void tex::math_ac ()
{
if (cur_cmd == ACCENT) {
print_err("Please use ");
print_esc("mathaccent");
print(" for accents in math mode");
help_math_accent();
error();
}
tail_append(new_node(ACCENT_NOAD_SIZE));
type(tail) = ACCENT_NOAD;
subtype(tail) = NORMAL;
mzero(nucleus(tail));
mzero(subscr(tail));
mzero(supscr(tail));
math_type(accent_chr(tail)) = MATH_CHAR;
scan_fifteen_bit_int();
character(accent_chr(tail)) = cur_val % 256;
if (cur_val >= VAR_CODE && fam_in_range()) {
fam(accent_chr(tail)) = cur_fam;
} else {
fam(accent_chr(tail)) = cur_val / 256 % 16;
}
scan_math(nucleus(tail));
}
void tex::math_radical ()
{
tail_append(new_node(RADICAL_NOAD_SIZE));
type(tail) = RADICAL_NOAD;
subtype(tail) = NORMAL;
mzero(nucleus(tail));
mzero(supscr(tail));
mzero(subscr(tail));
scan_delimiter(left_delimiter(tail), TRUE);
scan_math(nucleus(tail));
}
void tex::math_fraction ()
{
int c;
mcell garbage;
c = cur_chr;
if (incompleat_noad != null) {
if (c >= DELIMITED_CODE) {
scan_delimiter((ptr)&garbage, FALSE);
scan_delimiter((ptr)&garbage, FALSE);
}
if (c % DELIMITED_CODE == ABOVE_CODE)
scan_normal_dimen();
print_err("Ambiguous; you need another { and }");
help_fraction();
error();
} else {
incompleat_noad = new_node(FRACTION_NOAD_SIZE);
type(incompleat_noad) = FRACTION_NOAD;
subtype(incompleat_noad) = NORMAL;
math_type(numerator(incompleat_noad)) = SUB_MLIST;
math_link(numerator(incompleat_noad)) = link(head);
mzero(denominator(incompleat_noad));
mzero(left_delimiter(incompleat_noad));
mzero(right_delimiter(incompleat_noad));
link(head) = null;
tail = head;
if (c >= DELIMITED_CODE) {
scan_delimiter(left_delimiter(incompleat_noad), FALSE);
scan_delimiter(right_delimiter(incompleat_noad), FALSE);
}
switch (c % DELIMITED_CODE)
{
case ABOVE_CODE:
scan_normal_dimen();
thickness(incompleat_noad) = cur_val;
break;
case OVER_CODE:
thickness(incompleat_noad) = DEFAULT_CODE;
break;
case ATOP_CODE:
thickness(incompleat_noad) = 0;
break;
}
}
}
void
walsh(double in[N][N],double out[N][N]){
double tmp[N][N];
mzero(out);
mzero(tmp);
for(int y=0;y<N;y++)
for(int x=0;x<N;x++)
for(int iy=0;iy<N;iy++)
tmp[y][x]+=(double)w_j[y][iy]*in[iy][x];
for(int y=0;y<N;y++)
for(int x=0;x<N;x++)
for(int iy=0;iy<N;iy++)
out[y][x]+=tmp[y][iy]*(double)w_j[iy][x]/8.0;
}
void
dwt(double in[N][N],double out[N][N]){
double tmp[N][N];
mzero(out);
mzero(tmp);
for(int y=0;y<N;y++)
for(int x=0;x<N;x++){
in[y][x]*=2.0;
in[y][x]+=1.0;
}
for(int n=N;n>1;n/=2){
for(int y=0;y<n;y++)
for(int x=0;x<n/2;x++){
tmp[y][x] =0;
tmp[y][x+n/2]=0;
for(int i=0;i<4;i++){
int idx=(2*x+i)%n;
tmp[y][x] +=p4[i]*in[y][idx]/2.0;
tmp[y][x+n/2]+=q4[i]*in[y][idx];
}
}
for(int x=0;x<n;x++)
for(int y=0;y<n/2;y++){
out[y ][x]=0;
out[y+n/2][x]=0;
for(int i=0;i<4;i++){
int idx=(2*y+i)%n;
out[y ][x]+=p4[i]*tmp[idx][x]/2.0;
out[y+n/2][x]+=q4[i]*tmp[idx][x];
}
}
for(int x=0;x<n;x++)
for(int y=0;y<n;y++)
in[y][x]=out[y][x];
}
}
void
idwt(double in[N][N],double out[N][N]){
double tmp[N][N];
mzero(out);
mzero(tmp);
for(int n=2;n<=N;n*=2){
for(int x=0;x<n;x++)
for(int y=0;y<n/2;y++){
tmp[y*2 ][x]=0;
tmp[y*2+1][x]=0;
for(int i=0;i<4/2;i++){
int idx=(y-i+(n/2)*128)%(n/2);
