/*--------------------------------------------------------------------------*/
fint zos_forward_(fint* ftag,
fint* fm,
fint* fn,
fint* fk,
fdouble* fbase,
fdouble* fvalue) {
int rc=-1;
int tag=*ftag, m=*fm, n=*fn, k=*fk;
double* base=myalloc1(n);
double* value = myalloc1(m);
spread1(n,fbase,base);
rc=zos_forward(tag,m,n,k,base,value);
pack1(m,value,fvalue);
free((char*)base);
free((char*)value);
return rc;
}
/* hess_vec(tag, n, x[n], v[n], w[n]) */
fint hess_vec_(fint* ftag,
fint* fn,
fdouble *fargument,
fdouble *ftangent,
fdouble *fresult) {
int rc= -1;
int tag=*ftag, n=*fn;
double *argument = myalloc1(n);
double *tangent = myalloc1(n);
double *result = myalloc1(n);
spread1(n,fargument,argument);
spread1(n,ftangent,tangent);
rc= hess_vec(tag,n,argument,tangent,result);
pack1(n,result,fresult);
free((char*)argument);
free((char*)tangent);
free((char*)result);
return rc;
}
/* jac_vec(tag, m, n, x[n], v[n], u[m]); */
fint jac_vec_(fint* ftag,
fint* fm,
fint* fn,
fdouble* fargument,
fdouble* ftangent,
fdouble* fcolumn) {
int rc= -1;
int tag=*ftag, m=*fm, n=*fn;
double* argument = myalloc1(n);
double* tangent = myalloc1(n);
double* column = myalloc1(m);
spread1(n,ftangent,tangent);
spread1(n,fargument,argument);
rc= jac_vec(tag,m,n,argument,tangent,column);
pack1(m,column,fcolumn);
free((char*)argument);
free((char*)tangent);
free((char*)column);
return rc;
}
/* vec_jac(tag, m, n, repeat, x[n], u[m], v[n]) */
fint vec_jac_(fint* ftag,
fint* fm,
fint* fn,
fint* frepeat,
fdouble* fargument,
fdouble* flagrange,
fdouble* frow) {
int rc= -1;
int tag=*ftag, m=*fm, n=*fn, repeat=*frepeat;
double* argument = myalloc1(n);
double* lagrange = myalloc1(m);
double* row = myalloc1(n);
spread1(m,flagrange,lagrange);
spread1(n,fargument,argument);
rc= vec_jac(tag,m,n,repeat,argument,lagrange, row);
pack1(n,row,frow);
free((char*)argument);
free((char*)lagrange);
free((char*)row);
return rc;
}
BEGIN_C_DECLS
/****************************************************************************/
/* DRIVERS FOR OPTIMIZATION AND NONLINEAR EQUATIONS */
/*--------------------------------------------------------------------------*/
/* function */
/* function(tag, m, n, x[n], y[m]) */
fint function_(fint* ftag,
fint* fm,
fint* fn,
fdouble* fargument,
fdouble* fresult) {
int rc= -1;
int tag=*ftag, m=*fm, n=*fn;
double* argument = myalloc1(n);
double* result = myalloc1(m);
spread1(n,fargument,argument);
rc= function(tag,m,n,argument,result);
pack1(m,result,fresult);
free((char*)argument);
free((char*)result);
return rc;
}
/* lagra_hess_vec(tag, m, n, x[n], v[n], u[m], w[n]) */
fint lagra_hess_vec_(fint* ftag,
fint* fm,
fint* fn,
fdouble *fargument,
fdouble *ftangent,
fdouble *flagrange,
fdouble *fresult) {
int rc=-1;
int tag=*ftag, m=*fm, n=*fn;
double *argument = myalloc1(n);
double *tangent = myalloc1(n);
double *lagrange = myalloc1(m);
double *result = myalloc1(n);
spread1(n,fargument,argument);
spread1(n,ftangent,tangent);
spread1(m,flagrange,lagrange);
rc= lagra_hess_vec(tag,m,n,argument,tangent,lagrange,result);
pack1(n,result,fresult);
