def check_tangent_matrix( conf, vec_x0, fun, fun_grad ):
"""Verify the correctness of the tangent matrix as computed by fun_grad()
by comparing it with its finite difference approximation evaluated by
repeatedly calling fun() with vec_x items perturbed by a small delta."""
vec_x = vec_x0.copy()
delta = conf.delta
vec_r = fun( vec_x ) # Update state.
mtx_a0 = fun_grad( vec_x )
mtx_a = mtx_a0.tocsc()
mtx_d = mtx_a.copy()
mtx_d.data[:] = 0.0
vec_dx = nm.zeros_like( vec_r )
for ic in range( vec_dx.shape[0] ):
vec_dx[ic] = delta
xx = vec_x.copy() - vec_dx
vec_r1 = fun( xx )
vec_dx[ic] = -delta
xx = vec_x.copy() - vec_dx
vec_r2 = fun( xx )
vec_dx[ic] = 0.0;
vec = 0.5 * (vec_r2 - vec_r1) / delta
## ir = mtx_a.indices[mtx_a.indptr[ic]:mtx_a.indptr[ic+1]]
## for ii in ir:
## mtx_d[ii,ic] = vec[ii]
ir = mtx_a.indices[mtx_a.indptr[ic]:mtx_a.indptr[ic+1]]
mtx_d.data[mtx_a.indptr[ic]:mtx_a.indptr[ic+1]] = vec[ir]
vec_r = fun( vec_x ) # Restore.
tt = time.clock()
print mtx_a, '.. analytical'
print mtx_d, '.. difference'
import sfepy.base.plotutils as plu
plu.plot_matrix_diff( mtx_d, mtx_a, delta, ['difference', 'analytical'],
conf.check )
return time.clock() - tt
def check_tangent_matrix( conf, vec_x0, mtx_a0, evaluator ):
vec_x = vec_x0.copy()
delta = conf.delta
vec_r, status = evaluator.eval_residual( vec_x ) # Update state.
mtx_a0, status = evaluator.eval_tangent_matrix( vec_x, mtx_a0 )
mtx_a = mtx_a0.tocsc()
mtx_d = mtx_a.copy()
mtx_d.data[:] = 0.0
vec_dx = nm.zeros_like( vec_r )
for ic in range( vec_dx.shape[0] ):
vec_dx[ic] = delta
xx = vec_x.copy()
evaluator.update_vec( xx, vec_dx )
vec_r1, status = evaluator.eval_residual( xx )
vec_dx[ic] = -delta
xx = vec_x.copy()
evaluator.update_vec( xx, vec_dx )
vec_r2, status = evaluator.eval_residual( xx )
vec_dx[ic] = 0.0;
vec = 0.5 * (vec_r2 - vec_r1) / delta
## ir = mtx_a.indices[mtx_a.indptr[ic]:mtx_a.indptr[ic+1]]
## for ii in ir:
## mtx_d[ii,ic] = vec[ii]
ir = mtx_a.indices[mtx_a.indptr[ic]:mtx_a.indptr[ic+1]]
mtx_d.data[mtx_a.indptr[ic]:mtx_a.indptr[ic+1]] = vec[ir]
vec_r, status = evaluator.eval_residual( vec_x ) # Restore.
tt = time.clock()
print mtx_a, '.. analytical'
print mtx_d, '.. difference'
plu.plot_matrix_diff( mtx_d, mtx_a, delta, ['difference', 'analytical'],
conf.check )
return time.clock() - tt