/*
******** ell_3m_svd_d
**
** singular value decomposition:
** mat = uu * diag(sval) * vv
**
** singular values are square roots of eigenvalues of mat * mat^T
** columns of uu are eigenvectors of mat * mat^T
** rows of vv are eigenvectors of mat^T * mat
**
** returns info about singular values according to ellCubeRoot enum
**
** HEY: I think this does the wrong thing when given a symmetric
** matrix with negative eigenvalues . . .
*/
int
ell_3m_svd_d(double uu[9], double sval[3], double vv[9],
const double mat[9], const int newton) {
double trn[9], msqr[9], eval[3], evec[9];
int roots;
ELL_3M_TRANSPOSE(trn, mat);
ELL_3M_MUL(msqr, mat, trn);
roots = ell_3m_eigensolve_d(eval, evec, msqr, newton);
sval[0] = sqrt(eval[0]);
sval[1] = sqrt(eval[1]);
sval[2] = sqrt(eval[2]);
ELL_3M_TRANSPOSE(uu, evec);
ELL_3M_MUL(msqr, trn, mat);
_ell_3m_evecs_d(vv, eval, roots, msqr);
return roots;
}
void
_gageVecAnswer(gageContext *ctx, gagePerVolume *pvl) {
char me[]="_gageVecAnswer";
double cmag, tmpMat[9], mgevec[9], mgeval[3];
double symm[9], asym[9], tran[9], eval[3], tmpVec[3], norm;
gage_t *vecAns, *normAns, *jacAns, *curlAns, *hesAns, *curlGradAns,
*helGradAns, *dirHelDirAns, *curlnormgradAns;
/* int asw; */
vecAns = pvl->directAnswer[gageVecVector];
normAns = pvl->directAnswer[gageVecNormalized];
jacAns = pvl->directAnswer[gageVecJacobian];
curlAns = pvl->directAnswer[gageVecCurl];
hesAns = pvl->directAnswer[gageVecHessian];
curlGradAns = pvl->directAnswer[gageVecCurlGradient];
curlnormgradAns = pvl->directAnswer[gageVecCurlNormGrad];
helGradAns = pvl->directAnswer[gageVecHelGradient];
dirHelDirAns = pvl->directAnswer[gageVecDirHelDeriv];
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecVector)) {
/* done if doV */
if (ctx->verbose) {
fprintf(stderr, "vec = ");
ell_3v_PRINT(stderr, vecAns);
}
}
/* done if doV
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecVector{0,1,2})) {
}
*/
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecLength)) {
pvl->directAnswer[gageVecLength][0] = AIR_CAST(gage_t, ELL_3V_LEN(vecAns));
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecNormalized)) {
if (pvl->directAnswer[gageVecLength][0]) {
ELL_3V_SCALE_TT(normAns, gage_t,
1.0/pvl->directAnswer[gageVecLength][0], vecAns);
} else {
ELL_3V_COPY(normAns, gageZeroNormal);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecJacobian)) {
/* done if doD1 */
/*
0:dv_x/dx 1:dv_x/dy 2:dv_x/dz
3:dv_y/dx 4:dv_y/dy 5:dv_y/dz
6:dv_z/dx 7:dv_z/dy 8:dv_z/dz
*/
if (ctx->verbose) {
fprintf(stderr, "%s: jac = \n", me);
ell_3m_PRINT(stderr, jacAns);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecDivergence)) {
pvl->directAnswer[gageVecDivergence][0] = jacAns[0] + jacAns[4] + jacAns[8];
if (ctx->verbose) {
fprintf(stderr, "%s: div = %g + %g + %g = %g\n", me,
jacAns[0], jacAns[4], jacAns[8],
pvl->directAnswer[gageVecDivergence][0]);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecCurl)) {
ELL_3V_SET(curlAns,
jacAns[7] - jacAns[5],
jacAns[2] - jacAns[6],
jacAns[3] - jacAns[1]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecCurlNorm)) {
pvl->directAnswer[gageVecCurlNorm][0] =
AIR_CAST(gage_t, ELL_3V_LEN(curlAns));