free((char*)argument);
free((char*)tangent);
free((char*)lagrange);
free((char*)result);
return rc;
}
/* jacobian(tag, m, n, x[n], J[m][n]) */
fint jacobian_(fint* ftag,
fint* fdepen,
fint* findep,
fdouble *fargument,
fdouble *fjac) {
int rc= -1;
int tag=*ftag, depen=*fdepen, indep=*findep;
double** Jac = myalloc2(depen,indep);
double* argument = myalloc1(indep);
spread1(indep,fargument,argument);
rc= jacobian(tag,depen,indep,argument,Jac);
pack2(depen,indep,Jac,fjac);
free((char*)*Jac);
free((char*)Jac);
free((char*)argument);
return rc;
}
/*--------------------------------------------------------------------------*/
void GauszSolve( double** J, int n, int* RI, int* CI, double* b ) {
double* tmpZ;
int i,j;
tmpZ = myalloc1(n);
for (i=0; i<n; i++) {
tmpZ[i]=b[RI[i]];
for (j=0; j<i; j++)
tmpZ[i]-=J[RI[i]][CI[j]]*tmpZ[j];
}
for (i=n-1; i>=0; i--) {
b[CI[i]]=tmpZ[i];
for (j=i+1; j<n; j++)
b[CI[i]]-=J[RI[i]][CI[j]]*b[CI[j]];
b[CI[i]]/=J[RI[i]][CI[i]];
}
free(tmpZ);
}
/*--------------------------------------------------------------------------*/
fint hos_reverse_(fint* ftag,
fint* fm,
fint* fn,
fint* fd,
fdouble* fu,
fdouble* fz) {
int rc=-1;
int tag=*ftag, m=*fm, n=*fn, d=*fd;
double** Z = myalloc2(n,d+1);
double* u = myalloc1(m);
spread1(m,fu,u);
rc=hos_reverse(tag,m,n,d,u,Z);
pack2(n,d+1,Z,fz);
free((char*)*Z);
free((char*)Z);
free((char*)u);
return rc;
}
/* hessian(tag, n, x[n], lower triangle of H[n][n]) */
fint hessian_(fint* ftag,
fint* fn,
fdouble* fx,
fdouble* fh) /* length of h should be n*n but the
upper half of this matrix remains unchanged */
{
int rc= -1;
int tag=*ftag, n=*fn;
double** H = myalloc2(n,n);
double* x = myalloc1(n);
spread1(n,fx,x);
rc= hessian(tag,n,x,H);
pack2(n,n,H,fh);
free((char*)*H);
free((char*)H);
free((char*)x);
return rc;
}
int inverse_Taylor_prop( unsigned short tag, int n, int d,
double** Y, double** X ) {
int i,j,l,q;
static double **I;
register double bi;
static double** Xhelp;
static double** W;
static double* xold;
static double ***A;
static double *w;
static int *dd;
static double *b;
static int nax,dax,bd,cgd;
static short **nonzero;
short* nz;
double* Aij;
double* Xj;
int ii, di, da, Di;
int rc = 3;
/* Re/Allocation Stuff */
if ((n != nax) || (d != dax)) {
if (nax) {
free(**A);
free(*A);
free(A);
free(*I);
free(I);
free(*W);
free(W);
free(*Xhelp);
free(Xhelp);
free(w);
free(xold);
free(*nonzero);
free(nonzero);
free(dd);
free(b);
}
A = myalloc3(n,n,d+1);
I = myalloc2(n,n);
W = myalloc2(n,d);
Xhelp = myalloc2(n,d);
w = myalloc1(n);
dd = (int*)malloc((d+1)*sizeof(int));
b = (double*)malloc(n*sizeof(double));
xold = (double*)malloc(n*sizeof(double));
nonzero = (short**)malloc(n*sizeof(short*));
nz = (short*)malloc(n*n*sizeof(short));
for (i=0; i<n; i++) {
nonzero[i] = nz;
nz = nz + n;
xold[i] = 0;
for (j=0; j<n; j++)
I[i][j]=(i==j)?1.0:0.0;
}
cgd = 1;
nax=n;
dax=d;
dd[0] = d+1;
i = -1;
while(dd[++i] > 1)
dd[i+1] = (int)ceil(dd[i]*0.5);
bd = i+1;
}
if (cgd == 0)
for (i=0; i<n; i++)
if (X[i][0] != xold[i])
cgd = 1;
if (cgd == 1) {
cgd = 0;
