void solve_reduced(int n, int m, double h_x[], double h_y[],
double a[], double x_x[], double x_y[],
double c_x[], double c_y[],
double workspace[], int step)
{
int i,j,k;
double *p_x;
double *p_y;
double *t_a;
double *t_c;
double *t_y;
p_x = workspace; /* together n + m + n*m + n + m = n*(m+2)+2*m */
p_y = p_x + n;
t_a = p_y + m;
t_c = t_a + n*m;
t_y = t_c + n;
if (step == PREDICTOR) {
choldc(h_x, n, p_x); /* do cholesky decomposition */
for (i=0; i<m; i++) /* forward pass for A' */
chol_forward(h_x, n, p_x, a+i*n, t_a+i*n);
for (i=0; i<m; i++) /* compute (h_y + a h_x^-1A') */
for (j=i; j<m; j++)
for (k=0; k<n; k++)
h_y[m*i + j] += t_a[n*j + k] * t_a[n*i + k];
choldc(h_y, m, p_y); /* and cholesky decomposition */
}
chol_forward(h_x, n, p_x, c_x, t_c);
/* forward pass for c */
for (i=0; i<m; i++) { /* and solve for x_y */
t_y[i] = c_y[i];
for (j=0; j<n; j++)
t_y[i] += t_a[i*n + j] * t_c[j];
}
cholsb(h_y, m, p_y, t_y, x_y);
for (i=0; i<n; i++) { /* finally solve for x_x */
t_c[i] = -t_c[i];
for (j=0; j<m; j++)
t_c[i] += t_a[j*n + i] * x_y[j];
}
chol_backward(h_x, n, p_x, t_c, x_x);
}
void linsys_solve(double a[], int n, int k, double b[], double x[], int flag, double f[])
{
unsigned int i,j ;
double *p=calloc(n, sizeof(double)) ;
choldc(a, n, p, f) ;
if (*f>0) /* check result */
{
free(p) ; /* matrix is not positiv definite */
return ;
} ;
for (i=0; i<k; i++)
cholsb(a, n, p, &b[i*n], &x[i*n]) ;
if (flag)
for (i=0; i<n; i++)
for (j=i+1; j<n; j++)
a[j*n+i]=a[j+i*n] ;
free(p) ;
}
