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/*
Find the largest value for alpha<=1 such that X+alpha*dX is PD.
Return the optimal X+alpha*dX in work1. If the search fails,
return alpha=-1.0.
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <csdp/declarations.h>
#define LANCZOSITS 30
double linesearch(
int n,
struct blockmatrix dX,
struct blockmatrix work1,
struct blockmatrix work2,
struct blockmatrix work3,
struct blockmatrix cholinv,
double *q,
double *z,
double *workvec,
double stepfrac,
double start,
int printlevel)
{
int i,j,jj;
double alpha;
double scale1;
double scale2;
int inc;
double lalpha[LANCZOSITS+1];
double lbeta[LANCZOSITS+1];
double lbeta2[LANCZOSITS+1];
double evalues[LANCZOSITS+2];
double maxeigs[LANCZOSITS+1];
double reorth[LANCZOSITS+1];
double maxeig;
int maxn,blk,method;
double *lanczosvectors;
/*
* Allocate space for storing the Lanczos vectors.
*/
lanczosvectors=(double *) malloc((LANCZOSITS+1)*n*sizeof(double));
if (lanczosvectors==NULL)
{
printf("Storage Allocation Failed!\n");
exit(205);
};
/*
* First, figure out which method to use. If maxn is big, then use
* lots of matrix/vector mults. If maxn is small, then multiply the
* matrices once and for all.
*/
maxn=0;
for (blk=1; blk<=work1.nblocks; blk++)
{
if ((work1.blocks[blk].blocksize > maxn) &&
(work1.blocks[blk].blockcategory==MATRIX))
maxn=work1.blocks[blk].blocksize;
};
if (maxn > 6*LANCZOSITS)
{
method=1; /* matrix vector mults. */
if (printlevel >= 4)
{
printf("linesearch method 1 \n");
};
}
else
{
method=2; /* matrix matrix mults. */
if (printlevel >= 4)
{
printf("linesearch method 2 \n");
};
};
/*
*
*/
if (method==1)
{
scale1=-1.0;
zero_mat(work1);
store_unpacked(cholinv,work3);
triu(work3);
addscaledmat(work1,scale1,work3,work2);
trans(work2);
}
else
{
/*
* method=2.
*/
/*
* First, multiply dX*cholinv. Store it in work3.
*/
scale1=1.0;
scale2=0.0;
store_unpacked(cholinv,work2);
triu(work2);
mat_mult(scale1,scale2,dX,work2,work3);
/*
* Now, find R^{-T}
*/
trans(work2);
scale1=-1.0;
scale2=0.0;
mat_mult(scale1,scale2,work2,work3,work1);
};
/*
* Initialize q.
*/
for (i=1; i<=n; i++)
q[i]=1.0/sqrt(n*1.0);
for (i=1; i<=n; i++)
lanczosvectors[ijtok(i,1,n)]=q[i];
/*
* Next, perform the Lancoz iterations.
*/
maxeig=-1.0e200;
for (j=1; j<=LANCZOSITS; j++)
{
maxeigs[j]=-1.0e100;
if (method == 1)
{
matvec(work3,q,z);
matvec(dX,z,workvec);
matvec(work2,workvec,z);
}
else
{
matvec(work1,q,z);
};
lalpha[j]=0.0;
for (i=1; i<=n; i++)
lalpha[j]=lalpha[j]+q[i]*z[i];
/*
* We'll use BLAS routines to do the reorthogonalization. First,
* Compute reorth=lanczosvectors'*z. Then compute
* z=z-lanczosvectors*reorth.
*
* lanczosvectors is of size n by j, with lda=n.
