// pivot on element _r, _c
void MATRIX(_pivot)(T * _X, unsigned int _XR, unsigned int _XC, unsigned int _r, unsigned int _c)
{
T v = matrix_access(_X,_XR,_XC,_r,_c);
if (v==0) {
fprintf(stderr, "warning: matrix_pivot(), pivoting on zero\n");
return;
}
unsigned int r,c;
// pivot using back-substitution
T g; // multiplier
for (r=0; r<_XR; r++) {
// skip over pivot row
if (r == _r)
continue;
// compute multiplier
g = matrix_access(_X,_XR,_XC,r,_c) / v;
// back-substitution
for (c=0; c<_XC; c++) {
matrix_access(_X,_XR,_XC,r,c) = g*matrix_access(_X,_XR,_XC,_r,c) -
matrix_access(_X,_XR,_XC, r,c);
}
}
}
void MATRIX(_swaprows)(T * _X, unsigned int _XR, unsigned int _XC, unsigned int _r1, unsigned int _r2)
{
if (_r1 == _r2)
return;
unsigned int c;
T v_tmp;
for (c=0; c<_XC; c++) {
v_tmp = matrix_access(_X,_XR,_XC,_r1,c);
matrix_access(_X,_XR,_XC,_r1,c) = matrix_access(_X,_XR,_XC,_r2,c);
matrix_access(_X,_XR,_XC,_r2,c) = v_tmp;
}
}
void MATRIX(_inv)(T * _X, unsigned int _XR, unsigned int _XC)
{
// ensure lengths are valid
if (_XR != _XC ) {
fprintf(stderr, "error: matrix_inv(), invalid dimensions\n");
exit(1);
}
// X:
// x11 x12 ... x1n
// x21 x22 ... x2n
// ...
// xn1 xn2 ... xnn
// allocate temporary memory
T x[2*_XR*_XC];
unsigned int xr = _XR;
unsigned int xc = _XC*2;
// x:
// x11 x12 ... x1n 1 0 ... 0
// x21 x22 ... x2n 0 1 ... 0
// ...
// xn1 xn2 ... xnn 0 0 ... 1
unsigned int r,c;
for (r=0; r<_XR; r++) {
// copy matrix elements
for (c=0; c<_XC; c++)
matrix_access(x,xr,xc,r,c) = matrix_access(_X,_XR,_XC,r,c);
// append identity matrix
for (c=0; c<_XC; c++)
matrix_access(x,xr,xc,r,_XC+c) = (r==c) ? 1 : 0;
}
// perform Gauss-Jordan elimination on x
// x:
// 1 0 ... 0 y11 y12 ... y1n
// 0 1 ... 0 y21 y22 ... y2n
// ...
// 0 0 ... 1 yn1 yn2 ... ynn
MATRIX(_gjelim)(x,xr,xc);
// copy result from right half of x
for (r=0; r<_XR; r++) {
for (c=0; c<_XC; c++)
matrix_access(_X,_XR,_XC,r,c) = matrix_access(x,xr,xc,r,_XC+c);
}
}
int main()
{
matrix_construction();
matrix_access();
test_cblas_dgemm();
test_basic_alloc();
test_asum();
test_axpy();
test_copy();
test_dot();
test_sdot();
test_dotc();
test_dotu();
test_nrm2();
test_rot();
test_rotg();
test_scal();
test_swap();
test_iamax();
test_iamin();
test_dcabs1();
test_gemv();
test_gemm();
test_vmul();
test_vml();
test_std_vector_vml();
test_gemm_boost();
return 0;
}
// Gauss-Jordan elmination
void MATRIX(_gjelim)(T * _X, unsigned int _XR, unsigned int _XC)
{
unsigned int r, c;
// choose pivot rows based on maximum element along column
float v;
float v_max=0.;
unsigned int r_opt=0;
unsigned int r_hat;
for (r=0; r<_XR; r++) {
// check values along this column and find the maximum
for (r_hat=r; r_hat<_XR; r_hat++) {
v = T_ABS( matrix_access(_X,_XR,_XC,r_hat,r) );
// swap rows if necessary
if (v > v_max || r_hat==r) {
r_opt = r_hat;
v_max = v;
}
}
// if the maximum is zero, matrix is singular
if (v_max == 0.0f) {
fprintf(stderr,"warning: matrix_gjelim(), matrix singular to machine precision\n");
}
// if row does not match column (e.g. maximum value does not
// lie on the diagonal) swap the rows
if (r != r_opt) {
MATRIX(_swaprows)(_X,_XR,_XC,r,r_opt);