for (i=0; i<n; i++)
xold[i] = X[i][0];
MINDEC(rc,jac_solv(tag,n,xold,b,0,1));
if (rc == -3)
return -3;
}
ii = bd;
for (i=0; i<n; i++)
for (j=0; j<d; j++)
Xhelp[i][j] = X[i][j+1];
while (--ii > 0) {
di = dd[ii-1]-1;
Di = dd[ii-1]-dd[ii]-1;
MINDEC(rc,hos_forward(tag,n,n,di,Di+1,xold,Xhelp,w,W));
MINDEC(rc,hov_reverse(tag,n,n,Di,n,I,A,nonzero));
da = dd[ii];
for (l=da; l<dd[ii-1]; l++) {
for (i=0; i<n; i++) {
if (l == 0)
bi = w[i]-Y[i][0];
else
bi = W[i][l-1]-Y[i][l];
for (j=0; j<n; j++)
if (nonzero[i][j]>1) {
Aij = A[i][j];
Xj = X[j]+l;
for (q=da; q<l; q++)
bi += (*(++Aij))*(*(--Xj));
}
b[i] = -bi;
}
MINDEC(rc,jac_solv(tag,n,xold,b,0,2));
if (rc == -3)
return -3;
for (i=0; i<n; i++) {
X[i][l] += b[i];
/* 981214 new nl */
Xhelp[i][l-1] += b[i];
}
}
}
return rc;
}
int jac_solv( unsigned short tag, int n, double* x, double* b,
unsigned short sparse, unsigned short mode ) {
static double **J;
static double **I;
static double *y;
static double *xold;
static int* ri;
static int* ci;
static int nax,tagold,modeold,cgd;
int i,j;
int rc = 3;
if ((n != nax) || (tag != tagold)) {
if (nax) {
free(*J);
free(J);
free(*I);
free(I);
free(xold);
free(ri);
free(ci);
free(y);
}
J = myalloc2(n,n);
I = myalloc2(n,n);
y = myalloc1(n);
xold = myalloc1(n);
ri = (int*)malloc(n*sizeof(int));
ci = (int*)malloc(n*sizeof(int));
for (i=0; i<n; i++) {
xold[i] = 0;
for (j=0;j<n;j++)
I[i][j]=(i==j)?1.0:0.0;
}
cgd = 1;
modeold = 0;
nax = n;
tagold = tag;
}
if (cgd == 0)
for (i=0; i<n; i++)
if (x[i] != xold[i])
cgd = 1;
if (cgd == 1)
for (i=0; i<n; i++)
xold[i] = x[i];
switch(mode) {
case 0:
MINDEC(rc,zos_forward(tag,n,n,1,x,y));
MINDEC(rc,fov_reverse(tag,n,n,n,I,J));
break;
case 1:
if ((modeold == 0) || (cgd == 1)) {
MINDEC(rc,zos_forward(tag,n,n,1,x,y));
MINDEC(rc,fov_reverse(tag,n,n,n,I,J));
}
if (LUFactorization(J,n,ri,ci) < 0)
return -3;
modeold = 1;
break;
case 2:
if ((modeold < 1) || (cgd == 1)) {
MINDEC(rc,zos_forward(tag,n,n,1,x,y));
MINDEC(rc,fov_reverse(tag,n,n,n,I,J));
if (LUFactorization(J,n,ri,ci) < 0)
return -3;
}
GauszSolve(J,n,ri,ci,b);
modeold = 2;
break;
}
cgd = 0;
return rc;
}
/* MAIN PROGRAM */
int main() { /*------------------------------------------------------------------------*/
/* variables */
const int tag = 1; // tape tag
const int size = 5; // system size
const int indep = size*size+size; // # of indeps
const int depen = size; // # of deps
double A[size][size], a1[size], a2[size], // passive variables
b[size], x[size];
adouble **AA, *AAp, *Abx; // active variables
double *args = myalloc1(indep); // arguments
double **jac = myalloc2(depen,indep); // the Jacobian
double *laghessvec = myalloc1(indep); // Hessian-vector product
int i,j;
/*------------------------------------------------------------------------*/
/* Info */
fprintf(stdout,"LINEAR SYSTEM SOLVING by "
"LU-DECOMPOSITION (ADOL-C Example)\n\n");
/*------------------------------------------------------------------------*/
/* Allocation und initialization of the system matrix */
AA = new adouble*[size];
AAp = new adouble[size*size];
for (i=0; i<size; i++) {