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecHelicity)) {
pvl->directAnswer[gageVecHelicity][0] =
ELL_3V_DOT(vecAns, curlAns);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecNormHelicity)) {
cmag = ELL_3V_LEN(curlAns);
pvl->directAnswer[gageVecNormHelicity][0] =
AIR_CAST(gage_t, cmag ? ELL_3V_DOT(normAns, curlAns)/cmag : 0);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecLambda2)) {
ELL_3M_TRANSPOSE(tran, jacAns);
/* symmetric part */
ELL_3M_SCALE_ADD2(symm, 0.5, jacAns, 0.5, tran);
/* antisymmetric part */
ELL_3M_SCALE_ADD2(asym, 0.5, jacAns, -0.5, tran);
/* square symmetric part */
ELL_3M_MUL(tmpMat, symm, symm);
ELL_3M_COPY(symm, tmpMat);
/* square antisymmetric part */
ELL_3M_MUL(tmpMat, asym, asym);
/* sum of both */
ELL_3M_ADD2(symm, symm, tmpMat);
/* get eigenvalues in sorted order */
/* asw = */ ell_3m_eigenvalues_d(eval, symm, AIR_TRUE);
pvl->directAnswer[gageVecLambda2][0] = AIR_CAST(gage_t, eval[1]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecImaginaryPart)) {
pvl->directAnswer[gageVecImaginaryPart][0] =
AIR_CAST(gage_t, gage_imaginary_part_eigenvalues(jacAns));
}
/* 2nd order vector derivative continued */
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecHessian)) {
/* done if doD2 */
/* the ordering is induced by the scalar hessian computation :
0:d2v_x/dxdx 1:d2v_x/dxdy 2:d2v_x/dxdz
3:d2v_x/dydx 4:d2v_x/dydy 5:d2v_x/dydz
6:d2v_x/dzdx 7:d2v_x/dzdy 8:d2v_x/dzdz
9:d2v_y/dxdx [...]
[...]
24:dv2_z/dzdx 25:d2v_z/dzdy 26:d2v_z/dzdz
*/
if (ctx->verbose) {
fprintf(stderr, "%s: hes = \n", me);
ell_3m_PRINT(stderr, hesAns); /* ?? */
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecDivGradient)) {
pvl->directAnswer[gageVecDivGradient][0] = hesAns[0] + hesAns[12] + hesAns[24];
pvl->directAnswer[gageVecDivGradient][1] = hesAns[1] + hesAns[13] + hesAns[25];
pvl->directAnswer[gageVecDivGradient][2] = hesAns[2] + hesAns[14] + hesAns[26];
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecCurlGradient)) {
pvl->directAnswer[gageVecCurlGradient][0] = hesAns[21]-hesAns[15];
pvl->directAnswer[gageVecCurlGradient][1] = hesAns[22]-hesAns[16];
pvl->directAnswer[gageVecCurlGradient][2] = hesAns[23]-hesAns[17];
pvl->directAnswer[gageVecCurlGradient][3] = hesAns[ 6]-hesAns[18];
pvl->directAnswer[gageVecCurlGradient][4] = hesAns[ 7]-hesAns[19];
pvl->directAnswer[gageVecCurlGradient][5] = hesAns[ 8]-hesAns[20];
pvl->directAnswer[gageVecCurlGradient][6] = hesAns[ 9]-hesAns[ 1];
pvl->directAnswer[gageVecCurlGradient][7] = hesAns[10]-hesAns[ 2];
pvl->directAnswer[gageVecCurlGradient][8] = hesAns[11]-hesAns[ 3];
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecCurlNormGrad)) {
norm = 1./ELL_3V_LEN(curlAns);
tmpVec[0] = hesAns[21] - hesAns[15];
tmpVec[1] = hesAns[ 6] - hesAns[18];
tmpVec[2] = hesAns[ 9] - hesAns[ 3];
pvl->directAnswer[gageVecCurlNormGrad][0]=
AIR_CAST(gage_t, norm*ELL_3V_DOT(tmpVec, curlAns));
tmpVec[0] = hesAns[22] - hesAns[16];
tmpVec[1] = hesAns[ 7] - hesAns[19];
tmpVec[2] = hesAns[10] - hesAns[ 4];
pvl->directAnswer[gageVecCurlNormGrad][1]=
AIR_CAST(gage_t, norm*ELL_3V_DOT(tmpVec, curlAns));
tmpVec[0] = hesAns[23] - hesAns[17];
tmpVec[1] = hesAns[ 8] - hesAns[20];
tmpVec[2] = hesAns[11] - hesAns[ 5];
