int gen_plot_kmeans(data *raw, int n, data *plot, int attempts){
int *which;
int i,j,k;
double *work;
extern double RunKMeansPlusPlus(int n, int k, int d, double *points, int attempts,
double *centers, int *assignments);
plot->n = n;
plot->xy = (double*)malloc(sizeof(double)*4*n);
plot->f = plot->xy + 2*n;
which = (int*)malloc(sizeof(int)*raw->n);
work = (double*)malloc(sizeof(double)*2*n);
for(i = 0; i < 2*n; ++i){
work[i] = 0;
plot->f[i] = 0;
}
RunKMeansPlusPlus(raw->n, n, 2, raw->xy, attempts, plot->xy, which);
for(i = 0; i < raw->n; ++i){
int c = which[i];
double d = pythag2(plot->xy[2*c+0] - raw->xy[2*i+0], plot->xy[2*c+1] - raw->xy[2*i+1]);
if(d > work[c]){ work[c] = d; }
}
for(i = 0; i < raw->n; ++i){
int c = which[i];
double d = pythag2(plot->xy[2*c+0] - raw->xy[2*i+0], plot->xy[2*c+1] - raw->xy[2*i+1]);
if(0 == work[c]){
d = 1.0;
}else{
d = 1.0 - d/work[c];
}
plot->f[2*c+0] += d*raw->f[2*i+0];
plot->f[2*c+1] += d*raw->f[2*i+1];
work[n+c] += d;
}
plot->max_len = 0;
for(i = 0; i < n; ++i){
if(work[n+i] > 0){
plot->f[2*i+0] /= work[n+i];
plot->f[2*i+1] /= work[n+i];
double d = pythag2(plot->f[2*i+0], plot->f[2*i+1]);
if(d > plot->max_len){ plot->max_len = d; }
if(plot->xy[2*i+0] < plot->bbox[0]){ plot->bbox[0] = plot->xy[2*i+0]; }
if(plot->xy[2*i+0] > plot->bbox[1]){ plot->bbox[1] = plot->xy[2*i+0]; }
if(plot->xy[2*i+1] < plot->bbox[2]){ plot->bbox[2] = plot->xy[2*i+1]; }
if(plot->xy[2*i+1] > plot->bbox[3]){ plot->bbox[3] = plot->xy[2*i+1]; }
}
//fprintf(stderr, "%f %f %f %f\n", plot->xy[2*i+0], plot->xy[2*i+1], plot->f[2*i+0], plot->f[2*i+1]);
}
free(work);
free(which);
return 0;
}
int data_cull_zeros(data *d, int n_arrows){
int i, c = 0;
int ret = 0;
int *flag = (int*)malloc(sizeof(int)*d->n);
for(i = 0; i < d->n; ++i){
flag[i] = 0;
if(pythag2(d->f[2*i+0], d->f[2*i+1]) < DBL_EPSILON*d->max_len){
flag[i] = 1;
++c;
}
}
if(d->n - c <= n_arrows){
// Remove all the zeros
c = 0;
for(i = 0; i < d->n; ++i){
if(!flag[i] && c != i){
d->xy[2*c+0] = d->xy[2*i+0];
d->xy[2*c+1] = d->xy[2*i+1];
d->f[2*c+0] = d->f[2*i+0];
d->f[2*c+1] = d->f[2*i+1];
++c;
}
}
d->n = c;
ret = 1;
}
free(flag);
return ret;
}
void internalschurdecomposition(ap::real_2d_array& h,
int n,
int tneeded,
int zneeded,
ap::real_1d_array& wr,
ap::real_1d_array& wi,
ap::real_2d_array& z,
int& info)
{
ap::real_1d_array work;
int i;
int i1;
int i2;
int ierr;
int ii;
int itemp;
int itn;
int its;
int j;
int k;
int l;
int maxb;
int nr;
int ns;
int nv;
double absw;
double ovfl;
double smlnum;
double tau;
double temp;
double tst1;
double ulp;
double unfl;
ap::real_2d_array s;
ap::real_1d_array v;
ap::real_1d_array vv;
ap::real_1d_array workc1;
ap::real_1d_array works1;
ap::real_1d_array workv3;
ap::real_1d_array tmpwr;
ap::real_1d_array tmpwi;
bool initz;
bool wantt;
bool wantz;
double cnst;
bool failflag;
int p1;
int p2;
int p3;
int p4;
double vt;
//
// Set the order of the multi-shift QR algorithm to be used.
