// Use SVD to solve linear least squares problem
// result is statically allocated
void polyfit_reuse( double *y, int n, int degree, double *coeffs, double *workspace )
{ int ncoeffs = degree + 1;
double *u = workspace,
*w = u + n*ncoeffs,
*v = w + ncoeffs;
#ifdef DEBUG_POLYFIT_REUSE
printf("\n---Got---\n");
printf("\nU:\n");
mat_print( u, n, ncoeffs);
printf("\nS:\n");
mat_print( w, ncoeffs, 1);
printf("\nV:\n");
mat_print( v, ncoeffs, ncoeffs);
printf("\nU S V':\n");
mat_print(
matmul_right_transpose_static(
matmul_right_vec_as_diag_static( u, n, ncoeffs,
w, ncoeffs),
n, ncoeffs,
v, ncoeffs, ncoeffs),
n, ncoeffs);
#endif
svd_backsub( u, w, v, n, ncoeffs, y, coeffs );
}
int main(int argc, char* argv[])
{ double v[4], s[2];
double **ia = mat_index(A,NROWS,NCOLS),
**iv = mat_index(v,NROWS,NCOLS);
printf("Input\n");
mat_print( A, NROWS, NCOLS);
assert( svd(ia, NROWS, NCOLS, s, iv) );
free(ia);
free(iv);
printf("\n---Got---\n");
printf("\nU:\n");
mat_print( A, NROWS, NCOLS);
printf("\nS:\n");
mat_print( s, NCOLS, 1);
printf("\nV:\n");
mat_print( v, NCOLS, NCOLS);
printf("\nU S V':\n");
mat_print(
matmul_right_transpose_static(
matmul_right_vec_as_diag_static( A, NROWS, NCOLS,
s, NCOLS),
NROWS, NCOLS,
v, NCOLS, NCOLS),
NROWS, NCOLS);
printf("\n---Expected---\n");
printf("\nU:\n");
mat_print( U, NROWS, NCOLS);
printf("\nS:\n");
mat_print( S, NCOLS, 1);
printf("\nV:\n");
mat_print( V, NCOLS, NCOLS);
printf("\nU S V':\n");
mat_print(
matmul_right_transpose_static(
matmul_right_vec_as_diag_static( U, NROWS, NCOLS,
S, NCOLS),
NROWS, NCOLS,
V, NCOLS, NCOLS),
NROWS, NCOLS);
return 0;
}
void polyfit( double *x, double *y, int n, int degree, double *coeffs, double *workspace )
{ int ncoeffs = degree + 1;
double *u = workspace,
*w = u + n*ncoeffs,
*v = w + ncoeffs;
double **iu = mat_index(u, n,ncoeffs),
**iv = mat_index(v,ncoeffs,ncoeffs);
Vandermonde_Build(x,n,ncoeffs,u);
#ifdef DEBUG_POLYFIT
printf("\nV:\n");
mat_print( u, n, ncoeffs);
#endif
svd( iu, n, ncoeffs, w, iv );
free(iu);
free(iv);
svd_threshold( POLYFIT_SINGULAR_THRESHOLD, w, ncoeffs );
#ifdef DEBUG_POLYFIT
printf("\n---Got---\n");
printf("\nU:\n");
mat_print( u, n, ncoeffs);
printf("\nS:\n");
mat_print( w, ncoeffs, 1);
printf("\nV:\n");
mat_print( v, ncoeffs, ncoeffs);
printf("\nU S V':\n");
mat_print(
matmul_right_transpose_static(
matmul_right_vec_as_diag_static( u, n, ncoeffs,
w, ncoeffs),
n, ncoeffs,
v, ncoeffs, ncoeffs),
n, ncoeffs);
#endif
polyfit_reuse( y, n, degree, coeffs, workspace );
}
