void zero_under_diag(Mat_DP& a) {
for (int i = 0; i < a.nrows(); i++) {
for (int j = 0; j < min(i, a.ncols()); j++) {
a[i][j] = 0;
}
}
}
void hilb(Mat_DP& A) {
for (int i = 0; i < A.nrows(); i++) {
for (int j = 0; j < A.ncols(); j++) {
A[i][j] = 1.0 / (i + j + 1);
}
}
}
bool is_tridiagonal(Mat_DP& a, double tolerance) {
for (int i = 0; i < a.nrows(); i++) {
for (int j = 0; j < a.ncols(); j++) {
if (abs(i - j) > 1 && abs(a[i][j]) > tolerance)
return false;
}
}
return true;
}
void random_tridiagonal(Mat_DP& a) {
for (int i = 0; i < a.nrows(); i++) {
for (int j = 0; j < a.ncols(); j++) {
if (abs(i - j) <= 1)
a[i][j] = rdm(minValue, maxValue);
else
a[i][j] = 0;
}
}
}
bool is_upper_triangular(Mat_DP const& a, double tolerance) {
int n = a.nrows();
int m = a.ncols();
for (int i = 0; i < n; i++) {
for (int j = 0; j < min(i, m); j++) {
if (abs(a[i][j]) > tolerance) {
cout << "For a " << n << " x " << m << " matrix: value at (" << i << ", " << j << ") = " << a[i][j] << endl;
return false;
}
}
}
return true;
}
Mat_DP MATHEMATICS::math_transpose(Mat_DP m) {
int x=m.nrows(), y=m.ncols();
Mat_DP transm(y,x);
for(int i=0; i<y; i++) {
for(int j=0; j<x; j++) {
transm[i][j]=m[j][i];
}
}
return transm;
}
void io_dataoutput(string filename, Mat_DP m) {
ofstream outfile(filename.c_str());
// outfile << m.nrows() << endl;
for (int i=0; i<m.nrows(); i++) {
for (int j=0; j<m.ncols(); j++) {
outfile << m[i][j] << " ";
}
outfile << endl;
}
outfile.close();
return;
}
void random_upper_triangular(Mat_DP& a) {
// could be done like this, but we do it more efficiently
// ranmat2(a, minValue, maxValue);
// zero_under_diag(a);
for (int i = 0; i < a.nrows(); i++) {
for (int j = 0; j < a.ncols(); j++) {
if (i <= j)
a[i][j] = rdm(minValue, maxValue);
else
a[i][j] = 0;
}
}
}
double MATHEMATICS::math_det3(Mat_DP m) {
int x=m.nrows(), y=m.ncols();
double a=0;
Mat_DP b0(2,2), b1(2,2), b2(2,2);
if (x!=3||y!=3) {
cout << "Input matrix is not 3x3";
}
else {
b0[0][0]=m[1][1], b0[0][1]=m[1][2], b0[1][0]=m[2][1], b0[1][1]=m[2][2];
b1[0][0]=m[1][0], b1[0][1]=m[1][2], b1[1][0]=m[2][0], b1[1][1]=m[2][2];
b2[0][0]=m[1][0], b2[0][1]=m[1][1], b2[1][0]=m[2][0], b2[1][1]=m[2][1];
a=m[0][0]*MATHEMATICS::math_det2(b0)-m[0][1]*MATHEMATICS::math_det2(b1)+m[0][2]*MATHEMATICS::math_det2(b2);
}
return a;
}
void GSsolve_iter(Mat_DP &a, Vec_DP &b, Vec_DP &x, Vec_DP &xold) {
int i, j, rows = a.nrows();
if ((rows != a.ncols()) || (rows != b.size()) ||
(rows != x.size()) || (rows != xold.size())) {
cout << "Argument error in GaussSeidel_iter\n" << endl;
abort();
}
double s;
for (i = 0; i < rows; i++) {
s = 0;
for (j = 0; j < rows; j++) {
s += (j <= i - 1) ? a[i][j] * x[j] :
