UFLDL Exercise: Softmax Regression （softmax回归）

#include <math.h> #include "mex.h" double mymax(double x, double y) { if (x > y) return x; else return y; } double absolute(double x) { if (x >= -x) return x; else return -x; } void permuteInt(int *x, int p, int q) { int temp; temp = x[p]; x[p] = x[q]; x[q] = temp; } void permute(double *x, int p, int q) { double temp; temp = x[p]; x[p] = x[q]; x[q] = temp; } void permuteRows(double *x, int p, int q,int n) { int i; double temp; for(i = 0; i < n; i++) { temp = x[p+i*n]; x[p+i*n] = x[q+i*n]; x[q+i*n] = temp; } } void permuteCols(double *x, int p, int q,int n) { int i; double temp; for(i = 0; i < n; i++) { temp = x[i+p*n]; x[i+p*n] = x[i+q*n]; x[i+q*n] = temp; } } void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { int n,sizL[2],sizD[2],i,j,q,s, *P; double mu,gamma,xi,delta,beta,maxVal,theta, *c, *H, *L, *D, *A; /* Input */ H = mxGetPr(prhs[0]); if (nrhs == 1) { mu = 1e-12; } else { mu = mxGetScalar(prhs[1]); } /* Compute Sizes */ n = mxGetDimensions(prhs[0])[0]; /* Form Output */ sizL[0] = n; sizL[1] = n; plhs[0] = mxCreateNumericArray(2,sizL,mxDOUBLE_CLASS,mxREAL); L = mxGetPr(plhs[0]); sizD[0] = n; sizD[1] = 1; plhs[1] = mxCreateNumericArray(2,sizD,mxDOUBLE_CLASS,mxREAL); D = mxGetPr(plhs[1]); plhs[2] = mxCreateNumericArray(2,sizD,mxINT32_CLASS,mxREAL); P = (int*)mxGetData(plhs[2]); /* Initialize */ c = mxCalloc(n*n,sizeof(double)); A = mxCalloc(n*n,sizeof(double)); for (i = 0; i < n; i++) { P[i] = i; for (j = 0;j < n; j++) { A[i+n*j] = H[i+n*j]; } } gamma = 0; for (i = 0; i < n; i++) { L[i+n*i] = 1; c[i+n*i] = A[i+n*i]; } /* Compute modification parameters */ gamma = -1; xi = -1; for (i = 0; i < n; i++) { gamma = mymax(gamma,absolute(A[i+n*i])); for (j = 0;j < n; j++) { //printf("A(%d,%d) = %f, %f\n",i,j,A[i+n*j],absolute(A[i+n*j])); if (i != j) xi = mymax(xi,absolute(A[i+n*j])); } } delta = mu*mymax(gamma+xi,1); if (n > 1) { beta = sqrt(mymax(gamma,mymax(mu,xi/sqrt(n*n-1)))); } else { beta = sqrt(mymax(gamma,mu)); } for (j = 0; j < n; j++) { /* Find q that results in Best Permutation with j */ maxVal = -1; q = 0; for(i = j; i < n; i++) { if (absolute(c[i+n*i]) > maxVal) { maxVal = mymax(maxVal,absolute(c[i+n*i])); q = i; } } /* Permute D,c,L,A,P */ permute(D,j,q); permuteInt(P,j,q); permuteRows(c,j,q,n); permuteCols(c,j,q,n); permuteRows(L,j,q,n); permuteCols(L,j,q,n); permuteRows(A,j,q,n); permuteCols(A,j,q,n); for(s = 0; s <= j-1; s++) L[j+n*s] = c[j+n*s]/D[s]; for(i = j+1; i < n; i++) { c[i+j*n] = A[i+j*n]; for(s = 0; s <= j-1; s++) { c[i+j*n] -= L[j+n*s]*c[i+n*s]; } } theta = 0; if (j < n-1) { for(i = j+1;i < n; i++) theta = mymax(theta,absolute(c[i+n*j])); } D[j] = mymax(absolute(c[j+n*j]),mymax(delta,theta*theta/(beta*beta))); if (j < n-1) { for(i = j+1; i < n; i++) { c[i+n*i] = c[i+n*i] - c[i+n*j]*c[i+n*j]/D[j]; } } } for(i = 0; i < n; i++) P[i]++; mxFree(c); mxFree(A); }