linalg_inline.hpp

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template <int N>
int ludcmp(double a[N][N], int indx[N], double vv[N]) {
  int i, imax, j, k, d;
  double big, dum, sum, temp;
 
  d = 1;
  for (i = 0; i < N; i++) {
    big = 0.0;
    for (j = 0; j < N; j++)
      if ((temp = fabs(a[i][j])) > big) big = temp;
    if (big == 0.0) {
      fprintf(stderr, "Singular matrix in routine ludcmp");
      exit(1);
    }
    vv[i] = 1.0 / big;
  }
  for (j = 0; j < N; j++) {
    for (i = 0; i < j; i++) {
      sum = a[i][j];
      for (k = 0; k < i; k++) sum -= a[i][k] * a[k][j];
      a[i][j] = sum;
    }
    big = 0.0;
    for (i = j; i < N; i++) {
      sum = a[i][j];
      for (k = 0; k < j; k++) sum -= a[i][k] * a[k][j];
      a[i][j] = sum;
      if ((dum = vv[i] * fabs(sum)) >= big) {
        big = dum;
        imax = i;
      }
    }
    if (j != imax) {
      for (k = 0; k < N; k++) {
        dum = a[imax][k];
        a[imax][k] = a[j][k];
        a[j][k] = dum;
      }
      d = -d;
      vv[imax] = vv[j];
    }
    indx[j] = imax;
    if (j != N - 1) {
      dum = (1.0 / a[j][j]);
      for (i = j + 1; i < N; i++) a[i][j] *= dum;
    }
  }
 
  return d;
}
 
template <int N>
void lubksb(double a[N][N], int indx[N], double b[N]) {
  int i, ii = 0, ip, j;
  double sum;
 
  for (i = 0; i < N; i++) {
    ip = indx[i];
    sum = b[ip];
    b[ip] = b[i];
    if (ii)
      for (j = ii - 1; j < i; j++) sum -= a[i][j] * b[j];
    else if (sum)
      ii = i + 1;
    b[i] = sum;
  }
  for (i = N - 1; i >= 0; i--) {
    sum = b[i];
    for (j = i + 1; j < N; j++) sum -= a[i][j] * b[j];
    b[i] = sum / a[i][i];
  }
}