eigk.c

matlab中uwb波形优化算法经常会使用的工具包:SeDuMi_1_1R3.

/*
   [lab,q] = eigK(x,K)
   Computes spectral coefficients of x w.r.t. K
   Arguments "q" is optional - without it's considerably
   faster in case of PSD blocks.
   FLOPS indication: 1.3 nk^3 versus 9.0 nk^3 for nk=500,
                     1.5 nk^3        9.8 nk^3 for nk=50.

% 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 <math.h>
#include <string.h>
#include "mex.h"
#include "blksdp.h"

#define LAB_OUT plhs[0]
#define Q_OUT plhs[1]
#define NPAROUT 2

#define X_IN prhs[0]
#define K_IN prhs[1]
#define NPARIN 2

/* ============================================================
   LORENTZ SPECTRAL VALUE
   ============================================================ */

/* ************************************************************
   PROCEDURE qeig  -  computes the 2 spectral values w.r.t. Lorentz cone
   INPUT:
     x - full n x 1
     n - length of x
   OUTPUT:
     lab - 2*1, the two spectral values qeig(x).
   ************************************************************ */
void qeig(double *lab,const double *x,const int n)
{
 double x1, nx2;
  /* ------------------------------------------------------------
     x1 = x(1),  x2ssqr = norm( x(2:n) );
     labx = [x1 - nx2; x1 + nx2]/sqrt(2);
     ------------------------------------------------------------ */
 x1 = x[0];
 nx2 = sqrt(realssqr(x+1,n-1));
 lab[0] = (x1 - nx2) / M_SQRT2;
 lab[1] = (x1 + nx2) / M_SQRT2;
}

/* ************************************************************
   PROCEDURE cxqeig  -  computes the 2 spectral values w.r.t. Lorentz cone,
     complex version.
   INPUT:
     x,xpi - full n x 1, real and imaginary parts
     n - length of x
   OUTPUT:
     lab - 2*1, the two spectral values cxqeig(x).
   ************************************************************ */
void cxqeig(double *lab,const double *x,const double *xpi,const int n)
{
 double x1, nx2;
  /* ------------------------------------------------------------
     x1 = x(1),  x2ssqr = norm( x(2:n) + i* xpi(2:n) );
     labx = [x1 - nx2; x1 + nx2]/sqrt(2);
     ------------------------------------------------------------ */
 x1 = x[0];
 nx2 = sqrt(realssqr(x+1,n-1) + realssqr(xpi+1,n-1));
 lab[0] = (x1 - nx2) / M_SQRT2;
 lab[1] = (x1 + nx2) / M_SQRT2;
}

/* ============================================================
   RCONE (rotated Lorentz) SPECTRAL VALUE
   ============================================================ */

/* ************************************************************
   PROCEDURE rconeeig  -  computes the 2 spectral values w.r.t. Rcone
   INPUT:
     x - full n x 1
     n - length of x
   OUTPUT:
     lab - 2*1, the two spectral values rconeeig(x).
   ************************************************************ */
void rconeeig(double *lab,const double x1,const double x2,const double x3sqr)
{
 double t, trx, radius;
  /* ------------------------------------------------------------
     lab(1,2) is root of "lab^2 - (x1+x2)*lab + (x1*x2-x3sqr)/2 = 0"
     ------------------------------------------------------------ */
 trx = x1+x2;
 t = (1 - 2*(trx < 0)) * sqrt( SQR(x1-x2) + 2*x3sqr );
 if( (radius = (trx + t)/2) != 0.0){
   lab[0] = (x1*x2 - x3sqr/2) / radius;
   lab[1] = radius;
 }
}

/* ============================================================
   PSD: projection onto symmetric/ skew-symmetric routines.
   ============================================================ */
/* ************************************************************
   PROCEDURE symproj -- Y = (X+X')/2
   INPUT x, n - full n x n matrix x.
   OUTPUT y - on output, contains (x+x')/2
   ************************************************************ */
void symproj(double *y, const double *x, const int n)
{
  int colp,i,j;
  double yij;

  /* ------------------------------------------------------------
     x points to x(:,i);     x+colp = x(:,j).
     ------------------------------------------------------------ */
  for(i = 0; i < n; x += n, y += n, i++){
    y[i] = x[i];                         /* diagonal entry */
    for(colp = n + i, j=i+1; j<n; j++, colp += n){
      yij = (x[j] + x[colp]) / 2;         /* x(i,j)+x(j,i) */
      y[j] = yij;
      y[colp] = yij;
    }
  }
}

/* ************************************************************
   PROCEDURE skewproj -- Y = (X-X')/2
   INPUT x, n - full n x n matrix x.
   OUTPUT y - on output, contains (x-x')/2
   ************************************************************ */
void skewproj(double *y, const double *x, const int n)
{
  int colp,i,j;
  double yij;

  /* ------------------------------------------------------------
     x points to x(:,i);     x+colp = x(:,j).
     ------------------------------------------------------------ */
  for(i = 0; i < n; x += n, y += n, i++){
    y[i] = 0.0;                         /* diagonal entry */
    for(colp = n + i, j=i+1; j<n; j++, colp += n){
      yij = (x[j] - x[colp]) / 2;         /* x(j,i) - x(i,j) */
      y[j] = yij;
      y[colp] = -yij;                   /* conjugate */
    }
  }
}


/* ============================================================
   MAIN: MEXFUNCTION
   ============================================================ */
/* ************************************************************
   PROCEDURE mexFunction - Entry for Matlab
     [lab,q] = eigK(x,K)
     Computes spectral coefficients of x w.r.t. K
   REMARK If this function is used internally by SeDuMi, then
     complex numbers are stored in a single real vector. To make
     it invokable from the Matlab command-line by the user, we
     also allow Matlab complex vector x.
   ************************************************************ */
void mexFunction(const int nlhs, mxArray *plhs[],
  const int nrhs, const mxArray *prhs[])
{
 mxArray *output_array[3], *Xk, *hXk;
 coneK cK;
 int k, nk, nksqr, lendiag,i,ii,nkp1, lenfull;
 double *lab,*q,*qpi,*labk,*xwork,*xpiwork;
 const double *x,*xpi;

/* ------------------------------------------------------------
   Check for proper number of arguments
   ------------------------------------------------------------ */
  mxAssert(nrhs >= NPARIN, "eigK requires more input arguments");
  mxAssert(nlhs <= NPAROUT, "eigK produces less output arguments");
/* ------------------------------------------------------------
   Disassemble cone K structure
   ------------------------------------------------------------ */
  conepars(K_IN, &cK);
/* ------------------------------------------------------------
   Compute statistics based on cone K structure
   ------------------------------------------------------------ */
  lendiag = cK.lpN + 2 * (cK.lorN + cK.rconeN) + cK.rLen + cK.hLen;
  lenfull = cK.lpN + cK.qDim + cK.rDim + cK.hDim;
  if(cK.rconeN > 0)