tmp[y*2 ][x]+=(p4[i*2 ]*in[idx][x]+q4[i*2 ]*in[idx+n/2][x]/2.0);
tmp[y*2+1][x]+=(p4[i*2+1]*in[idx][x]+q4[i*2+1]*in[idx+n/2][x]/2.0);
}
}
for(int y=0;y<n;y++)
for(int x=0;x<n/2;x++){
out[y][x*2 ]=0;
out[y][x*2+1]=0;
for(int i=0;i<4/2;i++){
int idx=(x-i+(n/2)*128)%(n/2);
out[y][x*2 ]+=(p4[i*2 ]*tmp[y][idx]+q4[i*2 ]*tmp[y][idx+n/2]/2.0);
out[y][x*2+1]+=(p4[i*2+1]*tmp[y][idx]+q4[i*2+1]*tmp[y][idx+n/2]/2.0);
}
}
for(int x=0;x<n;x++)
for(int y=0;y<n;y++)
in[y][x]=out[y][x];
}
for(int y=0;y<N;y++)
for(int x=0;x<N;x++)
out[y][x]/=2.0;
}
void
ihaar(double in[N][N],double out[N][N]){
double tmp[N][N];
mzero(out);
mzero(tmp);
for(int n=2;n<=N;n*=2){
for(int x=0;x<n;x++)
for(int y=0;y<n/2;y++){
tmp[y*2 ][x]=(in[y][x]*2+in[y+n/2][x])/2;
tmp[y*2+1][x]=(in[y][x]*2-in[y+n/2][x])/2;
}
for(int y=0;y<n;y++)
for(int x=0;x<n/2;x++){
out[y][x*2 ]=(tmp[y][x]*2+tmp[y][x+n/2])/2;
out[y][x*2+1]=(tmp[y][x]*2-tmp[y][x+n/2])/2;
}
for(int x=0;x<n;x++)
for(int y=0;y<n;y++)
in[y][x]=out[y][x];
}
}
void
haar(double in[N][N],double out[N][N]){
double tmp[N][N];
mzero(out);
mzero(tmp);
for(int n=N;n>1;n/=2){
for(int y=0;y<n;y++)
for(int x=0;x<n/2;x++){
tmp[y][x] =(in[y][x*2]+in[y][x*2+1])/2;
tmp[y][x+n/2]= in[y][x*2]-in[y][x*2+1];
}
for(int x=0;x<n;x++)
for(int y=0;y<n/2;y++){
out[y ][x]=(tmp[y*2][x]+tmp[y*2+1][x])/2;
out[y+n/2][x]= tmp[y*2][x]-tmp[y*2+1][x];
}
for(int x=0;x<n;x++)
for(int y=0;y<n;y++)
in[y][x]=out[y][x];
}
}
void
idct(double in[N][N],double out[N][N]){
mzero(out);
for(int y=0;y<N;y++)
for(int x=0;x<N;x++)
for(int iy=0;iy<N;iy++)
for(int ix=0;ix<N;ix++)
out[y][x]+=
(ix==0?1/(sqrt(2)):1)*
(iy==0?1/(sqrt(2)):1)*
cos((2*x+1)*ix*M_PI/(2*N))*
cos((2*y+1)*iy*M_PI/(2*N))*
in[iy][ix]*
(2.0/N);
}
int
main(){
double out[8][8];
double out2[8][8];
double out3[8][8];
double in[8][8];
double in2[8][8];
for(int y=0;y<N;y++)
for(int x=0;x<N;x++){
mzero(in);
in[y][x]=1;
idct(in,out);
for(int iy=0;iy<N;iy++)
for(int ix=0;ix<N;ix++){
if(out[iy][ix]>=0)
in2[iy][ix]=255;
else
in2[iy][ix]=0;
}
dct(in2,out2);
if(x==0&&y==0)
out3[y][x]=out2[0][0];
else
out3[y][x]=mmax(out2);
}
// mmap(out3,(1.0/4)*);
mmap(out3,round);
mprint(out3);
return true;
}
/*******************************************************************
Subroutine to do the EM algorithm
matrix *D: the pointer to the matrix data
matrix *mean0_x: the pointer to a matrix containing the initial Means of clusters
vector *w0: the pointer to a vector containing the initial mixing proportion of clusters
double vv: the value for initializing the Covariance matrix of clusters
double error: the error threshold
vector *Zjk_up: the pointer to a vector containing Posterior probabilities of the up-level
cluster samples
matrix *mean1_x: the pointer to a matrix containing the Means of clusters in t-space
vector *w0_t: the pointer to a vector containing the mixing proportions of the identified
clusters in t-space
matrix *cov_mat: the pointer to a group of matrixs containing the Covariance
matrix of clusters in t-space
matrix *Zjk: the pointer to a matrix containing Posterior probabilities of all samples
belonging to all the sub-level clusters, each column is for one cluster.