}
// pivot on the diagonal element
MATRIX(_pivot)(_X,_XR,_XC,r,r);
}
// scale by diagonal
T g;
for (r=0; r<_XR; r++) {
g = 1 / matrix_access(_X,_XR,_XC,r,r);
for (c=0; c<_XC; c++)
matrix_access(_X,_XR,_XC,r,c) *= g;
}
}
//
// test Cholesky decomposition
//
void autotest_matrixcf_chol()
{
float tol = 1e-3f; // error tolerance
// lower triangular matrix with positive values on diagonal
float complex L[16]= {
1.01, 0, 0, 0,
-1.42 + _Complex_I*0.25, 0.50, 0, 0,
0.32 - _Complex_I*1.23, 2.01 + _Complex_I*0.78, 0.30, 0,
-1.02 + _Complex_I*1.02, -0.32 - _Complex_I*0.03, -1.65 + _Complex_I*2.01, 1.07};
float complex A[16]; // A = L * L^T
float complex Lp[16]; // output Cholesky decomposition
unsigned int i;
// compute A
matrixcf_mul_transpose(L,4,4,A);
// force A to be positive definite
for (i=0; i<4; i++)
matrix_access(A,4,4,i,i) = creal(matrix_access(A,4,4,i,i));
// run decomposition
matrixcf_chol(A,4,Lp);
if (liquid_autotest_verbose) {
printf("L :\n");
matrixcf_print(L,4,4);
printf("A :\n");
matrixcf_print(A,4,4);
printf("Lp:\n");
matrixcf_print(Lp,4,4);
}
for (i=0; i<16; i++) {
CONTEND_DELTA( crealf(L[i]), crealf(Lp[i]), tol );
CONTEND_DELTA( cimagf(L[i]), cimagf(Lp[i]), tol );
}
}
int main() {
unsigned int num_iterations=8;
#if 0
unsigned int n=4;
float A[16] = {
1,2,3,4,
5,5,7,8,
6,4,8,7,
1,0,3,1};
#else
unsigned int n=3;
float A[9] = {
1.0f, 1.0f, 1.0f,
1.0f, 2.0f, 1.0f,
1.0f, 1.0f, 2.0f};
#endif
float eig[n];
float A0[n*n];
float Q[n*n], R[n*n];
memmove(A0, A, n*n*sizeof(float));
printf("\n");
printf("testing Q/R decomposition [Gram-Schmidt]\n");
matrixf_qrdecomp_gramschmidt(A,n,n,Q,R);
//matrixf_print(Q,n,n);
//matrixf_print(R,n,n);
unsigned int k;
for (k=0; k<num_iterations; k++) {
// compute Q/R decomposition
matrixf_qrdecomp_gramschmidt(A0,n,n,Q,R);
// compute A1 = R*Q
matrixf_mul(R,n,n, Q,n,n, A0,n,n);
matrixf_print(A0,n,n);
}
// extract eigen values
unsigned int i;
for (i=0; i<n; i++)
eig[i] = matrix_access(A0,n,n,i,i);
for (i=0; i<n; i++)
printf("eig[%3u] = %12.8f\n", i, eig[i]);
printf("done.\n");
return 0;
}
// multiply two matrices modulo 2
void matrix2_mul(unsigned char * _x, unsigned int _mx, unsigned int _nx,
unsigned char * _y, unsigned int _my, unsigned int _ny,
unsigned char * _z, unsigned int _mz, unsigned int _nz)
{
// ensure lengths are valid
if (_mz != _mx || _nz != _ny || _nx != _my ) {
fprintf(stderr,"error: matrix2_mul(), invalid dimensions\n");
exit(1);
}
unsigned int r, c, i;
for (r=0; r<_mz; r++) {
for (c=0; c<_nz; c++) {
unsigned int sum = 0;
for (i=0; i<_nx; i++) {
sum += matrix_access(_x,_mx,_nx,r,i) *
matrix_access(_y,_my,_ny,i,c);
}
matrix_access(_z,_mz,_nz,r,c) = sum % 2;
}
}
}
void printMatrix(float *Matrix, unsigned int lines, unsigned int cols, char *mname) {
char name[100];
sprintf(name, "test_%s.txt", mname);
FILE *fp = fopen(name, "w");
assert(fp);
for (unsigned int j = 0; j < cols; j++) {
for (unsigned int i = 0; i < lines; i++) {
fprintf(fp, "%.5f", matrix_access(Matrix, lines, cols, i, j)*255);
}
fprintf(fp, "\n");
}
fclose(fp);
}
void POLY(_fit)(T * _x,
T * _y,
unsigned int _n,
T * _p,
unsigned int _k)
{
// ...