// If you want to tune algorithm, change this values
//
ns = 12;
maxb = 50;
//
// Now 2 < NS <= MAXB < NH.
//
maxb = ap::maxint(3, maxb);
ns = ap::minint(maxb, ns);
//
// Initialize
//
cnst = 1.5;
work.setbounds(1, ap::maxint(n, 1));
s.setbounds(1, ns, 1, ns);
v.setbounds(1, ns+1);
vv.setbounds(1, ns+1);
wr.setbounds(1, ap::maxint(n, 1));
wi.setbounds(1, ap::maxint(n, 1));
workc1.setbounds(1, 1);
works1.setbounds(1, 1);
workv3.setbounds(1, 3);
tmpwr.setbounds(1, ap::maxint(n, 1));
tmpwi.setbounds(1, ap::maxint(n, 1));
ap::ap_error::make_assertion(n>=0, "InternalSchurDecomposition: incorrect N!");
ap::ap_error::make_assertion(tneeded==0||tneeded==1, "InternalSchurDecomposition: incorrect TNeeded!");
ap::ap_error::make_assertion(zneeded==0||zneeded==1||zneeded==2, "InternalSchurDecomposition: incorrect ZNeeded!");
wantt = tneeded==1;
initz = zneeded==2;
wantz = zneeded!=0;
info = 0;
//
// Initialize Z, if necessary
//
if( initz )
{
z.setbounds(1, n, 1, n);
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
if( i==j )
{
z(i,j) = 1;
}
else
{
z(i,j) = 0;
}
}
}
}
//
// Quick return if possible
//
if( n==0 )
{
return;
}
if( n==1 )
{
wr(1) = h(1,1);
wi(1) = 0;
return;
}
//
// Set rows and columns 1 to N to zero below the first
// subdiagonal.
//
for(j = 1; j <= n-2; j++)
{
for(i = j+2; i <= n; i++)
{
h(i,j) = 0;
}
}
//
// Test if N is sufficiently small
//
if( ns<=2||ns>n||maxb>=n )
{
//
// Use the standard double-shift algorithm
//
internalauxschur(wantt, wantz, n, 1, n, h, wr, wi, 1, n, z, work, workv3, workc1, works1, info);
//
// fill entries under diagonal blocks of T with zeros
//
if( wantt )
{
j = 1;
while(j<=n)
{
if( wi(j)==0 )
{
for(i = j+1; i <= n; i++)
{
h(i,j) = 0;
}
j = j+1;
}
else
{
for(i = j+2; i <= n; i++)
{
h(i,j) = 0;
h(i,j+1) = 0;
}
j = j+2;
}
}
}
return;
}
unfl = ap::minrealnumber;
ovfl = 1/unfl;
ulp = 2*ap::machineepsilon;
smlnum = unfl*(n/ulp);
//
// I1 and I2 are the indices of the first row and last column of H
// to which transformations must be applied. If eigenvalues only are
// being computed, I1 and I2 are set inside the main loop.
//
if( wantt )
{
i1 = 1;
i2 = n;
}
//
// ITN is the total number of multiple-shift QR iterations allowed.
//
itn = 30*n;
//
// The main loop begins here. I is the loop index and decreases from
// IHI to ILO in steps of at most MAXB. Each iteration of the loop
// works with the active submatrix in rows and columns L to I.
// Eigenvalues I+1 to IHI have already converged. Either L = ILO or
// H(L,L-1) is negligible so that the matrix splits.