AA[i] = AAp;
AAp += size;
}
Abx = new adouble[size];
for(i=0; i<size; i++) {
a1[i] = i*0.25;
a2[i] = i*0.33;
}
for(i=0; i<size; i++) {
for(j=0; j<size; j++)
A[i][j] = a1[i]*a2[j];
A[i][i] += i+1;
b[i] = -i-1;
}
/*------------------------------------------------------------------------*/
/* Taping the computation of the determinant */
trace_on(tag);
/* marking indeps */
for(i=0; i<size; i++)
for(j=0; j<size; j++)
AA[i][j] <<= (args[i*size+j] = A[i][j]);
for(i=0; i<size; i++)
Abx[i] <<= (args[size*size+i] = b[i]);
/* LU-factorization and computation of solution */
LUfact(size,AA);
LUsolve(size,AA,Abx);
/* marking deps */
for (i=0; i<size; i++)
Abx[i] >>= x[i];
trace_off();
fprintf(stdout," x[0] (original): %16.4le\n",x[0]);
/*------------------------------------------------------------------------*/
/* Recomputation */
function(tag,depen,indep,args,x);
fprintf(stdout," x[0] (from tape): %16.4le\n",x[0]);
/*------------------------------------------------------------------------*/
/* Computation of Jacobian */
jacobian(tag,depen,indep,args,jac);
fprintf(stdout," Jacobian:\n");
for (i=0; i<depen; i++) {
for (j=0; j<indep; j++)
fprintf(stdout," %14.6le",jac[i][j]);
fprintf(stdout,"\n");
}
/*------------------------------------------------------------------------*/
/* Computation of Lagrange-Hessian-vector product */
lagra_hess_vec(tag,depen,indep,args,args,x,laghessvec);
fprintf(stdout," Part of Lagrange-Hessian-vector product:\n");
for (i=0; i<size; i++) {
for (j=0; j<size; j++)
fprintf(stdout," %14.6le",laghessvec[i*size+j]);
fprintf(stdout,"\n");
}
/*------------------------------------------------------------------------*/
/* Tape-documentation */
tape_doc(tag,depen,indep,args,x);
/*------------------------------------------------------------------------*/
/* Tape statistics */
int tape_stats[STAT_SIZE];
tapestats(tag,tape_stats);
fprintf(stdout,"\n independents %d\n",tape_stats[NUM_INDEPENDENTS]);
fprintf(stdout," dependents %d\n",tape_stats[NUM_DEPENDENTS]);
fprintf(stdout," operations %d\n",tape_stats[NUM_OPERATIONS]);
fprintf(stdout," operations buffer size %d\n",tape_stats[OP_BUFFER_SIZE]);
fprintf(stdout," locations buffer size %d\n",tape_stats[LOC_BUFFER_SIZE]);
fprintf(stdout," constants buffer size %d\n",tape_stats[VAL_BUFFER_SIZE]);
fprintf(stdout," maxlive %d\n",tape_stats[NUM_MAX_LIVES]);
fprintf(stdout," valstack size %d\n\n",tape_stats[TAY_STACK_SIZE]);
/*------------------------------------------------------------------------*/
/* That's it */
return 1;
}
BEGIN_C_DECLS
/****************************************************************************/
/* DRIVERS FOR ODEs */
/*--------------------------------------------------------------------------*/
/* forodec */
/* forodec(tag, n, tau, dold, dnew, X[n][d+1]) */
int forodec(short tag, /* tape identifier */
int n, /* space dimension */
double tau, /* scaling defaults to 1.0 */
int dol, /* previous degree defaults to zero */
int deg, /* New degree of consistency */
double** Y) /* Taylor series */
{
