mirror of https://github.com/Askill/AP-SCE.git
- added 5.4.2 (optim.) and started 4.1.2 (lin. interpol.)
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#include "mex.h"
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#include "matrix.h"
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#include "stdlib.h"
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#include "math.h"
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void mexFunction(int nlhs, mxArray *plhs[], // Output variables
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int nrhs, const mxArray *prhs[]) // Input variables
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{
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int variables = *mxGetPr(prhs[0]);
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double* x = (double *)mxCalloc(variables, sizeof(double)); //create solution array
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double* xx = (double *)mxCalloc(variables, sizeof(double));
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double* yy = (double *)mxCalloc(variables, sizeof(double));
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double** GA = (double **)mxCalloc(variables+1, sizeof(double*)); //create Gauss Array (GA)
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for (int i = 0; i <= variables; i++){
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GA[i] = (double *)mxCalloc(variables+1, sizeof(double));
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}
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for(int i=0;i<variables;i++){
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xx[i]=mxGetPr(prhs[1])[i];
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}
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for(int i=0;i<variables;i++){
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yy[i]=mxGetPr(prhs[2])[i];
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}
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for(int i=0;i<variables;i++){
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for(int j=0; j<variables;j++){
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GA[i][j] = pow(xx[i],j);
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}
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}
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for(int i=0;i<variables;i++){
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GA[i][variables] = yy[i];
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}
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int i, j, k;
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for (i = 0; i<variables; i++) //Pivotisation
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for (k = i + 1; k<variables; k++)
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if (abs(GA[i][i])<abs(GA[k][i]))
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for (j = 0; j <= variables; j++)
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{
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long double temp = GA[i][j];
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GA[i][j] = GA[k][j];
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GA[k][j] = temp;
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}
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for (i = 0; i<variables - 1; i++) //gauss elimination
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for (k = i + 1; k<variables; k++)
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{
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long double t = GA[k][i] / GA[i][i];
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for (j = 0; j <= variables; j++)
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GA[k][j] = GA[k][j] - t*GA[i][j]; //make the elements below the pivot elements equal to zero or elimnate the variables
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}
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for (i = variables - 1; i >= 0; i--) //back-substitution
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{ //x is an array whose values correspond to the values of x,y,z..
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x[i] = GA[i][variables]; //make the variable to be calculated equal to the rhs of the last equation
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for (j = i + 1; j<variables; j++)
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if (j != i) //then subtract all the lhs values except the coefficient of the variable whose value is being calculated
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x[i] = x[i] - GA[i][j] * x[j];
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x[i] = x[i] / GA[i][i]; //now finally divide the rhs by the coefficient of the variable to be calculated
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}
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nlhs = variables;
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for(int j=0; j < variables; j++){
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plhs[j]=mxCreateDoubleScalar(x[j]);
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}
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for(int l=0;l<variables;l++){
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char temp;
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if(x[variables-1-l] != 0)
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{
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if(l!=0){
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mexPrintf("+");
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}
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if(x[variables-1-l] < 0 ){
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mexPrintf("-");
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x[variables-l] *= -1;
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}
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temp=(char)(48+x[variables-1-l]);
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mexPrintf("%c",temp);
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if(variables-1-l != 0){
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mexPrintf("*");
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mexPrintf("x");
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mexPrintf("^");
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temp=(char)(48+variables-1-l);
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mexPrintf("%c",temp);
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}
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}
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}
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mexPrintf("\n");
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for (int i = 0; i <= variables; i++ ){
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free(GA[i]);
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}
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free(GA);
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free(x);
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return;
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}
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% function accepts 1 double and 1 double matrix (#of_variables, [row1;row2])
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% each row1 contains #of_variables+1 elements
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% returns solution vector
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% outputs the function
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% bsp.:
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% 6x^2+12x=30
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% 3x^2+ 3x= 9
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% a21(2,[6,12,30;3,3,9]);
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% 2*x^1+1 <-function
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%
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% OR
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%
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% 6x^2+12x=30
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% 3x^2+ 3x= 9
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% [a1,a2]=a21(2,[6,12,30;3,3,9])
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% 2*x^1+1 <-function
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% a1 = 1 <-factors of x^...
