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opt_dnn_subprob_Y.c
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opt_dnn_subprob_Y.c
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#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <time.h>
#include "mex.h"
#include "matrix.h"
void onedim(const double c, const double sig, const double L, const double U, double *val, double *x_);
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
size_t i, j, n;
double locval;
double *M;
double *L;
double *U;
double sig;
double *B; /* Matlab will pass B_ = prhs[4] in as double, I think. */
double *E;
double val;
double *Y;
const mxArray *M_;
const mxArray *L_;
const mxArray *U_;
const mxArray *sig_;
const mxArray *B_;
const mxArray *E_;
const mxArray *val_;
const mxArray *Y_;
if( nrhs != 6 )
mexErrMsgTxt("quadprob: Need six input arguments.");
if( nlhs != 2 )
mexErrMsgTxt("quadprob: Need two output arguments.");
M_ = prhs[0];
L_ = prhs[1];
U_ = prhs[2];
sig_ = prhs[3];
B_ = prhs[4];
E_ = prhs[5];
n = mxGetM(M_) - 1;
plhs[0] = mxCreateDoubleMatrix(1 , 1 , mxREAL);
plhs[1] = mxCreateDoubleMatrix(1+n, 1+n, mxREAL);
val_ = plhs[0];
Y_ = plhs[1];
if( mxGetM(M_) != 1+n || mxGetN(M_) != 1+n)
mexErrMsgTxt("quadprob: Input 1 must be a square matrix of the appropriate size.");
if( mxIsSparse(M_) )
mexErrMsgTxt("quadprob: Input 1 should not be sparse.");
if( mxIsDouble(M_) == 0 || mxIsComplex(M_) == 1 )
mexErrMsgTxt("quadprob: Input 1 should be of type double.");
if( mxGetM(L_) != 1+n || mxGetN(L_) != 1)
mexErrMsgTxt("quadprob: Input 2 must be a column vector of the appropriate size.");
if( mxIsSparse(L_) )
mexErrMsgTxt("quadprob: Input 2 should not be sparse.");
if( mxIsDouble(L_) == 0 || mxIsComplex(L_) == 1 )
mexErrMsgTxt("quadprob: Input 2 should be of type double.");
if( mxGetM(U_) != 1+n || mxGetN(U_) != 1)
mexErrMsgTxt("quadprob: Input 3 must be a column vector of the appropriate size.");
if( mxIsSparse(U_) )
mexErrMsgTxt("quadprob: Input 3 should not be sparse.");
if( mxIsDouble(U_) == 0 || mxIsComplex(U_) == 1 )
mexErrMsgTxt("quadprob: Input 3 should be of type double.");
if( mxGetM(sig_) * mxGetN(sig_) != 1)
mexErrMsgTxt("quadprob: Input 4 must be a scalar.");
if( mxIsSparse(sig_) )
mexErrMsgTxt("quadprob: Input 4 should not be sparse.");
if( mxIsDouble(sig_) == 0 || mxIsComplex(sig_) == 1 )
mexErrMsgTxt("quadprob: Input 4 should be of type double.");
if( mxGetM(B_) != 1+n || mxGetN(B_) != 1)
mexErrMsgTxt("quadprob: Input 5 must be a column vector of the appropriate size.");
if( mxIsSparse(B_) )
mexErrMsgTxt("quadprob: Input 5 should not be sparse.");
if( mxIsDouble(B_) == 0 || mxIsComplex(B_) == 1 )
mexErrMsgTxt("quadprob: Input 5 should be of type double.");
if( mxGetM(E_) != 1+n || mxGetN(E_) != 1+n)
mexErrMsgTxt("quadprob: Input 6 must be a matrix of the appropriate size.");
if( mxIsSparse(E_) )
mexErrMsgTxt("quadprob: Input 6 should not be sparse.");
if( mxIsDouble(E_) == 0 || mxIsComplex(E_) == 1 )
mexErrMsgTxt("quadprob: Input 6 should be of type double.");
M = mxGetPr(M_ ) ;
L = mxGetPr(L_ ) ;
U = mxGetPr(U_ ) ;
sig = *(mxGetPr(sig_));
B = mxGetPr(B_) ;
E = mxGetPr(E_) ;
Y = mxGetPr(Y_);
if( sig < 0 )
mexErrMsgTxt("quadprob: Input 4 should be nonegative.");
/* L[0] = U[0] = 1.0; */ /* Code below assumes L[0] = U[0] = 1.0, which
is now handled in opt_dnn.m */
/* Initialize val=0 */
val = 0.0;
/* Enforce Y_00=1; add to val */
Y[0] = 1.0;
val += M[0] + 0.5*sig;
/* Optimize x and diag(X) portion of Y.
* Also handle binary variables in B.
* Add to val. */
for(i = 1; i <= n; i++) {
if(B[i] == 1) {
/* This is tricky because we combine Y(i,i), Y(i,0), Y(0,i) together. */
onedim(2*M[i] + M[i*(1+n)+i], 3*sig, L[i], U[i], &locval, Y+i);
Y[i*(1+n)] = Y[i*(1+n)+i] = Y[i];
val += locval;
}
else {
onedim(M[i], sig, L[i], U[i], &locval, Y+i);
Y[i*(1+n)] = Y[i];
val += 2.0*locval;
onedim(M[i*(1+n)+i], sig, L[i]*L[i], U[i]*U[i], &locval, Y+i*(1+n)+i);
val += locval;
}
}
/* Optimize strictly lower triangular part of X. */
/* Handle complementarities. */
/* Add to val. */
for(j = 1; j <= n; j++) {
for(i = j+1; i <= n; i++) {
if(E[j*(1+n)+i] == 1.0) {
Y[i*(1+n)+j] = Y[j*(1+n)+i] = 0.0;
}
else {
onedim(M[j*(1+n)+i], sig, L[i]*L[j], U[i]*U[j], &locval, Y+j*(1+n)+i);
Y[i*(1+n)+j] = Y[j*(1+n)+i];
val += 2.0*locval;
}
}
}
*(mxGetPr(val_)) = val;
return;
}
void onedim(const double c, const double sig, const double L, const double U, double *val, double *x_)
{
double x;
/* Solve min { c*x + 0.5*sig*x^2 : L <= x <= U } */
/* sig may equal 0 */
if(sig > 0.0)
x = -c/sig;
else
x = L - 1.0;
if( !(L <= x && x <= U) ) {
if( c*L + 0.5*sig*L*L < c*U + 0.5*sig*U*U )
x = L;
else
x = U;
}
*val = c*x + 0.5*sig*x*x;
*x_ = x;
return;
}