*/
scale1=1.0;
scale2=0.0;
inc=1;
#ifdef HIDDENSTRLEN
dgemv_("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc,1);
#else
#ifdef NOUNDERBLAS
#ifdef CAPSBLAS
DGEMV("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#else
dgemv("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#endif
#else
#ifdef CAPSBLAS
DGEMV_("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#else
dgemv_("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#endif
#endif
#endif
scale1=-1.0;
scale2=1.0;
inc=1;
#ifdef HIDDENSTRLEN
dgemv_("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc,1);
#else
#ifdef NOUNDERBLAS
#ifdef CAPSBLAS
DGEMV("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#else
dgemv("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#endif
#else
#ifdef CAPSBLAS
DGEMV_("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#else
dgemv_("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#endif
#endif
#endif
scale1=1.0;
scale2=0.0;
inc=1;
#ifdef HIDDENSTRLEN
dgemv_("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc,1);
#else
#ifdef NOUNDERBLAS
#ifdef CAPSBLAS
DGEMV("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#else
dgemv("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#endif
#else
#ifdef CAPSBLAS
DGEMV_("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#else
dgemv_("T",&n,&j,&scale1,lanczosvectors,&n,z+1,&inc,&scale2,reorth+1,&inc);
#endif
#endif
#endif
scale1=-1.0;
scale2=1.0;
inc=1;
#ifdef HIDDENSTRLEN
dgemv_("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc,1);
#else
#ifdef NOUNDERBLAS
#ifdef CAPSBLAS
DGEMV("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#else
dgemv("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#endif
#else
#ifdef CAPSBLAS
DGEMV_("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#else
dgemv_("N",&n,&j,&scale1,lanczosvectors,&n,reorth+1,&inc,&scale2,z+1,&inc);
#endif
#endif
#endif
/*
* Compute the norm of z.
*/
lbeta[j]=norm2(n,z+1);
if (fabs(lbeta[j])<1.0e-16)
{
if (printlevel >= 3)
printf("Small beta[j]\n");
j=j-1;
jj=j;
goto DONEEARLY;
};
for (i=1; i<=n; i++)
q[i]=z[i]/lbeta[j];
/*
* Store the Lanczos vector.
*/
for (i=1; i<=n; i++)
lanczosvectors[ijtok(i,j+1,n)]=q[i];
if (j>=5)
{
/*
* Now, get ready to call qreig to get the eigenvalues.
*/
for (i=1; i<=j-1; i++)
lbeta2[i]=lbeta[i]*lbeta[i];
for (i=1; i<=j; i++)
evalues[i]=lalpha[i];
qreig(j,evalues,lbeta2);
maxeigs[j]=-1.0e100;
for (i=1; i<=j; i++)
{
if (printlevel >= 4)
printf ("qreig evalue %e \n",evalues[i]);
if (evalues[i] > maxeigs[j])
maxeigs[j]=evalues[i];
};
if (maxeigs[j] > maxeig)
maxeig=maxeigs[j];
};
/*
* Now, decide whether or not to stop.
*/
if ((j>=7) && (maxeigs[j] <= 1/(3*start)) &&
(fabs((maxeigs[j]-maxeigs[j-2])/(0.000001+fabs(maxeigs[j]))) < 0.2))
{
if (printlevel >= 4)
printf("Stopping on <1/3s j=%d \n",j);
jj=j;
goto DONEEARLY;
};
if ((j>=8) && (fabs((maxeigs[j]-maxeigs[j-2])/(0.000001+fabs(maxeigs[j]))) < 0.02))
{
if (printlevel >= 4)
printf("Stopping here, on tightness j=%d \n",j);
maxeig=maxeig+0.01*fabs(maxeig);
jj=j;
goto DONEEARLY;
};
};
jj=LANCZOSITS;
DONEEARLY:
if (printlevel >= 4)
{
for (i=1; i<=jj; i++)
printf("maxeigs[%d]=%e \n",i,maxeigs[i]);
printf("maxeig %e \n",maxeig);
};
if (printlevel >= 4)
printf("Lancoz converged after %d iters\n",jj);
if (printlevel >= 3)
{
if (maxeig >0.0)
printf("eigsearch: alpha=%e \n",stepfrac/maxeig);
else
printf("eigsearch: alpha=+Inf\n");
};
if (((stepfrac/maxeig) < start) && (maxeig > 0))
alpha=stepfrac/maxeig;
else
alpha=start;
free(lanczosvectors);
return(alpha);
}
|