pvl->directAnswer[gageVecCurlNormGrad][2]=
AIR_CAST(gage_t, norm*ELL_3V_DOT(tmpVec, curlAns));
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecNCurlNormGrad)) {
norm = 1./ELL_3V_LEN(curlnormgradAns);
ELL_3V_SCALE_TT(pvl->directAnswer[gageVecNCurlNormGrad], gage_t,
norm, pvl->directAnswer[gageVecCurlNormGrad]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecHelGradient)) {
pvl->directAnswer[gageVecHelGradient][0] =
jacAns[0]*curlAns[0]+
jacAns[3]*curlAns[1]+
jacAns[6]*curlAns[2]+
curlGradAns[0]*vecAns[0]+
curlGradAns[3]*vecAns[1]+
curlGradAns[6]*vecAns[2];
pvl->directAnswer[gageVecHelGradient][1] =
jacAns[1]*curlAns[0]+
jacAns[4]*curlAns[1]+
jacAns[7]*curlAns[2]+
curlGradAns[1]*vecAns[0]+
curlGradAns[4]*vecAns[1]+
curlGradAns[7]*vecAns[2];
pvl->directAnswer[gageVecHelGradient][0] =
jacAns[2]*curlAns[0]+
jacAns[5]*curlAns[1]+
jacAns[8]*curlAns[2]+
curlGradAns[2]*vecAns[0]+
curlGradAns[5]*vecAns[1]+
curlGradAns[8]*vecAns[2];
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecDirHelDeriv)) {
pvl->directAnswer[gageVecDirHelDeriv][0] =
ELL_3V_DOT(normAns, helGradAns);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecProjHelGradient)) {
pvl->directAnswer[gageVecDirHelDeriv][0] =
helGradAns[0]-dirHelDirAns[0]*normAns[0];
pvl->directAnswer[gageVecDirHelDeriv][1] =
helGradAns[1]-dirHelDirAns[0]*normAns[1];
pvl->directAnswer[gageVecDirHelDeriv][2] =
helGradAns[2]-dirHelDirAns[0]*normAns[2];
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecGradient0)) {
ELL_3V_SET(pvl->directAnswer[gageVecGradient0],
jacAns[0],
jacAns[1],
jacAns[2]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecGradient1)) {
ELL_3V_SET(pvl->directAnswer[gageVecGradient1],
jacAns[3],
jacAns[4],
jacAns[5]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecGradient2)) {
ELL_3V_SET(pvl->directAnswer[gageVecGradient2],
jacAns[6],
jacAns[7],
jacAns[8]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecMultiGrad)) {
ELL_3M_IDENTITY_SET(pvl->directAnswer[gageVecMultiGrad]);
ELL_3MV_OUTER_ADD(pvl->directAnswer[gageVecMultiGrad],
pvl->directAnswer[gageVecGradient0],
pvl->directAnswer[gageVecGradient0]);
ELL_3MV_OUTER_ADD(pvl->directAnswer[gageVecMultiGrad],
pvl->directAnswer[gageVecGradient1],
pvl->directAnswer[gageVecGradient1]);
ELL_3MV_OUTER_ADD(pvl->directAnswer[gageVecMultiGrad],
pvl->directAnswer[gageVecGradient2],
pvl->directAnswer[gageVecGradient2]);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecMGFrob)) {
pvl->directAnswer[gageVecMGFrob][0]
= AIR_CAST(gage_t, ELL_3M_FROB(pvl->directAnswer[gageVecMultiGrad]));
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecMGEval)) {
ELL_3M_COPY(tmpMat, pvl->directAnswer[gageVecMultiGrad]);
/* HEY: look at the return value for root multiplicity? */
ell_3m_eigensolve_d(mgeval, mgevec, tmpMat, AIR_TRUE);
ELL_3V_COPY_TT(pvl->directAnswer[gageVecMGEval], gage_t, mgeval);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageVecMGEvec)) {
ELL_3M_COPY_TT(pvl->directAnswer[gageVecMGEvec], gage_t, mgevec);
}
return;
}
/* Calculates 2 new centroids (and a new segmentation) from distances
between Q-balls and centroids, returns true if segmentation changed
*/
int