//
i = n;
while(true)
{
l = 1;
if( i<1 )
{
//
// fill entries under diagonal blocks of T with zeros
//
if( wantt )
{
j = 1;
while(j<=n)
{
if( wi(j)==0 )
{
for(i = j+1; i <= n; i++)
{
h(i,j) = 0;
}
j = j+1;
}
else
{
for(i = j+2; i <= n; i++)
{
h(i,j) = 0;
h(i,j+1) = 0;
}
j = j+2;
}
}
}
//
// Exit
//
return;
}
//
// Perform multiple-shift QR iterations on rows and columns ILO to I
// until a submatrix of order at most MAXB splits off at the bottom
// because a subdiagonal element has become negligible.
//
failflag = true;
for(its = 0; its <= itn; its++)
{
//
// Look for a single small subdiagonal element.
//
for(k = i; k >= l+1; k--)
{
tst1 = fabs(h(k-1,k-1))+fabs(h(k,k));
if( tst1==0 )
{
tst1 = upperhessenberg1norm(h, l, i, l, i, work);
}
if( fabs(h(k,k-1))<=ap::maxreal(ulp*tst1, smlnum) )
{
break;
}
}
l = k;
if( l>1 )
{
//
// H(L,L-1) is negligible.
//
h(l,l-1) = 0;
}
//
// Exit from loop if a submatrix of order <= MAXB has split off.
//
if( l>=i-maxb+1 )
{
failflag = false;
break;
}
//
// Now the active submatrix is in rows and columns L to I. If
// eigenvalues only are being computed, only the active submatrix
// need be transformed.
//
if( !wantt )
{
i1 = l;
i2 = i;
}
if( its==20||its==30 )
{
//
// Exceptional shifts.
//
for(ii = i-ns+1; ii <= i; ii++)
{
wr(ii) = cnst*(fabs(h(ii,ii-1))+fabs(h(ii,ii)));
wi(ii) = 0;
}
}
else
{
//
// Use eigenvalues of trailing submatrix of order NS as shifts.
//
copymatrix(h, i-ns+1, i, i-ns+1, i, s, 1, ns, 1, ns);
internalauxschur(false, false, ns, 1, ns, s, tmpwr, tmpwi, 1, ns, z, work, workv3, workc1, works1, ierr);
for(p1 = 1; p1 <= ns; p1++)
{
wr(i-ns+p1) = tmpwr(p1);
wi(i-ns+p1) = tmpwi(p1);
}
if( ierr>0 )
{
//
// If DLAHQR failed to compute all NS eigenvalues, use the
// unconverged diagonal elements as the remaining shifts.
//
for(ii = 1; ii <= ierr; ii++)
{
wr(i-ns+ii) = s(ii,ii);
wi(i-ns+ii) = 0;
}
}
}
//
// Form the first column of (G-w(1)) (G-w(2)) . . . (G-w(ns))
// where G is the Hessenberg submatrix H(L:I,L:I) and w is
// the vector of shifts (stored in WR and WI). The result is
// stored in the local array V.
//
v(1) = 1;
for(ii = 2; ii <= ns+1; ii++)
{
v(ii) = 0;
}
nv = 1;
for(j = i-ns+1; j <= i; j++)
{
if( wi(j)>=0 )
{
if( wi(j)==0 )
{
//
// real shift
//
p1 = nv+1;
ap::vmove(&vv(1), &v(1), ap::vlen(1,p1));
matrixvectormultiply(h, l, l+nv, l, l+nv-1, false, vv, 1, nv, 1.0, v, 1, nv+1, -wr(j));
nv = nv+1;
}
else
{
if( wi(j)>0 )
{
//
// complex conjugate pair of shifts
//
p1 = nv+1;
ap::vmove(&vv(1), &v(1), ap::vlen(1,p1));
matrixvectormultiply(h, l, l+nv, l, l+nv-1, false, v, 1, nv, 1.0, vv, 1, nv+1, -2*wr(j));
itemp = vectoridxabsmax(vv, 1, nv+1);
temp = 1/ap::maxreal(fabs(vv(itemp)), smlnum);
p1 = nv+1;
ap::vmul(&vv(1), ap::vlen(1,p1), temp);
absw = pythag2(wr(j), wi(j));
temp = temp*absw*absw;
matrixvectormultiply(h, l, l+nv+1, l, l+nv, false, vv, 1, nv+1, 1.0, v, 1, nv+2, temp);
nv = nv+2;
}
}
//
// Scale V(1:NV) so that max(abs(V(i))) = 1. If V is zero,
// reset it to the unit vector.
