void w_init(w_state * buf, unsigned int prep, bool lorw[128][128])
{
if(buf!=NULL)
{
buf->push=1000;
buf->slant=1;
for(unsigned int x=0;x<256;x++)
{
for(unsigned int y=0;y<128;y++)
{
buf->p[x][y]=984+drandu(32.0);
buf->t[x][y]=8+drandu(8.0); // this is not absolute Celsius, but relative to seasonal variations
}
}
for(unsigned int p=0;p<prep;p++)
{
w_iter(buf, lorw);
}
}
}
void w_iter(w_state * ptr, bool lorw[128][128])
{
if(ptr!=NULL)
{
ptr->push=(ptr->push*.9996)+drandu(0.8);
ptr->slant=(ptr->slant*.9992)+drandu(0.0016);
double tmp[256][128];
for(unsigned int x=0;x<256;x++)
{
for(unsigned int y=0;y<128;y++)
{
ptr->t[x][y]=(ptr->t[x][y]*.96)+drandu(0.96);
if(x) ptr->t[x][y]=(ptr->t[x][y]*.9+ptr->t[x-1][y]*.1);
if(y) ptr->t[x][y]=(ptr->t[x][y]*.9+ptr->t[x][y-1]*.1);
double base=(988+ptr->t[x][y]+ptr->push)/2.0;
if((x<131)||(x>253))
ptr->p[x][y]+=drandu(2.0)-1.0;
else
ptr->p[x][y]+=drandu(5.0)-2.5;
double d2px=ptr->p[(x+255)%256][y]+ptr->p[(x+1)%256][y]-2*ptr->p[x][y];
double d2py=ptr->p[x][max(y, 1)-1]+ptr->p[x][min(y+1, 127)]-2*ptr->p[x][y];
double divp=d2px+d2py;
double big=(abs(d2px)>abs(d2py))?d2px:d2py;
tmp[x][y]=ptr->p[x][y]+divp*.09+big*.07+(ptr->p[(x+255)%256][y]-base)*.07;
if(x<128)
{
if(lorw[x][y])
{
tmp[x][y]+=(tmp[x][y]-base)*0.05+(ptr->p[x][max(y, 1)-1]-base)*.04+(ptr->p[x][(y+1)%128]-base)*.04;
}
else tmp[x][y]-=(tmp[x][y]-base)*0.02;
}
tmp[x][y]-=pow((tmp[x][y]-base)*0.11, 3);
}
}
if(brandp(0.2))
{
double bias=drandu(6.0)+6.0;
if(brandp(0.5)) bias = -bias;
double m=drandu(1.0)-0.5;
for(int dx=-5;dx<6;dx++)
//for(int dy=-7;dy<8;dy++)
for(int y=0;y<128;y++)
tmp[192+dx+(int)floor((y-64)*m)][y]+=bias*ptr->slant;
}
for(unsigned int x=0;x<256;x++)
{
for(unsigned int y=0;y<128;y++)
{
ptr->p[x][y]=min(max(tmp[x][y], 872), 1127);
}
}
}
}
int main(int argc, char * argv[])
{
srand(time(NULL));
if ((argc != 2)){
printf("Correct function call = ./fmkronbench type\n");
printf("Options for type name include: \n");
printf("\t \"0\": time vs. order, \"1\": time vs k, \"2\": time vs r \n");
printf("\t Recall that we are performing Ckron(A,B) where \n");
printf("\t\t C is k x r^2 matrix and \n");
printf("\t\t A,B are r x r matrix valued functions \n");
return 0;
}
double lb = -1.0;
double ub = 1.0;
size_t r11 = 5;
size_t r12 = 5;
size_t r21 = 5;
size_t r22 = 5;
size_t k = 5;
size_t maxorder = 5;
double diff;
size_t nrepeats = 50;
if (strcmp(argv[1],"0") == 0){
size_t nOrders = 40;
double * results = calloc_double(nOrders*3);
size_t ii,jj;
for (ii = 0; ii < nOrders; ii++){
maxorder = 1 + ii;
results[ii] = maxorder;
for (jj = 0; jj < nrepeats; jj++){
double * mat = drandu(k*r11*r21);
struct Qmarray * mat1 =
qmarray_poly_randu(LEGENDRE,r11,r12,
maxorder,lb,ub);
struct Qmarray * mat2 =
qmarray_poly_randu(LEGENDRE,r21,r22,
maxorder,lb,ub);
// method 1
clock_t tic = clock();
struct Qmarray * mat3 = qmarray_kron(mat1,mat2);
struct Qmarray * shouldbe = mqma(mat,mat3,k);
clock_t toc = clock();
results[nOrders+ii] += (double)(toc - tic) / CLOCKS_PER_SEC;
// method 2
tic = clock();
struct Qmarray * is = qmarray_mat_kron(k,mat,mat1,mat2);
toc = clock();
