int tensor_eval( int tag, int m, int n, int d, int p,
double* x, double **tensor, double **S ) {
static int bd,dim;
static int dold,pold;
static struct item *coeff_list;
int i,j,k,dimten,ctr;
int **jm, jmbd=0;
int *it = (int*) malloc(d*sizeof(int));
double *y = (double*) malloc(m*sizeof(double));
double*** X;
double*** Y;
struct item *ptr[10];
int rc = 3;
dimten=binomi(p+d,d);
for (i=0; i<m; i++)
for (j=0; j<dimten; j++)
tensor[i][j] = 0;
if (d == 0) {
MINDEC(rc,zos_forward(1,m,n,0,x,y));
} else {
if ((d != dold) || (p != pold)) {
if (pold) {
dim = binomi(pold+dold-1,dold);
freecoefflist(dim,coeff_list);
free((char*) coeff_list);
}
dim = binomi(p+d-1,d);
if (dim < 10)
bd = dim;
else
bd = 10;
coeff_list = (struct item *) malloc(sizeof(struct item)*dim);
coeff(p,d, coeff_list);
dold = d;
pold = p;
}
jmbd = bd;
jm = (int **) malloc(jmbd*sizeof(int*));
for (i=0; i<jmbd; i++)
jm[i] = (int *) malloc(p*sizeof(int));
if (d == 1) {
X = myalloc3(1,n,bd);
Y = myalloc3(1,m,bd);
ctr = 0;
it[0] = 0;
for (i=0; i<dim; i++) /* sum over all multiindices jm with |jm| = d */
{ it[0] = it[0]+1;
convert(p,d,it,jm[ctr]);
ptr[ctr] = &coeff_list[i];
if (ctr < bd-1)
ctr += 1;
else {
multma2vec2(n,p,bd,X[0],S,jm);
MINDEC(rc,fov_forward(tag,m,n,bd,x,X[0],y,Y[0]));
for (k=0; k<bd; k++)
do {
for (j=0; j<m; j++)
tensor[j][ptr[k]->a] += Y[0][j][k]*ptr[k]->c;
ptr[k] = ptr[k]->next;
} while (ptr[k] != NULL);
if (dim-i < bd)
bd = dim-i-1;
ctr = 0;
}
}
} else {
X = myalloc3(n,bd,d);
Y = myalloc3(m,bd,d);
ctr = 0;
for (i=0; i<d-1; i++)
it[i] = 1;
it[d-1] = 0;
for (i=0; i<dim; i++) /* sum over all multiindices jm with |jm| = d */
{ it[d-1] = it[d-1]+1;
for (j=d-2; j>=0; j--)
it[j] = it[j] + it[j+1]/(p+1);
for (j=1; j<d; j++)
if (it[j] > p)
it[j] = it[j-1];
convert(p,d,it,jm[ctr]);
ptr[ctr] = &coeff_list[i];
if (ctr < bd-1)
ctr += 1;
else {
multma3vec2(n,p,d,bd,X,S,jm);
MINDEC(rc,hov_forward(tag,m,n,d,bd,x,X,y,Y));
for (k=0; k<bd; k++)
do {
for (j=0; j<m; j++)
tensor[j][ptr[k]->a] += Y[j][k][ptr[k]->b-1]*ptr[k]->c;
ptr[k] = ptr[k]->next;
} while (ptr[k] != NULL);
if (dim-i < bd)
bd = dim-i-1;
ctr = 0;
}
}
}
for (i=0; i<jmbd; i++)
free((char*) *(jm+i));
free((char*) jm);
free((char*) **X);
free((char*) *X);
free((char*) X);
free((char*) **Y);
free((char*) *Y);
free((char*) Y);
}
for(i=0;i<m;i++)
tensor[i][0] = y[i];
bd = jmbd;
free((char*) y);
free((char*) it);
return rc;
}
int inverse_tensor_eval( int tag, int n, int d, int p,
double *x, double **tensor, double** S ) {
static int dim;
static int dold,pold;
static struct item *coeff_list;
int i,j,dimten;
int *it = (int*) malloc(d*sizeof(int));
double** X;
double** Y;
int *jm;
double *y = (double*) malloc(n*sizeof(double));
struct item *ptr;
int rc = 3;
dimten=binomi(p+d,d);
for(i=0;i<n;i++)
for(j=0;j<dimten;j++)
tensor[i][j] = 0;
MINDEC(rc,zos_forward(1,n,n,0,x,y));
if (d > 0) {
if ((d != dold) || (p != pold)) {
if (pold) { /* olvo 980728 */
dim = binomi(pold+dold-1,dold);
freecoefflist(dim,coeff_list);
free((char*) coeff_list);
}
dim = binomi(p+d-1,d);
coeff_list = (struct item *) malloc(sizeof(struct item)*dim);
coeff(p,d, coeff_list);
dold = d;
pold = p;
}
jm = (int *)malloc(sizeof(int)*p);
X = myalloc2(n,d+1);
Y = myalloc2(n,d+1);
for (i=0; i<n; i++) {
X[i][0] = x[i];
for (j=1; j<d; j++)
X[i][j] = 0;
Y[i][0] = y[i];
}
if (d == 1) {
it[0] = 0;
for (i=0; i<dim; i++) /* sum over all multiindices jm with |jm| = d */
{ it[0] = it[0]+1;
convert(p,d,it,jm);
ptr = &coeff_list[i];
multma2vec1(n,p,d,Y,S,jm);
MINDEC(rc,inverse_Taylor_prop(tag,n,d,Y,X));
if (rc == -3)
return -3;
do {
for(j=0;j<n;j++)
tensor[j][ptr->a] += X[j][ptr->b]*ptr->c;
ptr = ptr->next;
} while (ptr != NULL);
}
} else {
for (i=0; i<d-1; i++)
it[i] = 1;
it[d-1] = 0;
for (i=0; i<dim; i++) /* sum over all multiindices jm with |jm| = d */
{ it[d-1] = it[d-1]+1;
for (j=d-2; j>=0; j--)
it[j] = it[j] + it[j+1]/(p+1);
for (j=1; j<d; j++)
if (it[j] > p) it[j] = it[j-1];
convert(p,d,it,jm);
multma2vec1(n,p,d,Y,S,jm); /* Store S*jm in Y */
MINDEC(rc,inverse_Taylor_prop(tag,n,d,Y,X));
if (rc == -3)
return -3;
ptr = &coeff_list[i];
do {
for(j=0;j<n;j++)
tensor[j][ptr->a] += X[j][ptr->b]*ptr->c;
ptr = ptr->next;
} while (ptr != NULL);
}
}
free((char*) jm);
free((char*) *X);
free((char*) X);
free((char*) *Y);
free((char*) Y);
}
for(i=0;i<n;i++)
tensor[i][0] = x[i];
free((char*) y);
free((char*) it);
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;
}
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;
}
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;
}