//
itemp = vectoridxabsmax(v, 1, nv);
temp = fabs(v(itemp));
if( temp==0 )
{
v(1) = 1;
for(ii = 2; ii <= nv; ii++)
{
v(ii) = 0;
}
}
else
{
temp = ap::maxreal(temp, smlnum);
vt = 1/temp;
ap::vmul(&v(1), ap::vlen(1,nv), vt);
}
}
}
//
// Multiple-shift QR step
//
for(k = l; k <= i-1; k++)
{
//
// The first iteration of this loop determines a reflection G
// from the vector V and applies it from left and right to H,
// thus creating a nonzero bulge below the subdiagonal.
//
// Each subsequent iteration determines a reflection G to
// restore the Hessenberg form in the (K-1)th column, and thus
// chases the bulge one step toward the bottom of the active
// submatrix. NR is the order of G.
//
nr = ap::minint(ns+1, i-k+1);
if( k>l )
{
p1 = k-1;
p2 = k+nr-1;
ap::vmove(v.getvector(1, nr), h.getcolumn(p1, k, p2));
}
generatereflection(v, nr, tau);
if( k>l )
{
h(k,k-1) = v(1);
for(ii = k+1; ii <= i; ii++)
{
h(ii,k-1) = 0;
}
}
v(1) = 1;
//
// Apply G from the left to transform the rows of the matrix in
// columns K to I2.
//
applyreflectionfromtheleft(h, tau, v, k, k+nr-1, k, i2, work);
//
// Apply G from the right to transform the columns of the
// matrix in rows I1 to min(K+NR,I).
//
applyreflectionfromtheright(h, tau, v, i1, ap::minint(k+nr, i), k, k+nr-1, work);
if( wantz )
{
//
// Accumulate transformations in the matrix Z
//
applyreflectionfromtheright(z, tau, v, 1, n, k, k+nr-1, work);
}
}
}
//
// Failure to converge in remaining number of iterations
//
if( failflag )
{
info = i;
return;
}
//
// A submatrix of order <= MAXB in rows and columns L to I has split
// off. Use the double-shift QR algorithm to handle it.
//
internalauxschur(wantt, wantz, n, l, i, h, wr, wi, 1, n, z, work, workv3, workc1, works1, info);
if( info>0 )
{
return;
}
//
// Decrement number of remaining iterations, and return to start of
// the main loop with a new value of I.
//
itn = itn-its;
i = l-1;
}
}
static void aux2x2schur(double& a,
double& b,
double& c,
double& d,
double& rt1r,
double& rt1i,
double& rt2r,
double& rt2i,
double& cs,
double& sn)
{
double multpl;
double aa;
double bb;
double bcmax;
double bcmis;
double cc;
double cs1;
double dd;
double eps;
double p;
double sab;
double sac;
double scl;
double sigma;
double sn1;
double tau;
double temp;
double z;
multpl = 4.0;
eps = ap::machineepsilon;
if( c==0 )
{
cs = 1;
sn = 0;
}
else
{
if( b==0 )
{
//
// Swap rows and columns
//
cs = 0;
sn = 1;
temp = d;
d = a;
a = temp;
b = -c;
c = 0;
}
else
{
if( a-d==0&&extschursigntoone(b)!=extschursigntoone(c) )
{
cs = 1;
sn = 0;
}
else
{
temp = a-d;
p = 0.5*temp;
bcmax = ap::maxreal(fabs(b), fabs(c));
bcmis = ap::minreal(fabs(b), fabs(c))*extschursigntoone(b)*extschursigntoone(c);
scl = ap::maxreal(fabs(p), bcmax);
z = p/scl*p+bcmax/scl*bcmis;
//
// If Z is of the order of the machine accuracy, postpone the
// decision on the nature of eigenvalues
//
if( z>=multpl*eps )
{
//
// Real eigenvalues. Compute A and D.
