/* ************************************************************
PROCEDURE mexFunction - Entry for Matlab
[ux,ispos] = psdfactor(x,K);
************************************************************ */
void mexFunction(const int nlhs, mxArray *plhs[],
const int nrhs, const mxArray *prhs[])
{
mxArray *myplhs[NPAROUT];
coneK cK;
mwIndex k,nk,nksqr, sdplen,sdpdim,lenfull, ispos;
const double *x;
double *ux;
/* ------------------------------------------------------------
Check for proper number of arguments
------------------------------------------------------------ */
mxAssert(nrhs >= NPARIN, "psdfactor requires more input arguments");
mxAssert(nlhs <= NPAROUT, "psdfactor produces less output arguments");
/* ------------------------------------------------------------
Disassemble cone K structure
------------------------------------------------------------ */
conepars(K_IN, &cK);
/* ------------------------------------------------------------
Compute statistics: sdpdim = rdim+hdim, sdplen = sum(K.s).
------------------------------------------------------------ */
lenfull = cK.lpN + cK.qDim + cK.rDim + cK.hDim;
sdpdim = cK.rDim + cK.hDim;
sdplen = cK.rLen + cK.hLen;
/* ------------------------------------------------------------
Get input vector x, skip LP + Lorentz part
------------------------------------------------------------ */
x = mxGetPr(X_IN);
if(mxGetM(X_IN) * mxGetN(X_IN) == lenfull)
x += cK.lpN + cK.qDim;
else mxAssert(mxGetM(X_IN) * mxGetN(X_IN) == sdpdim, "x size mismatch.");
/* ------------------------------------------------------------
Allocate output UX(sdpdim), ispos(1).
------------------------------------------------------------ */
UX_OUT = mxCreateDoubleMatrix(sdpdim, (mwSize)1, mxREAL);
ux = mxGetPr(UX_OUT);
ISPOS_OUT = mxCreateDoubleMatrix((mwSize)1,(mwSize)1,mxREAL);
/* ------------------------------------------------------------
PSD: Cholesky factorization.
Initialize ispos = 1 and ux = x.
------------------------------------------------------------ */
ispos = 1;
memcpy(ux, x, sdpdim * sizeof(double)); /* copy real + complex */
for(k = 0; k < cK.rsdpN; k++){ /* real symmetric */
nk = cK.sdpNL[k];
/* ------------------------------------------------------------
Attempt Cholesky on block k. Returns 1 if fail (i.e. not psd).
------------------------------------------------------------ */
if(cholnopiv(ux,nk)){
ispos = 0;
break;
}
triu2sym(ux,nk);
ux += SQR(nk);
}
/* ------------------------------------------------------------
Complex Hermitian PSD Cholesky factorization, no pivoting.
------------------------------------------------------------ */
if(ispos)
for(; k < cK.sdpN; k++){ /* complex Hermitian */
nk = cK.sdpNL[k];
nksqr = SQR(nk);
if(prpicholnopiv(ux,ux+nksqr,nk)){
ispos = 0;
break;
}
triu2herm(ux,ux+nksqr,nk);
ux += 2 * nksqr;
}
/* ------------------------------------------------------------
Return parameter ispos
------------------------------------------------------------ */
*mxGetPr(ISPOS_OUT) = ispos;
/* ------------------------------------------------------------
Copy requested output parameters (at least 1), release others.
------------------------------------------------------------ */
k = MAX(nlhs, 1);
memcpy(plhs,myplhs, k * sizeof(mxArray *));
for(; k < NPAROUT; k++)
mxDestroyArray(myplhs[k]);
}
/* ************************************************************
PROCEDURE mexFunction - Entry for Matlab
[qdetx,ux,ispos,perm] = factorK(x,K);
************************************************************ */
void mexFunction(const int nlhs, mxArray *plhs[],
const int nrhs, const mxArray *prhs[])
{
mxArray *myplhs[NPAROUT];
coneK cK;
int i,k,nk,nksqr, sdplen,sdpdim,lenfull, fwsiz, ispos;
const double *x;
double *ux, *fwork, *permPr, *qdetx, *up, *uppi;
int *iwork, *perm;
double uxk;
char use_pivot;
/* ------------------------------------------------------------
Check for proper number of arguments
------------------------------------------------------------ */
mxAssert(nrhs >= NPARIN, "factorK requires more input arguments");
mxAssert(nlhs <= NPAROUT, "factorK produces less output arguments");
use_pivot = (nlhs == NPAROUT);
/* ------------------------------------------------------------
Disassemble cone K structure
------------------------------------------------------------ */
conepars(K_IN, &cK);
/* ------------------------------------------------------------
Compute statistics: sdpdim = rdim+hdim, sdplen = sum(K.s).
------------------------------------------------------------ */
lenfull = cK.lpN + cK.qDim + cK.rDim + cK.hDim;
sdpdim = cK.rDim + cK.hDim;
sdplen = cK.rLen + cK.hLen;
/* ------------------------------------------------------------
Get input vector x, skip LP part
------------------------------------------------------------ */
mxAssert(mxGetM(X_IN) * mxGetN(X_IN) == lenfull, "x size mismatch.");
x = mxGetPr(X_IN) + cK.lpN;
/* ------------------------------------------------------------
Allocate output qdetx(lorN), UX(sdpdim), perm(sdplen), ispos(1).