results[2*nOrders+ii] += (double)(toc - tic) / CLOCKS_PER_SEC;
diff = qmarray_norm2diff(shouldbe,is);
assert ( (diff < 1e-10) == 1);
free(mat); mat = NULL;
qmarray_free(mat1); mat1 = NULL;
qmarray_free(mat2); mat2 = NULL;
qmarray_free(mat3); mat3 = NULL;
qmarray_free(shouldbe); shouldbe = NULL;
qmarray_free(is); is = NULL;
}
results[nOrders+ii] /= nrepeats;
results[2*nOrders+ii] /= nrepeats;
printf("On order %zu, total times are (%G,%G)\n",maxorder,results[nOrders+ii],results[2*nOrders+ii]);
}
darray_save(nOrders,3,results,"time_vs_order.dat",1);
free(results); results = NULL;
}
else if (strcmp(argv[1],"1") == 0){
size_t nks = 20;
double * results = calloc_double(nks*3);
size_t ii,jj;
for (ii = 0; ii < nks; ii++){
k = 1 + 10*ii;
results[ii] = (double) k;
for (jj = 0; jj < nrepeats; jj++){
double * mat = drandu(k*r11*r21);
struct Qmarray * mat1 =
qmarray_poly_randu(LEGENDRE,r11,r12,
maxorder,lb,ub);
struct Qmarray * mat2 =
qmarray_poly_randu(LEGENDRE,r21,r22,
maxorder,lb,ub);
// method 1
clock_t tic = clock();
struct Qmarray * mat3 = qmarray_kron(mat1,mat2);
struct Qmarray * shouldbe = mqma(mat,mat3,k);
clock_t toc = clock();
results[nks+ii] += (double)(toc - tic) / CLOCKS_PER_SEC;
// method 2
tic = clock();
struct Qmarray * is = qmarray_mat_kron(k,mat,mat1,mat2);
toc = clock();
results[2*nks+ii] += (double)(toc - tic) / CLOCKS_PER_SEC;
diff = qmarray_norm2diff(shouldbe,is);
assert ( (diff < 1e-10) == 1);
free(mat); mat = NULL;
qmarray_free(mat1); mat1 = NULL;
qmarray_free(mat2); mat2 = NULL;
qmarray_free(mat3); mat3 = NULL;
qmarray_free(shouldbe); shouldbe = NULL;
qmarray_free(is); is = NULL;
}
results[nks+ii] /= nrepeats;
results[2*nks+ii] /= nrepeats;
printf("On k=%zu, total times are (%G,%G)\n",k,results[nks+ii],results[2*nks+ii]);
}
darray_save(nks,3,results,"time_vs_k.dat",1);
free(results); results = NULL;
}
else if (strcmp(argv[1],"2") == 0){
size_t nrs = 20;
double * results = calloc_double(nrs*3);
size_t ii,jj;
for (ii = 0; ii < nrs; ii++){
r11 = 1 + 2*ii;
r12 = r11;
r21 = r11;
r22 = r21;
results[ii] = (double) r11;
for (jj = 0; jj < nrepeats; jj++){
double * mat = drandu(k*r11*r21);
struct Qmarray * mat1 = qmarray_poly_randu(LEGENDRE,r11,r12,maxorder,lb,ub);
struct Qmarray * mat2 = qmarray_poly_randu(LEGENDRE,r21,r22,maxorder,lb,ub);
// method 1
clock_t tic = clock();
struct Qmarray * mat3 = qmarray_kron(mat1,mat2);
struct Qmarray * shouldbe = mqma(mat,mat3,k);
clock_t toc = clock();
results[nrs+ii] += (double)(toc - tic) / CLOCKS_PER_SEC;
// method 2
tic = clock();
struct Qmarray * is = qmarray_mat_kron(k,mat,mat1,mat2);
toc = clock();
results[2*nrs+ii] += (double)(toc - tic) / CLOCKS_PER_SEC;
diff = qmarray_norm2diff(shouldbe,is);
assert ( (diff < 1e-10) == 1);
free(mat); mat = NULL;
qmarray_free(mat1); mat1 = NULL;
qmarray_free(mat2); mat2 = NULL;
qmarray_free(mat3); mat3 = NULL;
qmarray_free(shouldbe); shouldbe = NULL;
qmarray_free(is); is = NULL;
}
results[nrs+ii] /= nrepeats;
results[2*nrs+ii] /= nrepeats;
printf("On r=%zu, total times are (%G,%G)\n",r11,results[nrs+ii],results[2*nrs+ii]);
}
darray_save(nrs,3,results,"time_vs_r.dat",1);
free(results); results = NULL;
}
return 0;
}