//
z = p+extschursign(sqrt(scl)*sqrt(z), p);
a = d+z;
d = d-bcmax/z*bcmis;
//
// Compute B and the rotation matrix
//
tau = pythag2(c, z);
cs = z/tau;
sn = c/tau;
b = b-c;
c = 0;
}
else
{
//
// Complex eigenvalues, or real (almost) equal eigenvalues.
// Make diagonal elements equal.
//
sigma = b+c;
tau = pythag2(sigma, temp);
cs = sqrt(0.5*(1+fabs(sigma)/tau));
sn = -p/(tau*cs)*extschursign(double(1), sigma);
//
// Compute [ AA BB ] = [ A B ] [ CS -SN ]
// [ CC DD ] [ C D ] [ SN CS ]
//
aa = a*cs+b*sn;
bb = -a*sn+b*cs;
cc = c*cs+d*sn;
dd = -c*sn+d*cs;
//
// Compute [ A B ] = [ CS SN ] [ AA BB ]
// [ C D ] [-SN CS ] [ CC DD ]
//
a = aa*cs+cc*sn;
b = bb*cs+dd*sn;
c = -aa*sn+cc*cs;
d = -bb*sn+dd*cs;
temp = 0.5*(a+d);
a = temp;
d = temp;
if( c!=0 )
{
if( b!=0 )
{
if( extschursigntoone(b)==extschursigntoone(c) )
{
//
// Real eigenvalues: reduce to upper triangular form
//
sab = sqrt(fabs(b));
sac = sqrt(fabs(c));
p = extschursign(sab*sac, c);
tau = 1/sqrt(fabs(b+c));
a = temp+p;
d = temp-p;
b = b-c;
c = 0;
cs1 = sab*tau;
sn1 = sac*tau;
temp = cs*cs1-sn*sn1;
sn = cs*sn1+sn*cs1;
cs = temp;
}
}
else
{
b = -c;
c = 0;
temp = cs;
cs = -sn;
sn = temp;
}
}
}
}
}
}
//
// Store eigenvalues in (RT1R,RT1I) and (RT2R,RT2I).
//
rt1r = a;
rt2r = d;
if( c==0 )
{
rt1i = 0;
rt2i = 0;
}
else
{
rt1i = sqrt(fabs(b))*sqrt(fabs(c));
rt2i = -rt1i;
}
}
int data_read(data *d, const char *filename){
FILE *fp;
int i;
char line[1024];
int ncap = 256;
int line_count = 0, count;
double x, y, fx, fy, fa;
double *temp;
if(NULL == d){ return -1; }
if(NULL == filename){ return -2; }
d->n = 0;
if(NULL != d->xy){ free(d->xy); }
temp = (double*)malloc(sizeof(double)*4*ncap);
fp = fopen(filename, "rt");
if(NULL == fp){ return -3; }
while(fgets(line, sizeof(line), fp) != NULL){ ++line_count;
if('#' == line[0]){ continue; }
count = sscanf(line, "%lf %lf %lf %lf", &x, &y, &fx, &fy);
if(0 < count && count < 4){
fprintf(stderr, "Expected 4 values on line %d but only got %d\n", line_count, count);
goto error;
}
if(count < 1){ continue; }
if(d->n >= ncap){
ncap *= 2;
temp = (double*)realloc(temp, sizeof(double)*4*ncap);
}
temp[4*(d->n)+0] = x;
temp[4*(d->n)+1] = y;
temp[4*(d->n)+2] = fx;
temp[4*(d->n)+3] = fy;
d->n++;
if(x < d->bbox[0]){ d->bbox[0] = x; }
if(x > d->bbox[1]){ d->bbox[1] = x; }
if(y < d->bbox[2]){ d->bbox[2] = y; }
if(y > d->bbox[3]){ d->bbox[3] = y; }
fa = pythag2(fx, fy);
if(fa > d->max_len){ d->max_len = fa; }
}
// Enlarge bounding box slightly
d->bbox[0] -= DBL_EPSILON*d->bbox[0];
d->bbox[1] += DBL_EPSILON*d->bbox[1];
d->bbox[2] -= DBL_EPSILON*d->bbox[2];
