kr::Mat3<Scalar> skewSymmetric2(const kr::Vec3<Scalar>& w) {
kr::Mat3<Scalar> W2;
W2(0, 0) = -(w[2] * w[2] + w[1] * w[1]);
W2(1, 1) = -(w[2] * w[2] + w[0] * w[0]);
W2(2, 2) = -(w[1] * w[1] + w[0] * w[0]);
W2(1, 0) = W2(0, 1) = w[0] * w[1];
W2(2, 0) = W2(0, 2) = w[0] * w[2];
W2(1, 2) = W2(2, 1) = w[1] * w[2];
return W2;
}
Array3d Analysis::getParticleFluxKy(int sp)
{
Array3d G(RFields, RkyLD, RsLD); G = 0.;
Array3z V2(RxLD, RkyLD, RzLD); V2 = 0.;
Array3z W2(RxLD, RkyLD, RzLD); W2 = 0.;
for(int s = NsLlD; s <= NsLuD; s++) {
const double d6Z = M_PI * plasma->species(s).n0 * plasma->species(s).T0 * plasma->B0 * dv * dm * scaleXYZ;
for(int m=NmLlD; m<= NmLuD;m++ ) { for(int z=NzLlD; z<= NzLuD;z++){
// multiply in real-space
for(int x=NxLlD; x <= NxLuD ; x++) { for(int y_k=NkyLlD; y_k<= NkyLuD;y_k++) {
const cmplxd ky=cmplxd(0.,-fft->ky(y_k));
V2(x,y_k,z) = ky * fields->phi(x,y_k,z,m,s);
// integrate over velocity space
W2(x,y_k,z) = sum(vlasov->f(x, y_k, z, RvLD, m, s)) * d6Z;
}}
// V2(RxLD, RkyLD, RzLD) =
fft->multiply(V2, W2, A_xyz);
// sum over x and z
for(int x=NxLlD; x <= NxLuD ; x++) { G(Field::phi, RkyLD, s) += abs(A_xyz(x, RkyLD,z)) ; }
} }
}
return parallel->collect(G);
};
// note the hear flux rate have to be calculted after getkinetic energy
// this should go hand-in-hand with the temperature calculation
Array4z Analysis::getHeatFlux(int sp)
{
A4_z = 0.;
Array3z V2(RxLD, RkyLD, RzLD);
Array3z W2(RxLD, RkyLD, RzLD);
//for(int s = ((sp == TOTAL) ? NsLlD : sp); s <= NsLuD && ((sp != TOTAL) ? s == sp : true) ; s++) {
// for(int s = ((sp == TOTAL) ? NsLlD : sp); (s <= ((sp == TOTAL) ? NsLuD : sp)) && ( (sp >= NsLlD) && (sp <= NsLuD)) ; s++) {
for(int s = NsLlD; s <= NsLuD; s++) {
const double d6Z = M_PI * plasma->species(s).n0 * plasma->species(s).T0 * plasma->B0 * dv * dm * scaleXYZ;
for(int m=NmLlD; m<= NmLuD;m++ ) {
V2 = 0.; W2 = 0.;
// multiply in real-space
for(int z=NzLlD; z<= NzLuD;z++){ for(int x=NxLlD; x <= NxLuD ; x++) { for(int y_k=NkyLlD; y_k<= NkyLuD;y_k++) {
const cmplxd ky=cmplxd(0.,-fft->ky(y_k));
V2(x,y_k,z) = ky * fields->phi(x,y_k,z,m,s);
// integrate over velocity space
for(int v=NvLlD; v<= NvLuD;v++) W2(x,y_k,z) += (pow2(V(v)) + M(m) * plasma->B0) * vlasov->f(x, y_k, z, v, m, s) * d6Z;
}}}
A4_z(RxLD, RkyLD, RzLD,s) = fft->multiply(V2, W2, A_xyz);
} }
return parallel->collect(A4_z, OP_SUM, DIR_VM);
};
// ------------------
TEST(Array, CrossConstruct2) {
array<long, 2> A(2, 3);
for (int i = 0; i < 2; ++i)
for (int j = 0; j < 3; ++j) A(i, j) = 10 * i + j;
std::vector<array<long, 2>> V(3, A);
std::vector<array_view<long, 2>> W;
for (auto& x : V) W.push_back(x);
std::vector<array_view<long, 2>> W2(W);
for (int i = 1; i < 3; ++i) V[i] *= i;
for (int i = 1; i < 3; ++i) EXPECT_ARRAY_NEAR(W2[i], i * A);
}
virtual void paintGL()
{
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
int xOffset = -70;
int yOffset = -50;
int zoom = -200;