T X[_n*_k];
unsigned int r,c;
T v;
for (r=0; r<_n; r++) {
v = 1;
for (c=0; c<_k; c++) {
matrix_access(X,_n,_k,r,c) = v;
v *= _x[r];
}
}
// compute transpose of X
T Xt[_k*_n];
memmove(Xt,X,_k*_n*sizeof(T));
MATRIX(_trans)(Xt,_n,_k);
// compute [X']*y
T Xty[_k];
MATRIX(_mul)(Xt, _k, _n,
_y, _n, 1,
Xty,_k, 1);
// compute [X']*X
T X2[_k*_k];
MATRIX(_mul)(Xt, _k, _n,
X, _n, _k,
X2, _k, _k);
// compute inv([X']*X)
T G[_k*_k];
memmove(G,X2,_k*_k*sizeof(T));
MATRIX(_inv)(G,_k,_k);
// compute coefficients
MATRIX(_mul)(G, _k, _k,
Xty,_k, 1,
_p, _k, 1);
}
int main() {
float x[6] = {
1, 2, 3,
4, 5, 6
};
float y[9] = {
1, 2, 3,
4, 5, 6,
7, 8, 9
};
float z[6];
// compute z = x * y
printf("z = x * y :\n");
matrixf_mul(x,2,3,y,3,3,z,2,3);
matrixf_print(z,2,3);
/*
// compute z = y * x'
matrixf_transpose(x);
printf("x' : \n");
matrixf_print(x);
matrixf_transpose(z);
matrixf_multiply(y,x,z);
printf("z = y * x' :\n");
matrixf_print(z);
matrixf_destroy(x);
matrixf_destroy(y);
matrixf_destroy(z);
*/
float s[16] = {
1,2,3,4,
5,5,7,8,
6,4,8,7,
1,0,3,1
};
float s_inv[16];
memmove(s_inv,s,16*sizeof(float));
matrixf_inv(s_inv,4,4);
float i4[16];
matrixf_mul(s,4,4,s_inv,4,4,i4,4,4);
printf("\ns:\n");
matrixf_print(s,4,4);
printf("\ninv(s):\n");
matrixf_print(s_inv,4,4);
printf("\ns*inv(s):\n");
matrixf_print(i4,4,4);
printf("\n");
float det = matrixf_det(s,4,4);
printf("det(s) = %12.8f\n", det);
#if 0
// pivot test (matrix inversion)
float t[32] = {
1,2,3,4, 1,0,0,0,
5,5,7,8, 0,1,0,0,
6,4,8,7, 0,0,1,0,
1,0,3,1, 0,0,0,1
};
unsigned int i;
for (i=0; i<4; i++) {
matrixf_pivot(t,4,8,i,i);
matrixf_print(t,4,8);
}
unsigned int j;
for (i=0; i<4; i++) {
float v = matrix_access(t,4,8,i,i);
for (j=0; j<8; j++)
matrix_access(t,4,8,i,j) /= v;
}
matrixf_print(t,4,8);
#endif
printf("\n");
printf("testing L/U decomposition [Crout's method]\n");
float L[16], U[16], P[16];
matrixf_ludecomp_crout(s,4,4,L,U,P);
matrixf_print(L,4,4);
matrixf_print(U,4,4);
printf("\n");
printf("testing L/U decomposition [Doolittle's method]\n");
matrixf_ludecomp_doolittle(s,4,4,L,U,P);
matrixf_print(L,4,4);
matrixf_print(U,4,4);
printf("\n\n");
float X[16] = {
0.84382, -2.38304, 1.43061, -1.66604,
3.99475, 0.88066, 4.69373, 0.44563,
7.28072, -2.06608, 0.67074, 9.80657,
6.07741, -3.93099, 1.22826, -0.42142
};
float Y[16];
printf("\nX:\n");
matrixf_print(X,4,4);
// swaprows
memmove(Y,X,16*sizeof(float));
matrixf_swaprows(Y,4,4,0,2);
printf("\nmatrixf_swaprows(X,4,4,0,2):\n");
matrixf_print(Y,4,4);
// pivot test
memmove(Y,X,16*sizeof(float));
matrixf_pivot(Y,4,4,1,2);
printf("\nmatrixf_pivot(X,4,4,1,2):\n");
matrixf_print(Y,4,4);
// inverse test
memmove(Y,X,16*sizeof(float));
matrixf_inv(Y,4,4);
printf("\nmatrixf_inv(X,4,4):\n");
matrixf_print(Y,4,4);
// determinant test
float D = matrixf_det(X,4,4);
printf("\nmatrixf_det(X,4) = %12.8f\n", D);
// L/U decomp (Crout's method)
matrixf_ludecomp_crout(X,4,4,L,U,P);
printf("\nmatrixf_ludecomp_crout(X,4,4,L,U,P)\n");
printf("L:\n");
matrixf_print(L,4,4);
printf("U:\n");
matrixf_print(U,4,4);
// L/U decomp (Doolittle's method)
matrixf_ludecomp_doolittle(X,4,4,L,U,P);
printf("\nmatrixf_ludecomp_doolittle(X,4,4,L,U,P)\n");
printf("L:\n");
matrixf_print(L,4,4);
printf("U:\n");
matrixf_print(U,4,4);
printf("\n");