return value: '1' - successfully exit
'0' - exit with waring/error
*******************************************************************/
int veSubEM(matrix *D, matrix *mean0_x, vector *w0, double vv, double error, vector *Zjk_up, //input
matrix *mean1_x, vector *w0_t, matrix *cov_mat, matrix *Zjk) //output
{
int k0, kc, n, p;
int i, j, k, u, s;
matrix *Var0;
matrix Gxn;
vector Fx;
matrix MUK;
matrix MU1;
int zeroFx_num = 1;
//double error = 0.01;
double err = error + (double)1;
vector Zjk_temp;
n = D->m;
p = D->n;
k0 = mean0_x->m;
kc = mean0_x->n;
Var0 = new matrix[k0];
for(i=0; i<k0; i++) {
mnew(Var0+i, p, p);
}
mnew(&Gxn, n, k0);
vnew(&Fx, n);
vnew(&Zjk_temp, n);
mnew(&MUK, k0, p);
mcopy(mean0_x, &MUK);
mnew(&MU1, k0, p);
vector D_j;
vector Zjk_k;
double sum_tmp = 0;
matrix Ck;
vector D_i;
vector MUK_k;
vector cen_D_i;
matrix mtmp;
vector vtmp;
vnew(&D_j, n);
vnew(&Zjk_k, n);
mnew(&Ck, p, p);
vnew(&D_i, p);
vnew(&MUK_k, p);
vnew(&cen_D_i, p);
mnew(&mtmp, p, p);
vnew(&vtmp, n);
//Initializing the parameters of mixture of Gaussians
//Initinalize the covariance matrix
//Use EM algorithm to perform the local training.
//Test intialization of covarinace matrix
//printf("Testing covariance matrix initialization... \n");
while (zeroFx_num != 0) {
for(i=0; i<k0; i++) {
meye(Var0+i);
for (j=0; j<p; j++) {
*((Var0+i)->pr+j*p+j) = vv;
}
}
veModel(D, mean0_x, Var0, w0, &Gxn, &Fx);
//printf("\n Gxn = :\n");
//mprint(&Gxn);
//printf("\n Fx = :\n");
//vprint(&Fx);
zeroFx_num = 0;
for (i=0; i<n; i++) {
if (*(Fx.pr+i) == 0) {
zeroFx_num++;
}
}
vv *= 2;
}
vones(&Zjk_temp);
//printf("\n EM in t-space starts ... \n");
//printf("\n Data = \n");
//mprint(D);
int l = 0;
while (err > error) {
#ifdef _DEBUG
printf(" \n...... in EM loop %d ......\n", ++l);
printf("\n L%d: w0 = \n", l);
vprint(w0);
printf("\n L%d: MUK = \n", l);
mprint(&MUK);
printf("\n L%d: Var0 = \n", l);
for(i=0; i<k0; i++) {
mprint(Var0+i);
printf("\n");
}
printf("\n L%d: Zjk = \n", l);
mprint(Zjk);
#endif
veModel(D, &MUK, Var0, w0, &Gxn, &Fx);
#ifdef _DEBUG
printf("\n L%d: Gxn = \n", l);
mprint(&Gxn);
printf("\n L%d: Fx = \n", l);
vprint(&Fx);
#endif
for (k=0; k<k0; k++) {
u = k*p;
double zz = 0;
double zz_up = 0;
for (i=0; i<n; i++) {
*(Zjk->pr+i*k0+k) = (*(w0->pr+k)) * Zjk_up->pr[i] * (*(Gxn.pr+i*k0+k)) / (*(Fx.pr+i));
zz += *(Zjk->pr+i*k0+k);
zz_up += Zjk_up->pr[i];
}
*(w0->pr+k) = zz/zz_up;
for (j=0; j<p; j++) {
getcolvec(D, j, &D_j);
getcolvec(Zjk, k, &Zjk_k);
sum_tmp = 0;
for (i=0; i<n; i++) {
sum_tmp += (*(Zjk_k.pr+i)) * (*(D_j.pr+i));
}
*(MU1.pr+u+j) = sum_tmp / zz;
}
mzero(&Ck);
for (i=0; i<n; i++) {
getrowvec(D, i, &D_i);
getrowvec(&MUK, k, &MUK_k);
for (j=0; j<p; j++) {
*(cen_D_i.pr+j) = *(D_i.pr+j) - *(MUK_k.pr+j);
}
vvMul(&cen_D_i, &cen_D_i, &mtmp);
for (j=0; j<p; j++) {
for (s=0; s<p; s++) {
*(Ck.pr+j*p+s) += (*(Zjk->pr+i*k0+k)) * (*(mtmp.pr+j*p+s));
}
}
}
for (j=0; j<p; j++) {
for (s=0; s<p; s++) {
*(Var0[k].pr+j*p+s) = (*(Ck.pr+j*p+s)) / zz;
}
}
} // for (k...
