RGAMSQ) .OR. (ABS(SD2).GE.GAMSQ) ) IF (SFLAG.EQ.ZERO) THEN SH11 = ONE SH22 = ONE SFLAG = -ONE ELSE SH21 = -ONE SH12 = ONE SFLAG = -ONE END IF IF (ABS(SD2).LE.RGAMSQ) THEN SD2 = SD2*GAM**2 SH21 = SH21/GAM SH22 = SH22/GAM ELSE SD2 = SD2/GAM**2 SH21 = SH21*GAM SH22 = SH22*GAM END IF END DO END IF END IF IF (SFLAG.LT.ZERO) THEN SPARAM(2) = SH11 SPARAM(3) = SH21 SPARAM(4) = SH12 SPARAM(5) = SH22 ELSE IF (SFLAG.EQ.ZERO) THEN SPARAM(3) = SH21 SPARAM(4) = SH12 ELSE SPARAM(2) = SH11 SPARAM(5) = SH22 END IF SPARAM(1) = SFLAG RETURN * * End of SROTMG * END