_tenCalccent2(const int gradcount, const double qpoints[],
const double dists[], double centroid[6], unsigned int seg[]) {
#if 0
/* HEY: Attempt to implement better line-adding by adding
outerproducts of points and estimating major eigenvector
afterwards */
int i,changed=AIR_FALSE;
double sum0[9],sum1[9],mat[9], eval[3],evec[9];
ELL_3M_ZERO_SET( sum0 );
ELL_3M_ZERO_SET( sum1 );
for( i = 0; i < gradcount; i++ ) {
if( dists[i] < dists[gradcount+i] ) {
ELL_3MV_OUTER( mat, qpoints +3*i, qpoints +3*i );
ELL_3M_ADD2( sum0, sum0, mat );
changed = changed || (seg[i] != 0);
seg[i] = 0;
} else {
ELL_3MV_OUTER( mat, qpoints +3*i +gradcount, qpoints +3*i +gradcount );
ELL_3M_ADD2( sum1, sum1, mat );
changed = changed || (seg[i] != 1);
seg[i] = 1;
}
}
ell_3m_eigensolve_d( eval, evec, sum0, 0 );
ELL_3V_COPY( centroid, evec + 3*ELL_MAX3_IDX( eval[0], eval[1], eval[2] ) );
/* ELL_3V_SCALE( centroid, ELL_3V_LEN( centroid ), centroid ); */
ell_3m_eigensolve_d( eval, evec, sum1, 0 );
ELL_3V_COPY( centroid +3, evec + 3*ELL_MAX3_IDX( eval[0], eval[1], eval[2] ) );
/* ELL_3V_SCALE( centroid +3, ELL_3V_LEN( centroid ), centroid +3); Normalize */
return changed;
#endif
int i, sign, seg0count=0, seg1count=0, changed=AIR_FALSE;
double oldcentroid[6], diff[3], sum[3];
memcpy( oldcentroid, centroid, 6 * sizeof( double ));
for( i = 0; i < gradcount; i++ ) {
if( dists[ 0*gradcount +i] < dists[1*gradcount +i] ) {
/* Try to resolve sign so that centroid do not end up as all 0 */
/* Choose signs so that the point lies "on the same side" as */
/* the previous centroid. */
diff[0] = oldcentroid[0] - qpoints[3*i +0];
diff[1] = oldcentroid[1] - qpoints[3*i +1];
diff[2] = oldcentroid[2] - qpoints[3*i +2];
sum[0] = oldcentroid[0] + qpoints[3*i +0];
sum[1] = oldcentroid[1] + qpoints[3*i +1];
sum[2] = oldcentroid[2] + qpoints[3*i +2];
sign = (diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]) <
(sum[0]*sum[0] + sum[1]*sum[1] + sum[2]*sum[2]) ? -1 : +1;
changed = changed || (seg[i] != 0);
seg[i] = 0;
centroid[0] += sign * qpoints[3*i +0];
centroid[1] += sign * qpoints[3*i +1];
centroid[2] += sign * qpoints[3*i +2];
seg0count++;
} else {
diff[0] = oldcentroid[3+0] - qpoints[3*i +0];
diff[1] = oldcentroid[3+1] - qpoints[3*i +1];
diff[2] = oldcentroid[3+2] - qpoints[3*i +2];
sum[0] = oldcentroid[3+0] + qpoints[3*i +0];
sum[1] = oldcentroid[3+1] + qpoints[3*i +1];
sum[2] = oldcentroid[3+2] + qpoints[3*i +2];
sign = (diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]) <
(sum[0]*sum[0] + sum[1]*sum[1] + sum[2]*sum[2]) ? -1 : +1;
changed = changed || (seg[i] != 1);
seg[i] = 1;
centroid[3+0] += sign * qpoints[3*i +0];
centroid[3+1] += sign * qpoints[3*i +1];
centroid[3+2] += sign * qpoints[3*i +2];
seg1count++;
}
}
centroid[0] /= seg0count;
centroid[1] /= seg0count;
centroid[2] /= seg0count;
centroid[3+0] /= seg1count;
centroid[3+1] /= seg1count;
centroid[3+2] /= seg1count;
/* printf("cent = %f %f %f %f %f %f\n", centroid[0],centroid[1],centroid[2],centroid[3],centroid[4],centroid[5] ); */
/*
Should give error if any segment contains less than 6 elements,
i.e. if( seg0count < 6 || seg1count < 6 ), since that would
imply that a tensor cannot be computed for that segment.