printf("testing Q/R decomposition [Gram-Schmidt]\n");
float Q[16], R[16];
matrixf_qrdecomp_gramschmidt(X,4,4,Q,R);
matrixf_print(Q,4,4);
matrixf_print(R,4,4);
/*
float b[4] = {
0.91489,
0.71789,
1.06553,
-0.81707};
*/
float Xb[20] = {
0.84382, -2.38304, 1.43061, -1.66604, 0.91489,
3.99475, 0.88066, 4.69373, 0.44563, 0.71789,
7.28072, -2.06608, 0.67074, 9.80657, 1.06553,
6.07741, -3.93099, 1.22826, -0.42142, -0.81707
};
printf("\n[X b] =\n");
matrixf_print(Xb,4,5);
matrixf_gjelim(Xb,4,5);
printf("\nmatrixf_gjelim(Xb,4,5)\n");
matrixf_print(Xb,4,5);
// compute a*a'
float a[20] = {
-0.24655, -1.78843, 0.39477, 0.43735, -1.08998,
-0.42751, 0.62496, 1.43802, 0.19814, 0.78155,
-0.35658, -0.81875, -1.09984, 1.87006, -0.94191,
0.39553, -2.02036, 1.17393, 1.54591, 1.29663
};
printf("\na =\n");
matrixf_print(a,4,5);
printf("\n\n");
printf("computing a*a'\n");
float aaT[16];
matrixf_mul_transpose(a,4,5,aaT);
matrixf_print(aaT,4,4);
printf("\n\n");
printf("computing a'*a\n");
float aTa[25];
matrixf_transpose_mul(a,4,5,aTa);
matrixf_print(aTa,5,5);
printf("\n");
printf("testing Gram-Schmidt\n");
float Xgs[12] = {
1., 2., 1.,
0., 2., 0.,
2., 3., 1.,
1., 1., 0.
};
float Ugs[12];
float Ugs_test[12] = {
sqrtf(6.)/6., sqrtf(2.)/6., 2./3.,
0., 2.*sqrtf(2.)/3.,-1./3.,
sqrtf(6.)/3., 0., 0.,
sqrtf(6.)/6., -sqrtf(2.)/6., -2./3.
};
matrixf_gramschmidt(Xgs,4,3,Ugs);
printf("X:\n");
matrixf_print(Xgs,4,3);
printf("normalized X:\n");
matrixf_print(Ugs,4,3);
printf("expected:\n");
matrixf_print(Ugs_test,4,3);
//
// test Cholesky decomposition
//
printf("\n");
printf("testing Cholesky decomposition\n");
// generate input matrix
float complex Lp[9] = { 1.0, 0.0, 0.0,
-3.1 + 0.2*_Complex_I, 0.3, 0.0,
1.7 + 0.5*_Complex_I, -0.6 - 0.3*_Complex_I, 2.9
};
float complex Ap[9];
matrixcf_mul_transpose(Lp, 3, 3, Ap);
float complex Lc[9];
matrixcf_chol(Ap, 3, Lc);
printf("Lp:\n");
matrixcf_print(Lp, 3, 3);
printf("Ap:\n");
matrixcf_print(Ap, 3, 3);
printf("Lc:\n");
matrixcf_print(Lc, 3, 3);
printf("done.\n");
return 0;
}
// compute Hessian
void qnsearch_compute_Hessian(qnsearch _q)
{
unsigned int i, j;
unsigned int n = _q->num_parameters;
float f00, f01, f10, f11;
float f0, f1, f2;
float m0, m1;
float delta = 1e-2f;
// reset v_prime
memmove(_q->v_prime, _q->v, (_q->num_parameters)*sizeof(float));
for (i=0; i<_q->num_parameters; i++) {
//for (j=0; j<_q->num_parameters; j++) {
for (j=0; j<=i; j++) {
if (i==j) {
_q->v_prime[i] = _q->v[i] - delta;
f0 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
_q->v_prime[i] = _q->v[i];
f1 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
_q->v_prime[i] = _q->v[i] + delta;
f2 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
m0 = (f1 - f0) / delta;
m1 = (f2 - f1) / delta;
matrix_access(_q->H, n, n, i, j) = (m1 - m0) / delta;
} else {
// 0 0
_q->v_prime[i] = _q->v[i] - delta;
_q->v_prime[j] = _q->v[j] - delta;
f00 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
// 0 1
_q->v_prime[i] = _q->v[i] - delta;
_q->v_prime[j] = _q->v[j] + delta;
f01 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
// 1 0
_q->v_prime[i] = _q->v[i] + delta;
_q->v_prime[j] = _q->v[j] - delta;
f10 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
// 1 1
_q->v_prime[i] = _q->v[i] + delta;