mcopy(&MU1, &MUK);
for (i=0; i<n; i++) {
*(vtmp.pr+i) = fabs(*(Zjk_k.pr+i) - *(Zjk_temp.pr+i));
}
err = vmean(&vtmp);
vcopy(&Zjk_k, &Zjk_temp);
} // while
vcopy(w0, w0_t);
mcopy(&MUK, mean1_x);
for(i=0; i<k0; i++) {
mcopy(Var0+i, cov_mat+i);
}
for(i=0; i<k0; i++) {
mdelete(Var0+i);
}
mdelete(&Gxn);
vdelete(&Fx);
vdelete(&Zjk_temp);
mdelete(&MUK);
mdelete(&MU1);
vdelete(&D_j);
vdelete(&Zjk_k);
mdelete(&Ck);
vdelete(&D_i);
vdelete(&MUK_k);
vdelete(&cen_D_i);
mdelete(&mtmp);
vdelete(&vtmp);
return 1;
}
int main(int argc, char *argv[])
{
(void)argc; (void)argv;
#ifdef __SSE__
printf("SSE ");
#endif
#ifdef __SSE2__
printf("SSE2 ");
#endif
#ifdef __SSE3__
printf("SSE3 ");
#endif
#ifdef __SSE4__
printf("SSE4 ");
#endif
#ifdef __SSE4_1__
printf("SSE4.1 ");
#endif
#ifdef __SSE4_2__
printf("SSE4.2 ");
#endif
#ifdef __AVX__
printf("AVX ");
#endif
#ifdef __FMA4__
printf("FMA4 ");
#endif
printf("\n");
printv(vec(1, 2, 3, 4));
printv(vzero());
printm(mzero());
printm(midentity());
vec4 a = { 1, 2, 3, 4 }, b = { 5, 6, 7, 8 };
printv(a);
printv(b);
printf("\nshuffles:\n");
printv(vshuffle(a, a, 0, 1, 2, 3));
printv(vshuffle(a, a, 3, 2, 1, 0));
printv(vshuffle(a, b, 0, 1, 0, 1));
printv(vshuffle(a, b, 2, 3, 2, 3));
printf("\ndot products:\n");
printv(vdot(a, b));
printv(vdot(b, a));
printv(vdot3(a, b));
printv(vdot3(b, a));
//vec4 blendmask = { 1, -1, 1, -1 };
//printv(vblend(x, y, blendmask));
vec4 x = { 1, 0, 0, 0 }, y = { 0, 1, 0, 0 }, z = { 0, 0, 1, 0 }, w = { 0, 0, 0, 1 };
printf("\ncross products:\n");
printv(vcross(x, y));
printv(vcross(y, x));
printv(vcross_scalar(x, y));
printv(vcross_scalar(y, x));
printf("\nquaternion products:\n");
printv(qprod(x, y));
printv(qprod(y, x));
printv(qprod_mad(x, y));
printv(qprod_mad(y, x));
printv(qprod_scalar(x, y));
printv(qprod_scalar(y, x));
printf("\nquaternion conjugates:\n");
printv(qconj(x));
printv(qconj(y));
printv(qconj(z));
printv(qconj(w));
printf("\nmat from quat:\n");
printm(quat_to_mat(w));
printm(quat_to_mat_mmul(w));
printm(quat_to_mat_scalar(w));
vec4 angles = { 0.0, 0.0, 0.0, 0.0 };
printf("\neuler to quaternion:\n");
printv(quat_euler(angles));
printv(quat_euler_scalar(angles));
printv(quat_euler_gems(angles));
printf("\neuler to matrix:\n");
printm(mat_euler(angles));
printm(mat_euler_scalar(angles));
printm(quat_to_mat(quat_euler(angles)));
printf("\nperspective matrix:\n");
printm(mat_perspective_fovy(M_PI/4.0, 16.0/9.0, 0.1, 100.0));
printm(mat_perspective_fovy_inf_z(M_PI/4.0, 16.0/9.0, 0.1));
printm(mat_perspective_fovy_scalar(M_PI/4.0, 16.0/9.0, 0.1, 100.0));
printf("\northogonal matrix:\n");
printm(mat_ortho(-1.0, 1.0, -1.0, 1.0, -1.0, 1.0));
printm(mat_ortho(-1.0, 2.0, -1.0, 2.0, -1.0, 2.0));
printf("\ntranslate matrix:\n");
printm(mtranslate(a));
printf("\nscale matrix:\n");
printm(mscale(a));
return 0;
}
// From List.
// You can't insert an element within an empty list; fail.
// insertWithin(Nil, ?x) == mzero()
ListOfLists insertWithin(Element x) {
return mzero();
}