*/
return changed;
}
void
_gageSclAnswer (gageContext *ctx, gagePerVolume *pvl) {
char me[]="_gageSclAnswer";
double gmag=0, *hess, *norm, *gvec, *gten, *k1, *k2, curv=0,
sHess[9]={0,0,0,0,0,0,0,0,0};
double tmpMat[9], tmpVec[3], hevec[9], heval[3];
double len, gp1[3], gp2[3], *nPerp, ncTen[9], nProj[9]={0,0,0,0,0,0,0,0,0};
double alpha = 0.5;
double beta = 0.5;
double gamma = 5;
double cc = 1e-6;
#define FD_MEDIAN_MAX 16
int fd, nidx, xi, yi, zi;
double *fw, iv3wght[2*FD_MEDIAN_MAX*FD_MEDIAN_MAX*FD_MEDIAN_MAX],
wghtSum, wght;
/* convenience pointers for work below */
hess = pvl->directAnswer[gageSclHessian];
gvec = pvl->directAnswer[gageSclGradVec];
norm = pvl->directAnswer[gageSclNormal];
nPerp = pvl->directAnswer[gageSclNPerp];
gten = pvl->directAnswer[gageSclGeomTens];
k1 = pvl->directAnswer[gageSclK1];
k2 = pvl->directAnswer[gageSclK2];
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclValue)) {
/* done if doV */
if (ctx->verbose) {
fprintf(stderr, "%s: val = % 15.7f\n", me,
(double)(pvl->directAnswer[gageSclValue][0]));
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGradVec)) {
/* done if doD1 */
if (ctx->verbose) {
fprintf(stderr, "%s: gvec = ", me);
ell_3v_print_d(stderr, gvec);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGradMag)) {
/* this is the true value of gradient magnitude */
gmag = pvl->directAnswer[gageSclGradMag][0] = sqrt(ELL_3V_DOT(gvec, gvec));
}
/* NB: it would seem that gageParmGradMagMin is completely ignored ... */
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclNormal)) {
if (gmag) {
ELL_3V_SCALE(norm, 1/gmag, gvec);
/* polishing ...
len = sqrt(ELL_3V_DOT(norm, norm));
ELL_3V_SCALE(norm, 1/len, norm);
*/
} else {
ELL_3V_COPY(norm, gageZeroNormal);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclNPerp)) {
/* nPerp = I - outer(norm, norm) */
/* NB: this sets both nPerp and nProj */
ELL_3MV_OUTER(nProj, norm, norm);
ELL_3M_SCALE(nPerp, -1, nProj);
nPerp[0] += 1;
nPerp[4] += 1;
nPerp[8] += 1;
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessian)) {
/* done if doD2 */
if (ctx->verbose) {
fprintf(stderr, "%s: hess = \n", me);
ell_3m_print_d(stderr, hess);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclLaplacian)) {
pvl->directAnswer[gageSclLaplacian][0] = hess[0] + hess[4] + hess[8];
if (ctx->verbose) {
fprintf(stderr, "%s: lapl = %g + %g + %g = %g\n", me,
hess[0], hess[4], hess[8],
pvl->directAnswer[gageSclLaplacian][0]);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessFrob)) {
pvl->directAnswer[gageSclHessFrob][0] = ELL_3M_FROB(hess);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessEval)) {
/* HEY: look at the return value for root multiplicity? */
ell_3m_eigensolve_d(heval, hevec, hess, AIR_TRUE);
ELL_3V_COPY(pvl->directAnswer[gageSclHessEval], heval);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessEvec)) {
ELL_3M_COPY(pvl->directAnswer[gageSclHessEvec], hevec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessRidgeness)) {
double A, B, S;