(j >= i + 1) ? a[i][j] * xold[j] : 0;
}
xold[i] = x[i];
x[i] = (b[i] - s) / a[i][i];
}
}
Mat_DP MATHEMATICS::math_mxmply(Mat_DP a, Mat_DP b) {
int x=a.nrows(), y=b.ncols();
double initial=0;
Mat_DP c(initial, x, y);
if(x!=y) {
cout << "Matrix dimensions are invalid for multiplication";
return c;
}
else {
int i, j, k;
for(i=0; i<x; i++) {
for(j=0; j<y; j++) {
for(k=0; k<x; k++) {
c[i][j]+=a[i][k]*b[k][j];
}
}
}
return c;
}
}
int main(){
Mat_DP data = getmat("data/data705.mat");
Vec_DP xdata(data.nrows()), ydata(data.nrows()), zdata(data.nrows());
mutils::isolateCol(data, 0, xdata);
mutils::isolateCol(data, 1, ydata);
mutils::isolateCol(data, 2, zdata);
solve_system(xdata, ydata, zdata);
auto f = [](double x, double y) {return coeffs[0]*x + coeffs[1]*y + coeffs[2];};
myplot::surf_data_set container;
myplot::surf_data surface(".");
myplot::surf_data points("+");
myplot::generate_data(f, container, surface, -10, 10, -10, 10);
for (int i = 0; i < xdata.size(); i++) {
points.add_point(xdata[i], ydata[i], zdata[i]);
}
container.push_back(points);
cout << "coeffs = " << coeffs << endl;
myplot::surf(container, "Parameter fitting", true);
}
int main(){
Mat_DP A = getmat("data/A202.mat");
Mat_DP b = getmat("data/b202.mat");
Mat_DP invAtA(2,2);
Mat_DP x;
//A'
Mat_DP At = !A;
//A'A
Mat_DP AtA = At * A;
//A'b
Mat_DP Atb = At * b;
//inv(A'A)
invmat(AtA, invAtA);
x = invAtA * Atb;
showmat(x);
//-------------------plotting-----------------------------
const char* filename1 = "data/data.tmp";
const char* filename2 = "data/fitted.tmp";
generatePlottingData(A,b,filename1);
Mat_DP ydata(A.nrows(), 1);
for (int i = 0; i < A.nrows(); i++) {
ydata[i][0] = x[0][0] * A[i][0] + x[1][0];
}
generatePlottingData(A, ydata, filename2);
plot(filename1, "k.", filename2, "r-", NULL);
}
Vec_DP MATHEMATICS::math_mxmply(Mat_DP a, Vec_DP b) {
int x=a.nrows(), y=b.size();
double initial=0;
Vec_DP c(initial, y);
if(x!=y) {
cout << "Matrix dimensions are invalid for multiplication";
return c;
}
else {
int i, j;
for(i=0; i<x; i++) {
for(j=0; j<y; j++) {
c[i]+=a[i][j]*b[j];
}
}
return c;
}
}
int main(){
Mat_DP dirichlet = getmat("data/dirichlet1.mat");
Vec_DP b = getVec(), ans(dirichlet.nrows());
SVDsolve(dirichlet, b, ans);
print_results("answer", ans);
}
Vec_DP getVec(){
Mat_DP temp = getmat("data/b1.mat");
Vec_DP b(temp.nrows());
mutils::isolateCol(temp, 0, b);
return b;
}
void pinv_solve(Mat_DP &A, Vec_DP &x, Vec_DP &b) {
Mat_DP pinvA(A.ncols(), A.nrows());
pseudoinv(A, pinvA);
matvecmul(pinvA, b, x);
}
Vec_DP getVec(const char *fname){
Mat_DP temp = getmat(fname);
Vec_DP b(temp.nrows());
mutils::isolateCol(temp, 0, b);
return b;
}