_q->v_prime[j] = _q->v[j] + delta;
f11 = _q->get_utility(_q->userdata, _q->v_prime, _q->num_parameters);
// compute second partial derivative
m0 = (f01 - f00) / (2.0f*delta);
m1 = (f11 - f10) / (2.0f*delta);
matrix_access(_q->H, n, n, i, j) = (m1 - m0) / (2.0f*delta);
matrix_access(_q->H, n, n, j, i) = (m1 - m0) / (2.0f*delta);
}
}
}
//matrixf_print(_q->H, n, n);
//exit(1);
}
int main() {
// options
unsigned int n = 8;
unsigned int i;
// allocate memory for arrays
float A[n*n];
float b[n];
float x[n];
float x_hat[n];
// generate symmetric positive-definite matrix by first generating
// lower triangular matrix L and computing A = L*L'
float L[n*n];
unsigned int j;
for (i=0; i<n; i++) {
for (j=0; j<n; j++) {
#if 0
// sparse matrix
if (j > i) matrix_access(L,n,n,i,j) = 0.0;
else if (j == i) matrix_access(L,n,n,i,j) = randnf();
else if ((rand()%4)==0) matrix_access(L,n,n,i,j) = randnf();
else matrix_access(L,n,n,i,j) = 0.0;
#else
// full matrix
matrix_access(L,n,n,i,j) = (j < i) ? 0.0 : randnf();
#endif
}
}
matrixf_mul_transpose(L, n, n, A);
// generate random solution
for (i=0; i<n; i++)
x[i] = randnf();
// compute b
matrixf_mul(A, n, n,
x, n, 1,
b, n, 1);
// solve symmetric positive-definite system of equations
matrixf_cgsolve(A, n, b, x_hat, NULL);
//matrixf_linsolve(A, n, b, x_hat, NULL);
// print results
printf("A:\n"); matrixf_print(A, n, n);
printf("b:\n"); matrixf_print(b, n, 1);
printf("x (original):\n"); matrixf_print(x, n, 1);
printf("x (estimate):\n"); matrixf_print(x_hat, n, 1);
// compute error norm
float e = 0.0;
for (i=0; i<n; i++)
e += (x[i] - x_hat[i])*(x[i] - x_hat[i]);
e = sqrt(e);
printf("error norm: %12.4e\n", e);
printf("done.\n");
return 0;
}
bool PdfTransfer::NDPdfTransfer(float *input, float *palette, float **rotations) {
clock_t start, end;
FILE *fp = fopen("time.txt", "w");
unsigned long int var_time = 0;
float *finalPic = new float[_projections * _inputSize];
for (unsigned int i = 0; i < _iterations; ++i) {
start = clock();
float * ptrRotation = rotations[i];
assert(ptrRotation);
float *inputRotation = new float[_projections * _inputSize];
float *paletteRotation = new float[_projections * _paletteSize];
_matrixModule->matrix_multiply(ptrRotation, _projections, NUM_CHANNELS,
input, NUM_CHANNELS, _inputSize, inputRotation, _projections, _inputSize);
#ifdef DEBUG
if (!i) {
printMatrix(ptrRotation, _projections, NUM_CHANNELS, "ptrRotation", _height, _width);
printMatrix(input, NUM_CHANNELS, _inputSize, "input", _height, _width);
printMatrix(inputRotation, _projections, _inputSize, "inputRotation", _height, _width);
}
#endif
_matrixModule->matrix_multiply(ptrRotation, _projections, NUM_CHANNELS,
palette, NUM_CHANNELS, _paletteSize, paletteRotation, _projections, _paletteSize);
#ifdef DEBUG
if (!i) {
printMatrix(palette, NUM_CHANNELS, _paletteSize, "palette", _height, _width);
printMatrix(paletteRotation, _projections, _paletteSize, "paletteRotation", _height, _width);
}
#endif
Histogram ** histogramsInput = new Histogram*[_projections];
Histogram ** histogramsPalette = new Histogram*[_projections];
//Step1: Creation of Histograms
CreateHistograms(inputRotation, _inputSize,
paletteRotation, _paletteSize, _projections, histogramsInput, histogramsPalette);
