atl_srefrotg.c

来自「基于Blas CLapck的.用过的人知道是干啥的」· C语言 代码 · 共 147 行

/* ---------------------------------------------------------------------
 *
 * -- Automatically Tuned Linear Algebra Software (ATLAS)
 *    (C) Copyright 2000 All Rights Reserved
 *
 * -- ATLAS routine -- Version 3.2 -- December 25, 2000
 *
 * Author         : Antoine P. Petitet
 * Originally developed at the University of Tennessee,
 * Innovative Computing Laboratory, Knoxville TN, 37996-1301, USA.
 *
 * ---------------------------------------------------------------------
 *
 * -- Copyright notice and Licensing terms:
 *
 *  Redistribution  and  use in  source and binary forms, with or without
 *  modification, are  permitted provided  that the following  conditions
 *  are met:
 *
 * 1. Redistributions  of  source  code  must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce  the above copyright
 *    notice,  this list of conditions, and the  following disclaimer in
 *    the documentation and/or other materials provided with the distri-
 *    bution.
 * 3. The name of the University,  the ATLAS group,  or the names of its
 *    contributors  may not be used to endorse or promote products deri-
 *    ved from this software without specific written permission.
 *
 * -- Disclaimer:
 *
 * THIS  SOFTWARE  IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,  INCLUDING,  BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE UNIVERSITY
 * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,  INDIRECT, INCIDENTAL, SPE-
 * CIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
 * TO,  PROCUREMENT  OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
 * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEO-
 * RY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT  (IN-
 * CLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * ---------------------------------------------------------------------
 */
/*
 * Include files
 */
#include "atlas_refmisc.h"
#include "atlas_reflevel1.h"

void ATL_srefrotg
(
   float                      * A,
   float                      * B,
   float                      * C,
   float                      * S
)
{
/*
 * Purpose
 * =======
 *
 * ATL_srefrotg  constructs a Givens plane rotation. Given the scalars a
 * and b, this routine computes the following quantities:
 *
 *    sigma = sgn(a) if |a| > |b|, sgn(b) otherwise;
 *    r     = sigma * sqrt( a^2 + b^2 );
 *    c     = a / r if r <> 0, 1 otherwise;
 *    s     = b / r if r <> 0, 0 otherwise.
 *
 * The numbers c, s and r then satisfy the matrix equation:
 *
 *    [ c  s ] [ a ]    [ r ]
 *    [ -s c ] [ b ] =  [ 0 ].
 *
 * The introduction of  sigma  is not essential  to the computation of a
 * Givens rotation matrix, but it permits later stable reconstruction of
 * c and s from just one stored number.  For  this purpose, this routine
 * also computes
 *
 *         s        if |a| > |b|,
 *    z =  1 / c    if |b| >= |a| and c <> 0,
 *         1        if c = 0.
 *
 * This subroutine returns r overwriting a, and z overwriting b, as well
 * as returning c and s. If one later wishes to reconstruct c and s from
 * z, it can be done as follows:
 *
 *    if  z  = 1,    set c = 0             and s = 1,
 *    if |z| < 1,    set c = sqrt(1 - z^2) and s = z,
 *    if |z| > 1,    set c = 1 / z         and s = sqrt(1 - c^2).
 *
 * See ``Basic Linear Algebra Subprograms for Fortran Usage'' by C. Law-
 * son, R. Hanson, D. Kincaid and F. Krogh, ACM Transactions on Mathema-
 * tical Software, 1979, 5(3) pp 308-323, for further information.
 *
 * Arguments
 * =========
 *
 * A       (input/output)                float *
 *         On entry, A specifies the scalar a. On exit, A is overwritten
 *         by the scalar r defined above.
 *
 * B       (input/output)                float *
 *         On entry, B specifies the scalar b. On exit, B is overwritten
 *         by the scalar z defined above.
 *
 * C       (output)                      float *
 *         On exit, C  specifies the scalar c defined above.
 *
 * S       (output)                      float *
 *         On exit, S  specifies the scalar s defined above.
 *
 * ---------------------------------------------------------------------
 */
/*
 * .. Local Variables ..
 */
   register float             absa, absb, roe, scale, r, tmpa, tmpb, z;
/* ..
 * .. Executable Statements ..
 *
 */
   absa = Msabs( *A ); absb = Msabs( *B );
   roe  = ( absa > absb ? (*A) :  (*B) ); scale = absa + absb;

   if( scale != ATL_sZERO )
   {
      tmpa = (*A) / scale; tmpb = (*B) / scale;
      if( roe < ATL_sZERO )
      { r = - scale * sqrt( ( tmpa * tmpa ) + ( tmpb * tmpb ) ); }
      else
      { r =   scale * sqrt( ( tmpa * tmpa ) + ( tmpb * tmpb ) ); }
      *C = (*A) / r; *S = (*B) / r; z =  ATL_sONE;
      if(   absa >  absb ) { z = *S; }
      if( ( absb >= absa ) && ( (*C) != ATL_sZERO ) )
      { z = ATL_sONE / (*C); }
   }
   else { *C = ATL_sONE; *S = r = z = ATL_sZERO; }

   *A = r; *B = z;
/*
 * End of ATL_srefrotg
 */
}