/*********************************************************************
This is assumed to be the autonomous case.
Here we are just going around computing the vectors
y[][j] for dol < j <= deg
by successive calls to forward that works on the tape identified
by tag. This tape (array of file) must obviously have been
generated by a the execution of an active section between
trace_on and trace_off with n independent and n dependent variables
y must have been set up as pointer to an array of n pointers
to double arrays containing at least deg+1 components.
The scaling by tau is sometimes necessary to avoid overflow.
**********************************************************************/
int rc= 3;
int i, j, k;
double taut;
ADOLC_OPENMP_THREAD_NUMBER;
ADOLC_OPENMP_GET_THREAD_NUMBER;
if ( n > ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_nax ||
deg > ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_dax )
{
if (ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_nax) {
myfree1(ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_y);
myfree1(ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_z);
myfree2(ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_Z);
}
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_Z = myalloc2(n, deg);
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_z = myalloc1(n);
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_y = myalloc1(n);
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_nax = n;
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_dax = deg;
}
for (i = 0; i < n; ++i) {
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_y[i] = Y[i][0];
/*printf("y[%i] = %f\n",i,y[i]);*/
for (k = 0; k < deg; ++k) {
Y[i][k] = Y[i][k+1];
/*printf("Y[%i][%i] = %f\n",i,k,Y[i][k]);*/
}
}
/****** Here we get going ********/
if (dol == 0) {
j = dol; /* j = 0 */
k = (deg) * (j == deg-1 ) ; /* keep death values in prepration */
MINDEC(rc, zos_forward(tag, n, n, k,
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_y,
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_z));
/* for reverse called by jacode */
if(rc < 0) return rc;
taut = tau / (1 + j); /* only the last time through. */
for (i = 0; i < n; ++i)
Y[i][j] = taut * ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_z[i];
dol++; /* !!! */
}
for (j = dol; j < deg; ++j) {
k = (deg)*(j == deg-1) ; /* keep death values in prepration */
MINDEC(rc, hos_forward(tag, n, n, j, k,
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_y,
Y, ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_z,
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_Z));
/* for reverse called by jacode */
if( rc < 0) return rc;
taut = tau / (1 + j); /* only the last time through. */
for (i = 0; i < n; ++i)
Y[i][j] = taut *
ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_Z[i][j-1];
}
/****** Done ********/
for (i = 0; i < n; ++i) {
for (k = deg; k > 0; --k) {
Y[i][k] = Y[i][k-1];
/*printf("Y[%i][%i] = %f\n",i,k,Y[i][k]);*/
}
Y[i][0] = ADOLC_CURRENT_TAPE_INFOS.pTapeInfos.forodec_y[i];
/*printf("Y[%i][0] = %f\n",i,Y[i][0]);*/
}
return rc;
}