------------------------------------------------------------ */
QDETX_OUT = mxCreateDoubleMatrix(cK.lorN, 1, mxREAL);
qdetx = mxGetPr(QDETX_OUT);
UX_OUT = mxCreateDoubleMatrix(sdpdim, 1, mxREAL);
ux = mxGetPr(UX_OUT);
ISPOS_OUT = mxCreateDoubleMatrix(1,1,mxREAL);
PERM_OUT = mxCreateDoubleMatrix(sdplen, 1, mxREAL);
permPr = mxGetPr(PERM_OUT);
/* ------------------------------------------------------------
Allocate working arrays iwork(sdplen),
fwork(MAX(rmaxn^2,2*hmaxn^2) + MAX(rmaxn,hmaxn))
------------------------------------------------------------ */
iwork = (int *) mxCalloc(sdplen, sizeof(int));
perm = iwork;
fwsiz = MAX(cK.rMaxn,cK.hMaxn);
fwork = (double *) mxCalloc(fwsiz + MAX(SQR(cK.rMaxn),2*SQR(cK.hMaxn)),
sizeof(double));
up = fwork + fwsiz;
uppi = up + SQR(cK.hMaxn);
/* ------------------------------------------------------------
LORENTZ: qdetx = sqrt(qdet(x))
------------------------------------------------------------ */
ispos = 1;
for(k = 0; k < cK.lorN; k++){
nk = cK.lorNL[k];
if( (uxk = qdet(x,nk)) < 0.0){
ispos = 0;
break;
}
else
qdetx[k] = sqrt(uxk);
x += nk;
}
/* ------------------------------------------------------------
PSD: Cholesky factorization. If use_pivot, then do pivoting.
------------------------------------------------------------ */
if(use_pivot){
if(ispos)
for(k = 0; k < cK.rsdpN; k++){ /* real symmetric */
nk = cK.sdpNL[k];
if(cholpivot(up,perm, x,nk, fwork)){
ispos = 0;
break;
}
uperm(ux, up, perm, nk);
triu2sym(ux,nk);
nksqr = SQR(nk);
x += nksqr; ux += nksqr;
perm += nk;
}
/* ------------------------------------------------------------
Complex Hermitian PSD pivoted Cholesky factorization
------------------------------------------------------------ */
if(ispos)
for(; k < cK.sdpN; k++){ /* complex Hermitian */
nk = cK.sdpNL[k];
nksqr = SQR(nk);
if(prpicholpivot(up,uppi,perm, x,x+nksqr,nk, fwork)){
ispos = 0;
break;
}
uperm(ux, up, perm, nk); /* real part */
uperm(ux+nksqr, uppi, perm, nk); /* imaginary part */
triu2herm(ux,ux+nksqr,nk);
nksqr += nksqr; /* 2*n^2 for real+imag */
x += nksqr; ux += nksqr;
perm += nk;
}
/* ------------------------------------------------------------
Convert "perm" to Fortran-index in doubles.
------------------------------------------------------------ */
for(i = 0; i < sdplen; i++)
permPr[i] = 1.0 + iwork[i];
}
/* ------------------------------------------------------------
PSD, !use_pivot: Cholesky without pivoting.
First let ux = x, then ux=chol(ux).
------------------------------------------------------------ */
else{ /* Cholesky real sym PSD without pivoting */
if(ispos){
memcpy(ux, x, sdpdim * sizeof(double)); /* copy real + complex */
for(k = 0; k < cK.rsdpN; k++){ /* real symmetric */
nk = cK.sdpNL[k];
if(cholnopiv(ux,nk)){
ispos = 0;
break;
}
triu2sym(ux,nk);
ux += SQR(nk);
}
}
/* ------------------------------------------------------------
Complex Hermitian PSD Cholesky factorization, no pivoting.
------------------------------------------------------------ */
if(ispos)
for(; k < cK.sdpN; k++){ /* complex Hermitian */
nk = cK.sdpNL[k];
nksqr = SQR(nk);
if(prpicholnopiv(ux,ux+nksqr,nk)){
ispos = 0;
break;
}
triu2herm(ux,ux+nksqr,nk);
ux += 2 * nksqr;
}
} /* !use_pivot */
/* ------------------------------------------------------------
Return parameter ispos
------------------------------------------------------------ */
*mxGetPr(ISPOS_OUT) = ispos;
/* ------------------------------------------------------------
Release working arrays
------------------------------------------------------------ */
mxFree(iwork);
mxFree(fwork);
/* ------------------------------------------------------------
Copy requested output parameters (at least 1), release others.
------------------------------------------------------------ */
i = MAX(nlhs, 1);
memcpy(plhs,myplhs, i * sizeof(mxArray *));
for(; i < NPAROUT; i++)
mxDestroyArray(myplhs[i]);
}