if (heval[1] >0 || heval[2]>0) {
pvl->directAnswer[gageSclHessRidgeness][0] = 0;
}
else if (AIR_ABS(heval[1])<1e-10 || AIR_ABS(heval[2])<1e-10) {
pvl->directAnswer[gageSclHessRidgeness][0] = 0;
}
else {
double *ans;
A = AIR_ABS(heval[1])/AIR_ABS(heval[2]);
B = AIR_ABS(heval[0])/sqrt(AIR_ABS(heval[1]*heval[2]));
S = sqrt(heval[0]*heval[0] + heval[1]*heval[1] + heval[2]*heval[2]);
ans = pvl->directAnswer[gageSclHessRidgeness];
ans[0] = (1-exp(-A*A/(2*alpha*alpha))) *
exp(-B*B/(2*beta*beta)) *
(1-exp(-S*S/(2*gamma*gamma))) *
exp(-2*cc*cc/(AIR_ABS(heval[1])*heval[2]*heval[2]));
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessValleyness)) {
double A, B, S;
if (heval[0] <0 || heval[1]<0) {
pvl->directAnswer[gageSclHessValleyness][0] = 0;
}
else if (AIR_ABS(heval[0])<1e-10 || AIR_ABS(heval[1])<1e-10) {
pvl->directAnswer[gageSclHessValleyness][0] = 0;
}
else {
double *ans;
A = AIR_ABS(heval[1])/AIR_ABS(heval[0]);
B = AIR_ABS(heval[2])/sqrt(AIR_ABS(heval[1]*heval[0]));
S = sqrt(heval[0]*heval[0] + heval[1]*heval[1] + heval[2]*heval[2]);
ans = pvl->directAnswer[gageSclHessValleyness];
ans[0] = (1-exp(-A*A/(2*alpha*alpha))) *
exp(-B*B/(2*beta*beta)) *
(1-exp(-S*S/(2*gamma*gamma))) *
exp(-2*cc*cc/(AIR_ABS(heval[1])*heval[0]*heval[0]));
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessMode)) {
pvl->directAnswer[gageSclHessMode][0] = airMode3_d(heval);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageScl2ndDD)) {
ELL_3MV_MUL(tmpVec, hess, norm);
pvl->directAnswer[gageScl2ndDD][0] = ELL_3V_DOT(norm, tmpVec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGeomTens)) {
if (gmag > ctx->parm.gradMagCurvMin) {
/* parm.curvNormalSide applied here to determine the sense of the
normal when doing all curvature calculations */
ELL_3M_SCALE(sHess, -(ctx->parm.curvNormalSide)/gmag, hess);
/* gten = nPerp * sHess * nPerp */
ELL_3M_MUL(tmpMat, sHess, nPerp);
ELL_3M_MUL(gten, nPerp, tmpMat);
if (ctx->verbose) {
fprintf(stderr, "%s: gten: \n", me);
ell_3m_print_d(stderr, gten);
ELL_3MV_MUL(tmpVec, gten, norm);
len = ELL_3V_LEN(tmpVec);
fprintf(stderr, "%s: should be small: %30.15f\n", me, (double)len);
ell_3v_perp_d(gp1, norm);
ELL_3MV_MUL(tmpVec, gten, gp1);
len = ELL_3V_LEN(tmpVec);
fprintf(stderr, "%s: should be bigger: %30.15f\n", me, (double)len);
ELL_3V_CROSS(gp2, gp1, norm);
ELL_3MV_MUL(tmpVec, gten, gp2);
len = ELL_3V_LEN(tmpVec);
fprintf(stderr, "%s: should (also) be bigger: %30.15f\n",
me, (double)len);
}
} else {
ELL_3M_ZERO_SET(gten);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclTotalCurv)) {
curv = pvl->directAnswer[gageSclTotalCurv][0] = ELL_3M_FROB(gten);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclShapeTrace)) {
pvl->directAnswer[gageSclShapeTrace][0] = (curv
? ELL_3M_TRACE(gten)/curv
: 0);
}
if ( (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclK1)) ||
(GAGE_QUERY_ITEM_TEST(pvl->query, gageSclK2)) ){
double T, N, D;
T = ELL_3M_TRACE(gten);
N = curv;
D = 2*N*N - T*T;
/*
if (D < -0.0000001) {
fprintf(stderr, "%s: %g %g\n", me, T, N);