d->bbox[3] += DBL_EPSILON*d->bbox[3];
// Copy data into final arrays
d->xy = (double*)malloc(sizeof(double)*4*d->n);
d->f = d->xy + 2*d->n;
for(i = 0; i < d->n; ++i){
d->xy[2*i+0] = temp[4*i+0];
d->xy[2*i+1] = temp[4*i+1];
d->f[2*i+0] = temp[4*i+2];
d->f[2*i+1] = temp[4*i+3];
}
free(temp);
error:
fclose(fp);
}
/*
void get_ticks(double a, double b, double *tick, int nticks){
int m,b,p;
if(a <= 0 && b >= 0){ // includes zero
double m = (-a > b) ? -a : b;
double t = round_to_nice(0.33*m, &m,&b,&p);
}else{
double d = b-a;
double avg = 0.5*(b+a);
if(d < 0.01*avg){
}else{
double t = round_to_nice(0.25*m, &m,&b,&p);
if(a >= 0){ // positive
d = b-a;
}else{ // negative
}
}
}
}
*/
int output_plot(data *plot){
FILE *f = stdout;
int i, j;
double norm;
double p[2], q[2];
const double bbox[4] = {
-3,3, // x range
-3,3 // y range
};
double scale[2] = {72, 72};
fprintf(f, "%f %f scale\n", scale[0], scale[1]);
fprintf(f, "%f setlinewidth\n", 2./scale[0]);
fprintf(f, "%f %f translate\n", 8.5*0.5*72/scale[0], 11*0.5*72/scale[1]);
fprintf(f,
"/arrow{\n"
"gsave\n"
"5 3 roll translate\n"
"3 1 roll exch atan rotate\n"
"dup scale\n"
"\n"
"newpath\n"
"1.00 0.00 moveto\n"
"0.62 0.19 lineto\n"
"0.62 0.07 lineto\n"
"0.00 0.07 lineto\n"
"0.00 -0.07 lineto\n"
"0.62 -0.07 lineto\n"
"0.62 -0.19 lineto\n"
"closepath stroke\n"
"\n"
"grestore\n"
"} bind def\n");
// find closest pair of points
double min_spacing = DBL_MAX;
for(i = 0; i < plot->n; ++i){
for(j = i+1; j < plot->n; ++j){
double d = pythag2(plot->xy[2*i+0]-plot->xy[2*j+0], plot->xy[2*i+1]-plot->xy[2*j+1]);
if(d < min_spacing){ min_spacing = d; }
}
}
norm = min_spacing / plot->max_len;
for(i = 0; i < plot->n; ++i){
double vec[2] = {
plot->f[2*i+0] * norm,
plot->f[2*i+1] * norm };
double base[2] = {
plot->xy[2*i+0] - 0.5*vec[0],
plot->xy[2*i+1] - 0.5*vec[1] };
map_bb_aff(plot->bbox, bbox, base);
map_bb_lin(plot->bbox, bbox, vec);
double len = pythag2(vec[0], vec[1]);
if(len < 100*DBL_EPSILON){ continue; }
fprintf(f, "%f %f %f %f %f arrow\n", base[0], base[1], vec[0], vec[1], len);
}
// Draw frame and axes
p[0] = plot->bbox[0];
p[1] = plot->bbox[2];
q[0] = plot->bbox[1];
q[1] = plot->bbox[3];
map_bb_aff(plot->bbox, bbox, p);
map_bb_aff(plot->bbox, bbox, q);
fprintf(f, "newpath %f %f moveto %f %f lineto %f %f lineto %f %f lineto closepath stroke\n",
p[0], p[1],
q[0], p[1],
q[0], q[1],
p[0], q[1]
);
/*
// Draw ticks
for(i = 0; i < 2; ++i){ // which dimension
double ticks[8];
get_ticks(plot->bbox[2*i+0], plot->bbox[2*i+1], ticks, 8);
}
*/
fprintf(f, "showpage\n");
return 0;
}