glTranslatef(xOffset, yOffset, zoom);
glColor3f(0.0f, 0.0f, 0.0f);
glLineWidth(5.0);
float scale = 1.0;
if(showFilters)
{
Eigen::MatrixXd W1 = sae.getInputWeights();
Eigen::MatrixXd W2 = sae.getOutputWeights();
double mi = sae.getInputWeights().minCoeff();
double ma = sae.getInputWeights().maxCoeff();
double range = ma - mi;
for(int row = 0, filter = 0; row < neuronRows; row++)
{
for(int col = 0; col < neuronCols; col++, filter++)
{
glBegin(GL_QUADS);
for(int yIdx = 0; yIdx < 28; yIdx++)
{
for(int xIdx = 0; xIdx < 28; xIdx++)
{
int h = (filter + offset) / 2;
bool in = (filter + offset) % 2 == 0;
int idx = yIdx * 28 + xIdx;
float c = ((in ? W1(h, idx) : W2(idx, h)) - mi) / range;
float x = xIdx * scale + col * 29.0f * scale - 30.0f;
float y = (28.0f - yIdx) * scale - row * scale * 29.0f + 90.0f;
glColor3f(c, c, c);
glVertex2f(x, y);
glVertex2f(x + scale, y);
glVertex2f(x + scale, y + scale);
glVertex2f(x, y + scale);
}
}
glEnd();
}
}
}
else
{
for(int row = 0; row < neuronRows; row++)
{
for(int col = 0; col < neuronCols; col++)
{
Eigen::VectorXd out = sae.reconstruct(dataSet.getInstance(offset + row*neuronCols+col));
glBegin(GL_QUADS);
for(int yIdx = 0; yIdx < 28; yIdx++)
{
for(int xIdx = 0; xIdx < 28; xIdx++)
{
int idx = yIdx * 28 + xIdx;
float c = out(idx);
float x = xIdx * scale + col * 29.0f * scale - 30.0f;
float y = (28.0f - yIdx) * scale - row * scale * 29.0f + 90.0f;
glColor3f(c, c, c);
glVertex2f(x, y);
glVertex2f(x + scale, y);
glVertex2f(x + scale, y + scale);
glVertex2f(x, y + scale);
}
}
glEnd();
}
}
}
glColor3f(0.0f, 0.0f, 0.0f);
renderText(10, 35, "MNIST data set", QFont("Helvetica", 20));
glFlush();
}
void rotation(double *vo, double *vt, int n, symatrix &R)
{ int i,j,k;
symatrix A(4),AT(4),C(4),W(3),W2(3),RS(3);
double **B,**U,eval[5],gamma;
// char s[100];
B = dmatrix(1,4,1,4);
U = dmatrix(1,4,1,4);
for (i = 1; i <= 4; i++)
for (j = 1; j <= 4; j++)
B[i][j] = 0.0;
for (i = 0; i < 4; i++) A.el(i,i) = 0.0;
for (k = 0; k < n; k++)
{
A.el(0,1) = vo[3*k+2] + vt[3*k+2];
A.el(0,2) = -vo[3*k+1] - vt[3*k+1];
A.el(1,2) = vo[3*k] + vt[3*k];
for (i = 0; i < 3; i++) A.el(i,3) = vo[3*k+i] - vt[3*k+i];
for (i = 1; i < 4; i++)
for (j = 0; j < i; j++)
A.el(i,j) = -A.el(j,i);
AT = A.transpose();
C = A * AT;
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
{ B[i+1][j+1] += C.el(i,j);
}
}
djacobi(B,4,eval,U,&i);
deigsrt(eval,U,4);
R.identity();
RS.identity();
gamma = 2 * acos(U[4][4]);
for (i = 0; i < 3; i++) W.el(i,i) = 0.0;
W.el(0,1) = U[3][4] / sin(gamma/2);
W.el(0,2) = -U[2][4] / sin(gamma/2);
W.el(1,2) = U[1][4] / sin(gamma/2);
for (i = 1; i < 3; i++)
for (j = 0; j < i; j++)
W.el(i,j) = - W.el(j,i);
W2 = W * W;
for (i = 0; i < 3; i++)
{ W.multiply_col(i,sin(gamma));
W2.multiply_col(i,1-cos(gamma));
}
RS += (W + W2);
RS = RS.transpose();
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
R.el(i,j) = RS.el(i,j);
free_dmatrix(B,1,4,1,4);
free_dmatrix(U,1,4,1,4);
}