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% a2 = 2
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#include "mex.h"
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#include "matrix.h"
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#include "stdlib.h"
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#include "math.h"
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void mexFunction(int nlhs, mxArray *plhs[], // Output variables
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int nrhs, const mxArray *prhs[]) // Input variables
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{
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int variables = *mxGetPr(prhs[0]);
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double* x = (double *)mxCalloc(variables, sizeof(double)); //create solution array
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double* xx = (double *)mxCalloc(variables, sizeof(double));
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double* yy = (double *)mxCalloc(variables, sizeof(double));
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double** GA = (double **)mxCalloc(variables+1, sizeof(double*)); //create Gauss Array (GA)
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for (int i = 0; i <= variables; i++){
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GA[i] = (double *)mxCalloc(variables+1, sizeof(double));
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}
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for(int i=0;i<variables;i++){
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xx[i]=mxGetPr(prhs[1])[i];
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}
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for(int i=0;i<variables;i++){
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yy[i]=mxGetPr(prhs[2])[i];
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}
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for(int i=0;i<variables;i++){
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for(int j=0; j<variables;j++){
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GA[i][j] = pow(xx[i],j);
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}
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}
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for(int i=0;i<variables;i++){
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GA[i][variables] = yy[i];
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}
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int i, j, k;
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for (i = 0; i<variables; i++) //Pivotisation
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for (k = i + 1; k<variables; k++)
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if (abs(GA[i][i])<abs(GA[k][i]))
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for (j = 0; j <= variables; j++)
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{
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long double temp = GA[i][j];
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GA[i][j] = GA[k][j];
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GA[k][j] = temp;
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}
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for (i = 0; i<variables - 1; i++) //gauss elimination
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for (k = i + 1; k<variables; k++)
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{
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long double t = GA[k][i] / GA[i][i];
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for (j = 0; j <= variables; j++)
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GA[k][j] = GA[k][j] - t*GA[i][j]; //make the elements below the pivot elements equal to zero or elimnate the variables
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}
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for (i = variables - 1; i >= 0; i--) //back-substitution
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{ //x is an array whose values correspond to the values of x,y,z..
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x[i] = GA[i][variables]; //make the variable to be calculated equal to the rhs of the last equation
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for (j = i + 1; j<variables; j++)
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if (j != i) //then subtract all the lhs values except the coefficient of the variable whose value is being calculated
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x[i] = x[i] - GA[i][j] * x[j];
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x[i] = x[i] / GA[i][i]; //now finally divide the rhs by the coefficient of the variable to be calculated
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}
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nlhs = variables;
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for(int j=0; j < variables; j++){
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plhs[j]=mxCreateDoubleScalar(x[j]);
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}
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for(int l=0;l<variables;l++){
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char temp;
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if(x[variables-1-l] != 0)
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{
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if(l!=0){
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mexPrintf("+");
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}
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if(x[variables-1-l] < 0 ){
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mexPrintf("-");
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x[variables-l] *= -1;
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}
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temp=(char)(48+x[variables-1-l]);
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mexPrintf("%c",temp);
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if(variables-1-l != 0){
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mexPrintf("*");
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mexPrintf("x");
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mexPrintf("^");
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temp=(char)(48+variables-1-l);
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mexPrintf("%c",temp);
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}
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}
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}
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mexPrintf("\n");
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for (int i = 0; i <= variables; i++ ){
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free(GA[i]);
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}
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free(GA);
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free(x);
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return;
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}
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#include "mex.h"
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#include "matrix.h"
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#include "stdlib.h"
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#include "math.h"
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double g_von_theta(long double x, long double y)
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{
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return -(x*x + y*y);
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}
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void mexFunction(int nlhs, mxArray *plhs[], // Output variables
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int nrhs, const mxArray *prhs[]) // Input variables
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{
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double x = -2, y = -2,
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xnew, ynew,
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increments = 0.1,
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z = g_von_theta(x, y),
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znew = 0, zold = 1,
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zinitial = z;
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int xTOy = 1, iAThalf = 1000; //iAThalf: max iterations/2
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int i;
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for( i = 0 ; i <= 2 * iAThalf + 1; ++i) // add. exit crit. needed
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{
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if (xTOy == 1)
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{
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xnew = x;
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ynew = y;
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if (zinitial / 2 == z) //appropriate criteria?
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{
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iAThalf = i;
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ynew = y + increments;
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}
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else
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xnew = x + increments;
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}
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else
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{
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xnew = x;
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ynew = y + increments;
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}
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znew = g_von_theta(xnew, ynew);
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zold = z;
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if(znew > z)
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{
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z = znew;
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x = xnew;
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y = ynew;
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}
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else
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if (xTOy == 1)
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xTOy = 2;
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}
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// Output
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plhs[0] = mxCreateDoubleScalar(x);
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plhs[1] = mxCreateDoubleScalar(y);
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plhs[2] = mxCreateDoubleScalar(z);
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plhs[3] = mxCreateDoubleScalar(i);
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return;
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}
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