#ifdef DEBUG
printHistogr(histogramsInput, i);
#endif
std::vector<float> *inter = new std::vector<float>[_projections];
for (unsigned int j = 0; j < _projections; ++j) {
std::vector<float> ptr = SinglePdfTransfer(histogramsInput[j], histogramsPalette[j]);
std::vector<float> newPtr(ptr.begin() + 1, ptr.end() - 1);
float scale = bin_count / (histogramsInput[j]->GetOverallMax() -
histogramsInput[j]->GetOverallMin());
//populate X points before interpolation
std::vector<float> X(newPtr.size());
for (unsigned int k = 0; k < X.size(); ++k) {
X[k] = (float) k;
}
std::vector<float> Xq(_inputSize);
unsigned int itr = 0;
for (unsigned k = j * _inputSize; k < (j + 1) * _inputSize; ++k, ++itr) {
Xq[itr] = inputRotation[k];
Xq[itr] = (Xq[itr] - histogramsInput[j]->GetOverallMin()) * scale;
}
inter[j] = linearInterpolation(X, newPtr, Xq);
for (unsigned int k = 0; k < inter[j].size(); ++k) {
inter[j][k] = inter[j][k] / scale + histogramsInput[j]->GetOverallMin();
inter[j][k] -= matrix_access(inputRotation, _projections, _inputSize, j, k);
matrix_access(finalPic, _projections, _inputSize, j, k) = inter[j][k];
}
}
#ifdef DEBUG
char filename2[10];
sprintf(filename2, "finalPic%d", i);
printMatrix(finalPic, _projections, _inputSize, filename2, _height, _width);
#endif
//resolve linear system of ptrRotation*x = inter
_matrixModule->matrix_inverse(ptrRotation, _projections, NUM_CHANNELS);
float *aux = new float[ _projections * _inputSize ];
_matrixModule->matrix_multiply(ptrRotation, _projections, NUM_CHANNELS,
finalPic, _projections, _inputSize,
aux, _projections, _inputSize);
_matrixModule->matrix_add(input, aux, input, _projections, _inputSize);
#ifdef DEBUG
//if(!i)
//{
char filename[10];
sprintf(filename, "iter%d", i);
printMatrix(input, _projections, _inputSize, filename, _height, _width);
//}
#endif
end = clock();
var_time = (end - start) / (CLOCKS_PER_SEC);
fprintf(fp, "It took %lu seconds to complete %d iteration\n", var_time, i);
//freeing memory
delete [] inputRotation;
delete [] paletteRotation;
}
//freeing heap
delete [] finalPic;
//used for logging time
fclose(fp);
return true;
}
void PdfTransfer::CreateHistograms(float *input, unsigned int iSize,
float *palette, unsigned int pSize,
unsigned int projections,
Histogram **orig, Histogram **target) {
static int var = 0;
assert(orig);
assert(target);
for (unsigned int i = 0; i < projections; ++i) {
float minimum, maximum;
minimum = maximum = matrix_access(input, projections, iSize, i, 0);
//finding minumum and maximum per line for input matrix
for (unsigned int j = 0; j < iSize; ++j) {
if (matrix_access(input, projections, iSize, i, j) < minimum) {
minimum = matrix_access(input, projections, iSize, i, j);
}
if (matrix_access(input, projections, iSize, i, j) > maximum) {
maximum = matrix_access(input, projections, iSize, i, j);
}
}
//finding minumum and maximum per line for palette matrix
for (unsigned int j = 0; j < pSize; ++j) {
if (matrix_access(palette, projections, pSize, i, j) < minimum) {
minimum = matrix_access(palette, projections, pSize, i, j);
}
if (matrix_access(palette, projections, pSize, i, j) > maximum) {
maximum = matrix_access(palette, projections, pSize, i, j);
}
}
float step = (maximum - minimum) / (float) bin_count;
