/*
eigen_verify
Verify properties of the eigen vectors.
The eigenbasis should be ortonormal: R'*R - I == 0
The basis should be decomposed such that: MR - RD == 0
returns true if tests fail.
*/
int eigen_verify(Matrix M, Matrix lambda, Matrix R) {
Matrix RtR = transposeMultiplyMatrixL(R, R);
Matrix identity = makeIdentityMatrix(R->col_dim);
Matrix MR = multiplyMatrix(M, R);
Matrix D = makeIdentityMatrix(lambda->row_dim);
Matrix RD;
Matrix test;
int i, j;
int failed = 0;
const double tol = 1.0e-7;
for (i = 0; i < lambda->row_dim; i++) {
ME(D, i, i) = ME(lambda, i, 0);
}
RD = multiplyMatrix(R, D);
freeMatrix(D);
DEBUG(2, "Checking orthogonality of eigenvectors");
test = subtractMatrix(RtR, identity);
freeMatrix(RtR);
freeMatrix(identity);
for (i = 0; i < test->row_dim; i++) {
for (j = 0; j < test->col_dim; j++) {
if (!EQUAL_ZERO(ME(test, i, j), tol)) {
failed = 1;
MESSAGE("Eigenvectors are not orthogonal to within tolerance.");
DEBUG_DOUBLE(1, "Matrix Element", ME(test, i, j));
DEBUG_DOUBLE(1, "Tolerance", tol);
exit(1);
}
}
}
freeMatrix(test);
DEBUG(2, "Checking reconstruction property of eigensystem");
test = subtractMatrix(MR, RD);
freeMatrix(MR);
freeMatrix(RD);
for (i = 0; i < test->row_dim; i++) {
for (j = 0; j < test->col_dim; j++) {
if (!EQUAL_ZERO(ME(test, i, j), tol)) {
failed = 1;
MESSAGE("Covariance matrix is not reconstructable to within tolerance.");
DEBUG_DOUBLE(1, "Matrix Element", ME(test, i, j));
DEBUG_DOUBLE(1, "Tolerance", tol);
exit(1);
}
}
}
freeMatrix(test);
return failed;
}
/**
Verify properties of the eigen basis used for pca.
The eigenbasis should be ortonormal: U'*U - I == 0
The basis should be decomposed such that: X == U*D*V'
returns true if tests fail.
*/
int basis_verify(Matrix X, Matrix U) {
Matrix UtX = transposeMultiplyMatrixL(U, X);
Matrix UUtX = multiplyMatrix(U, UtX);
Matrix UtU = transposeMultiplyMatrixL(U, U);
Matrix identity = makeIdentityMatrix(U->col_dim);
Matrix test;
int i, j;
int failed = 0;
const double tol = 1.0e-7;
freeMatrix(UtX);
DEBUG(2, "Checking orthogonality of eigenbasis");
test = subtractMatrix(UtU, identity);
freeMatrix(UtU);
freeMatrix(identity);
for (i = 0; i < test->row_dim; i++) {
for (j = 0; j < test->col_dim; j++) {
if (!EQUAL_ZERO(ME(test, i, j), tol)) {
failed = 1;
MESSAGE("Eigenbasis is not orthogonal to within tolerance.");
DEBUG_DOUBLE(1, "Matrix Element", ME(test, i, j));
DEBUG_DOUBLE(1, "Tolerance", tol);
exit(1);
}
}
}
freeMatrix(test);
DEBUG(2, "Checking reconstruction property of the eigen decomposition");
test = subtractMatrix(X, UUtX);
freeMatrix(UUtX);
for (i = 0; i < test->row_dim; i++) {
for (j = 0; j < test->col_dim; j++) {
if (!EQUAL_ZERO(ME(test, i, j), tol)) {
failed = 1;
MESSAGE("Data matrix is not reconstructable to within tolerance.");
DEBUG_DOUBLE(1, "Matrix Element", ME(test, i, j));
DEBUG_DOUBLE(1, "Tolarence", tol);
exit(1);
}
}
}
freeMatrix(test);
return failed;
}
float CTween::Back_easeInOut(float t, float b, float c, float d, float s/* = 0.0f*/) {
if (EQUAL_ZERO(s))
s = 1.70158f;
if ((t /= d / 2) < 1)
return c / 2 * (t * t * (((s *= (1.525f)) + 1) * t - s)) + b;
return c / 2 * ((t -= 2) * t * (((s *= (1.525f)) + 1) * t + s) + 2) + b;
}
void fisherVerify(Matrix fisherBasis, Matrix fisherValues, Matrix Sw, Matrix Sb) {
Matrix SbW = multiplyMatrix(Sb, fisherBasis);
Matrix SwW = multiplyMatrix(Sw, fisherBasis);
Matrix D = makeIdentityMatrix(fisherBasis->row_dim);
Matrix DSwW;
Matrix zeroMat;
int i, j;
MESSAGE("Verifying Fisher Basis.");
for (i = 0; i < D->row_dim; i++) {
ME(D, i, i) = ME(fisherValues, i, 0);
}
DSwW = multiplyMatrix(D, SwW);
zeroMat = subtractMatrix(SbW, DSwW);
for (i = 0; i < zeroMat->row_dim; i++) {
for (j = 0; j < zeroMat->col_dim; j++) {
if (!EQUAL_ZERO(ME(zeroMat, i, j), 0.000001)) {
DEBUG( -1, "Fisher validation failed.");
printf("Element: (%d,%d) value = %f", i, j, ME(zeroMat, i, j));
exit(1);
}
}
}
}
float CTween::Back_easeOut(float t, float b, float c, float d, float s/* = 0.0f*/) {
if (EQUAL_ZERO(s))
s = 1.70158f;
return c * ((t = t / d - 1) * t * ((s + 1) * t + s) + 1) + b;
}
// Back
float CTween::Back_easeIn(float t, float b, float c, float d, float s/* = 0.0f*/) {
if (EQUAL_ZERO(s))
s = 1.70158f;
return c * (t /= d) * t * ((s + 1) * t - s) + b;
}
