/
auxgivens.c
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/
auxgivens.c
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/*
% This file is part of SeDuMi 1.1 by Imre Polik and Oleksandr Romanko
% Copyright (C) 2005 McMaster University, Hamilton, CANADA (since 1.1)
%
% Copyright (C) 2001 Jos F. Sturm (up to 1.05R5)
% Dept. Econometrics & O.R., Tilburg University, the Netherlands.
% Supported by the Netherlands Organization for Scientific Research (NWO).
%
% Affiliation SeDuMi 1.03 and 1.04Beta (2000):
% Dept. Quantitative Economics, Maastricht University, the Netherlands.
%
% Affiliations up to SeDuMi 1.02 (AUG1998):
% CRL, McMaster University, Canada.
% Supported by the Netherlands Organization for Scientific Research (NWO).
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA
*/
#include "givens.h"
/* ************************************************************
PROCEDURE givensrot - apply sequence of givens rotations to
a vector.
INPUT
g - length n: each entry is a givens rotation [x, y;y,-x], x^2+y^2=1.
We apply first g[n-1] to z[n-1:n], up to g[0] to z[0:1].
n - order of g, i.e. number of givens rotations.
UPDATED
z - length n+1 vector, to be rotated n times.
************************************************************ */
void givensrot(double *z, const twodouble *g, const mwIndex n)
{
twodouble gi;
double z1, z2;
mwIndex i;
z2 = z[n];
for(i = n; i > 0; i--){
gi = g[i-1];
z1 = z[i-1];
/* ------------------------------------------------------------
[z1NEW; [x, y; [z1;
z2NEW] := y, -x] * z2]
------------------------------------------------------------ */
z[i] = gi.y * z1 - gi.x * z2; /* z2NEW */
z2 = gi.x * z1 + gi.y * z2; /* z1NEW, is z2 in iter --i */
}
z[0] = z2;
}
/* ************************************************************
PROCEDURE prpigivensrot - apply sequence of givens rotations to
a vector. Complex case.
INPUT
g - length n: each entry is a givens rotation [conj(x), y;y,-x],
|x|^2+y^2=1. y is real.
We apply first g[n-1] to z[n-1:n], up to g[0] to z[0:1].
n - order of g, i.e. number of givens rotations.
UPDATED
z,zpi - length n+1 vector, to be rotated n times.
************************************************************ */
void prpigivensrot(double *z,double *zpi, const tridouble *g, const mwIndex n)
{
tridouble gi;
double z1, z2, z1im,z2im;
mwIndex i;
z2 = z[n];
z2im = zpi[n];
for(i = n; i > 0; i--){
gi = g[i-1];
z1 = z[i-1];
z1im = zpi[i-1];
/* ------------------------------------------------------------
[z1NEW; [conj(x), y; [z1;
z2NEW] := y, -x] * z2]
------------------------------------------------------------ */
/* z2NEW = y*z1 - x*z2 , y is real. */
z[i] = gi.y * z1 - gi.x * z2 + gi.xim * z2im;
zpi[i] = gi.y * z1im - gi.x * z2im - gi.xim * z2;
/* z1NEW, is z2 in iter --i. z1NEW = conj(x)*z1 + y*z2, y is real. */
z2 = gi.x * z1 + gi.xim * z1im + gi.y * z2;
z2im = gi.x * z1im - gi.xim * z1 + gi.y * z2im;
}
z[0] = z2;
zpi[0] = z2im;
}
/* ************************************************************
PROCEDURE givensrotuj - apply sequence of givens rotations to
a vector, whose last affected entry is now 0. Typical for
re-inserting columns in a U-factor. Same as "givensrot", except that
z[n]=0 by assumption on input.
INPUT
g - length n: each entry is a givens rotation [x, y;y,-x], x^2+y^2=1.
We apply first g[n-1] to z[n-1:n], up to g[0] to z[0:1].
n - order of g, i.e. number of givens rotations.
UPDATED
z - length n+1 vector, to be rotated n times. On input, z[n] = 0
by assumption (actual contents irrelevant).
************************************************************ */
void givensrotuj(double *z, const twodouble *g, const mwIndex n)
{
twodouble gi;
double z1, z2;
mwIndex i;
if(n < 1)
return;
/* ------------------------------------------------------------
[z2; [x, y; [z[n-1];
z[n]] := y, -x] * 0] = z[n-1] * [x;y]
------------------------------------------------------------ */
z2 = z[n-1];
z[n] = z2 * ((g+n-1)->y);
z2 *= (g+n-1)->x;
for(i = n-1; i > 0; i--){
gi = g[i-1];
z1 = z[i-1];
/* ------------------------------------------------------------
[z1NEW; [x, y; [z1;
z2NEW] := y, -x] * z2]
------------------------------------------------------------ */
z[i] = gi.y * z1 - gi.x * z2; /* z2NEW */
z2 = gi.x * z1 + gi.y * z2; /* z1NEW, is z2 in iter --i */
}
z[0] = z2;
}
/* ************************************************************
PROCEDURE prpigivensrotuj - apply sequence of givens rotations to
a vector, whose last affected entry is now 0, and the preceding
entry is real. On output, the last effected entry will be real.
Typical for re-inserting columns in a U-factor. Same as "givensrot",
except that z[n-1] is real and z[n]=0 by assumption on input.
INPUT
g - length n: each entry is a givens rotation [conj(x), y;y,-x],
|x|^2+y^2=1, y is real.
We apply first g[n-1] to z[n-1:n], up to g[0] to z[0:1].
n - order of g, i.e. number of givens rotations.
UPDATED
z - length n+1 vector, to be rotated n times. On input,
{zpi[n-1],z[n],zpi[n]} = 0 by assumption (actual contents irrelevant).
************************************************************ */
void prpigivensrotuj(double *z,double *zpi, const tridouble *g, const mwIndex n)
{
tridouble gi;
double z1, z2, z1im,z2im;
mwIndex i;
if(n < 1)
return;
/* ------------------------------------------------------------
[z2; [conj(x), y; [z[n-1];
z[n]] := y, -x] * 0] = z[n-1] * [conj(x);y],
where z[n-1] is real.
------------------------------------------------------------ */
z2 = z[n-1];
z[n] = z2 * ((g+n-1)->y);
z2im = -z2 * (g+n-1)->xim; /* z[n-1] * conj(x) */
z2 *= (g+n-1)->x;
for(i = n-1; i > 0; i--){
gi = g[i-1];
z1 = z[i-1];
z1im = zpi[i-1];
/* ------------------------------------------------------------
[z1NEW; [conj(x), y; [z1;
z2NEW] := y, -x] * z2]
------------------------------------------------------------ */
/* z2NEW = y*z1 - x*z2 , y is real. */
z[i] = gi.y * z1 - gi.x * z2 + gi.xim * z2im;
zpi[i] = gi.y * z1im - gi.x * z2im - gi.xim * z2;
/* z1NEW, is z2 in iter --i. z1NEW = conj(x)*z1 + y*z2, y is real. */
z2 = gi.x * z1 + gi.xim * z1im + gi.y * z2;
z2im = gi.x * z1im - gi.xim * z1 + gi.y * z2im;
}
z[0] = z2;
zpi[0] = z2im;
}