orig[i] = new Histogram[ bin_count + 1];
for (unsigned int j = 0; j < iSize; ++j) {
float element = matrix_access(input, projections, iSize, i, j);
float dblPos = (element - minimum) / step;
//int pos = static_cast<int>(floor(dblPos));
int pos = static_cast<int> (round(dblPos));
assert(pos < bin_count + 1);
assert(pos >= 0);
orig[i][pos].incrementCounter();
orig[i][pos].SetInferiorLimit(minimum + pos * step);
orig[i][pos].SetSuperiorLimit(minimum + (pos + 1) * step);
orig[i]->incrementGlobalCounter();
orig[i]->SetOverallMax(maximum);
orig[i]->SetOverallMin(minimum);
}
target[i] = new Histogram[ bin_count + 1];
for (unsigned int j = 0; j < pSize; ++j) {
float dblPos = (matrix_access(palette, projections, pSize, i, j) - minimum) / step;
//int pos = static_cast<int>(floor(dblPos));
int pos = static_cast<int> (round(dblPos));
assert(pos < bin_count + 1);
assert(pos >= 0);
target[i][pos].incrementCounter();
target[i][pos].SetInferiorLimit(minimum + pos * step);
target[i][pos].SetSuperiorLimit(minimum + (pos + 1) * step);
target[i]->incrementGlobalCounter();
target[i]->SetOverallMax(maximum);
target[i]->SetOverallMin(minimum);
}
#ifdef DEBUG
if (!var) {
FILE *fp = NULL;
char name[100];
char name2[100];
sprintf(name, "histo_orig%d.txt", i);
sprintf(name2, "histo_palette%d.txt", i);
fp = fopen(name, "w");
for (unsigned int j = 0; j < 301; ++j) {
fprintf(fp, "%d\n", orig[i][j].getCounter());
}
fclose(fp);
fp = fopen(name2, "w");
for (unsigned int j = 0; j < 301; ++j) {
fprintf(fp, "%d\n", target[i][j].getCounter());
}
fclose(fp);
}
#endif
}
var++;
}
// update BFGS estimate of Hessian matrix inverse
// _n : dimension
// _dx : step size (previous), [size: _n x 1]
// _y : gradient difference
// _H0 : Hessian matrix inverse estimate (previous), [size: _n x _n]
// _H1 : Hessian matrix inverse estimate [size: _n x _n]
void bfgs_update(unsigned int _n,
float * _dx,
float * _y,
float * _H0,
float * _H1)
{
#if DEBUG_BFGS
// print inputs
printf("********************\n");
print_vector(" dx ", _dx, _n);
print_vector(" y ", _y, _n);
printf("H0 = \n");
matrixf_print(_H0,_n,_n);
#endif
//
//float In[_n*_n]; // I(_n) [_n x _n]
float ydxT[_n*_n]; // _y * _dx' [_n x _n]
float yTdx; // _y' * _dx [1 x 1]
float q[_n*_n]; // I(_n) - (_y*_dx' / _y'_dx) [_n x _n]
float dxdxT[_n*_n]; // _dx * _dx' [_n x _n]
float tmp[_n*_n]; // temporary array [_n x _n]
// compute _y * _dx'
matrixf_mul(_y, _n, 1,
_dx, 1, _n,
ydxT, _n, _n);
#if DEBUG_BFGS
printf("y*dx' = \n");
matrixf_print(ydxT,_n,_n);
#endif
// compute _y' * _dx'
matrixf_mul(_y, 1, _n,
_dx, _n, 1,
&yTdx, 1, 1);
// compute _n x _n identity matrix
// compute q
unsigned int i;
unsigned int j;
for (i=0; i<_n; i++) {
for (j=0; j<_n; j++) {
matrix_access(q,_n,_n,i,j) = (i==j ? 1.0f : 0.0f) -
matrix_access(ydxT,_n,_n,i,j)/yTdx;
}
}
#if DEBUG_BFGS
printf("q = \n");
matrixf_print(q,_n,_n);
#endif
// compute _dx*_dx'
matrixf_mul(_dx, _n, 1,
_dx, 1, _n,
dxdxT, _n, _n);
#if DEBUG_BFGS
printf("dx*dx' = \n");
matrixf_print(dxdxT,_n,_n);
#endif
// compute _H0 * q, store in tmp
matrixf_mul(_H0, _n, _n,
q, _n, _n,
tmp, _n, _n);
// compute q' (transpose)
matrixf_trans(q, _n, _n);
// compute q' * _H0 * _q, store in _H1
matrixf_mul(q, _n, _n,
tmp, _n, _n,
_H1, _n, _n);
// add dxdxT / yTdx to _H1