fprintf(stderr, "%s: !!! D curv determinant % 22.10f < 0.0\n", me, D);
fprintf(stderr, "%s: gten: \n", me);
ell_3m_print_d(stderr, gten);
}
*/
D = AIR_MAX(D, 0);
D = sqrt(D);
k1[0] = 0.5*(T + D);
k2[0] = 0.5*(T - D);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclMeanCurv)) {
pvl->directAnswer[gageSclMeanCurv][0] = (*k1 + *k2)/2;
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGaussCurv)) {
pvl->directAnswer[gageSclGaussCurv][0] = (*k1)*(*k2);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclShapeIndex)) {
pvl->directAnswer[gageSclShapeIndex][0] =
-(2/AIR_PI)*atan2(*k1 + *k2, *k1 - *k2);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclCurvDir1)) {
/* HEY: this only works when K1, K2, 0 are all well mutually distinct,
since these are the eigenvalues of the geometry tensor, and this
code assumes that the eigenspaces are all one-dimensional */
ELL_3M_COPY(tmpMat, gten);
ELL_3M_DIAG_SET(tmpMat, gten[0] - *k1, gten[4]- *k1, gten[8] - *k1);
ell_3m_1d_nullspace_d(tmpVec, tmpMat);
ELL_3V_COPY(pvl->directAnswer[gageSclCurvDir1], tmpVec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclCurvDir2)) {
/* HEY: this only works when K1, K2, 0 are all well mutually distinct,
since these are the eigenvalues of the geometry tensor, and this
code assumes that the eigenspaces are all one-dimensional */
ELL_3M_COPY(tmpMat, gten);
ELL_3M_DIAG_SET(tmpMat, gten[0] - *k2, gten[4] - *k2, gten[8] - *k2);
ell_3m_1d_nullspace_d(tmpVec, tmpMat);
ELL_3V_COPY(pvl->directAnswer[gageSclCurvDir2], tmpVec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclFlowlineCurv)) {
if (gmag >= ctx->parm.gradMagCurvMin) {
/* because of the gageSclGeomTens prerequisite, sHess, nPerp, and
nProj are all already set */
/* ncTen = nPerp * sHess * nProj */
ELL_3M_MUL(tmpMat, sHess, nProj);
ELL_3M_MUL(ncTen, nPerp, tmpMat);
} else {
ELL_3M_ZERO_SET(ncTen);
}
/* there used to be a wrong extra sqrt() here */
pvl->directAnswer[gageSclFlowlineCurv][0] = ELL_3M_FROB(ncTen);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclMedian)) {
/* this item is currently a complete oddball in that it does not
benefit from anything done in the "filter" stage, which is in
fact a waste of time if the query consists only of this item */
fd = 2*ctx->radius;
if (fd > FD_MEDIAN_MAX) {
fprintf(stderr, "%s: PANIC: current filter diameter = %d "
"> FD_MEDIAN_MAX = %d\n", me, fd, FD_MEDIAN_MAX);
exit(1);
}
fw = ctx->fw + fd*3*gageKernel00;
/* HEY: this needs some optimization help */
wghtSum = 0;
nidx = 0;
for (xi=0; xi<fd; xi++) {
for (yi=0; yi<fd; yi++) {
for (zi=0; zi<fd; zi++) {
iv3wght[0 + 2*nidx] = pvl->iv3[nidx];
iv3wght[1 + 2*nidx] = fw[xi + 0*fd]*fw[yi + 1*fd]*fw[zi + 2*fd];
wghtSum += iv3wght[1 + 2*nidx];
nidx++;
}
}
}
qsort(iv3wght, fd*fd*fd, 2*sizeof(double), nrrdValCompare[nrrdTypeDouble]);
wght = 0;
for (nidx=0; nidx<fd*fd*fd; nidx++) {
wght += iv3wght[1 + 2*nidx];
if (wght > wghtSum/2) {
break;
}
}
pvl->directAnswer[gageSclMedian][0] = iv3wght[0 + 2*nidx];
}
return;
}