for (i=0; i<_n; i++) {
for (j=0; j<_n; j++) {
matrix_access(_H1,_n,_n,i,j) += matrix_access(dxdxT,_n,_n,i,j) / yTdx;
}
}
#if DEBUG_BFGS
printf("H1 = \n");
matrixf_print(_H1,_n,_n);
#endif
}
// Orthnormalization using the Gram-Schmidt algorithm
void MATRIX(_gramschmidt)(T * _x,
unsigned int _rx,
unsigned int _cx,
T * _v)
{
// validate input
if (_rx == 0 || _cx == 0) {
fprintf(stderr,"error: matrix_gramschmidt(), input matrix cannot have zero-length dimensions\n");
exit(1);
}
unsigned int i;
unsigned int j;
unsigned int k;
// copy _x to _u
memmove(_v, _x, _rx * _cx * sizeof(T));
unsigned int n = _rx; // dimensionality of each vector
T proj_ij[n];
for (j=0; j<_cx; j++) {
for (i=0; i<j; i++) {
// v_j <- v_j - proj(v_i, v_j)
#if DEBUG_MATRIX_GRAMSCHMIDT
printf("computing proj(v_%u, v_%u)\n", i, j);
#endif
// compute proj(v_i, v_j)
T vij = 0.; // dotprod(v_i, v_j)
T vii = 0.; // dotprod(v_i, v_i)
T ti;
T tj;
for (k=0; k<n; k++) {
ti = matrix_access(_v, _rx, _cx, k, i);
tj = matrix_access(_v, _rx, _cx, k, j);
T prodij = ti * conj(tj);
vij += prodij;
T prodii = ti * conj(ti);
vii += prodii;
}
// TODO : vii should be 1.0 from normalization step below
T g = vij / vii;
// complete projection
for (k=0; k<n; k++)
proj_ij[k] = matrix_access(_v, _rx, _cx, k, i) * g;
// subtract projection from v_j
for (k=0; k<n; k++)
matrix_access(_v, _rx, _cx, k, j) -= proj_ij[k];
}
// normalize v_j
T vjj = 0.; // dotprod(v_j, v_j)
T tj = 0.;
for (k=0; k<n; k++) {
tj = matrix_access(_v, _rx, _cx, k, j);
T prodjj = tj * conj(tj);
vjj += prodjj;
}
// TODO : check magnitude of vjj
T g = 1. / sqrt( creal(vjj) );
for (k=0; k<n; k++)
matrix_access(_v, _rx, _cx, k, j) *= g;
#if DEBUG_MATRIX_GRAMSCHMIDT
MATRIX(_print)(_v, _rx, _cx);
#endif
}
}
// Q/R decomposition using the Gram-Schmidt algorithm
void MATRIX(_qrdecomp_gramschmidt)(T * _x,
unsigned int _rx,
unsigned int _cx,
T * _Q,
T * _R)
{
// validate input
if (_rx != _cx) {
fprintf(stderr,"error: matrix_qrdecomp_gramschmidt(), input matrix not square\n");
exit(-1);
}
unsigned int n = _rx;
unsigned int i;
unsigned int j;
unsigned int k;
// generate and initialize matrices
T e[n*n]; // normalized...
for (i=0; i<n*n; i++)
e[i] = 0.0f;
for (k=0; k<n; k++) {
// e(i,k) <- _x(i,k)
for (i=0; i<n; i++)
matrix_access(e,n,n,i,k) = matrix_access(_x,n,n,i,k);
// subtract...
for (i=0; i<k; i++) {
// compute dot product _x(:,k) * e(:,i)
T g = 0;
for (j=0; j<n; j++) {
T prod = matrix_access(_x,n,n,j,k) * conj( matrix_access(e,n,n,j,i) );
g += prod;
}
//printf(" i=%2u, g = %12.4e\n", i, crealf(g));
for (j=0; j<n; j++)
matrix_access(e,n,n,j,k) -= matrix_access(e,n,n,j,i) * g;
}
// compute e_k = e_k / |e_k|
float ek = 0.0f;
T ak;
for (i=0; i<n; i++) {
ak = matrix_access(e,n,n,i,k);
ek += fabsf( ak*conjf(ak) );
}
ek = sqrtf(ek);
// normalize e
for (i=0; i<n; i++)
matrix_access(e,n,n,i,k) /= ek;
}
// move Q
memmove(_Q, e, n*n*sizeof(T));
// compute R
// j : row
// k : column
for (j=0; j<n; j++) {
for (k=0; k<n; k++) {
if (k < j) {
matrix_access(_R,n,n,j,k) = 0.0f;
} else {
// compute dot product between and Q(:,j) and _x(:,k)
T g = 0;
for (i=0; i<n; i++) {
T prod = conj( matrix_access(_Q,n,n,i,j) ) * matrix_access(_x,n,n,i,k);
g += prod;
}
matrix_access(_R,n,n,j,k) = g;
}
}
}
}