def test_compose_sparse(self): import numpy as nm import scipy.sparse as sps from sfepy.linalg import compose_sparse ok = True # basic ma = sps.csr_matrix([[1, 0], [0, 1]]) mb = sps.coo_matrix([[1, 1]]) mk = compose_sparse([[ma, mb.T], [mb, 0]]) expected = nm.array([[1, 0, 1], [0, 1, 1], [1, 1, 0]]) _ok = nm.alltrue(mk.toarray() == expected) self.report('basic: %s' % _ok) ok = ok and _ok # sizes and slices ma = sps.csr_matrix([[2, 3]]) mb = sps.coo_matrix([[4, 5, 6]]) mk = compose_sparse([[ma, mb]], col_sizes=[2, 3]) expected = nm.array([[2, 3, 4, 5, 6]]) _ok = nm.alltrue(mk.toarray() == expected) self.report('sizes: %s' % _ok) ok = ok and _ok i1 = slice(1, 3) i2 = slice(8, 11) mk = compose_sparse([[ma, mb]], col_sizes=[i1, i2]) expected = nm.array([[0, 2, 3, 0, 0, 0, 0, 0, 4, 5, 6]]) _ok = nm.alltrue(mk.toarray() == expected) self.report('slices: %s' % _ok) ok = ok and _ok # zero block sizes and slices mk = compose_sparse([[0, ma, 0, mb, 0]], col_sizes=[1, 2, 5, 3, 1]) expected = nm.array([[0, 2, 3, 0, 0, 0, 0, 0, 4, 5, 6, 0]]) _ok = nm.alltrue(mk.toarray() == expected) self.report('zero block sizes: %s' % _ok) ok = ok and _ok expected = nm.array([[0, 2, 3, 0, 4, 5, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 5, 6]]) i0 = slice(0, 1) i1 = slice(1, 3) i2 = slice(4, 7) i3 = slice(8, 11) mk = compose_sparse([[0, ma, mb, 0], [0, 0, 0, mb]], col_sizes=[i0, i1, i2, i3]) _ok = nm.alltrue(mk.toarray() == expected) self.report('zero block slices: %s' % _ok) ok = ok and _ok return ok
def compute_jacobian(self, vec_x, fun_smooth_grad, fun_a_grad, fun_b_grad, vec_smooth_r, vec_a_r, vec_b_r): conf = self.conf mtx_s = fun_smooth_grad(vec_x) mtx_a = fun_a_grad(vec_x) mtx_b = fun_b_grad(vec_x) n_s = vec_smooth_r.shape[0] n_ns = vec_a_r.shape[0] if conf.semismooth: aa = nm.abs(vec_a_r) ab = nm.abs(vec_b_r) iz = nm.where((aa < (conf.macheps * max(aa.max(), 1.0))) & (ab < (conf.macheps * max(ab.max(), 1.0))))[0] inz = nm.setdiff1d(nm.arange(n_ns), iz) output('non_active/active: %d/%d' % (len(inz), len(iz))) mul_a = nm.empty_like(vec_a_r) mul_b = nm.empty_like(mul_a) # Non-active part of the jacobian. if len(inz) > 0: a_r_nz = vec_a_r[inz] b_r_nz = vec_b_r[inz] sqrt_ab = nm.sqrt(a_r_nz**2.0 + b_r_nz**2.0) mul_a[inz] = (a_r_nz / sqrt_ab) - 1.0 mul_b[inz] = (b_r_nz / sqrt_ab) - 1.0 # Active part of the jacobian. if len(iz) > 0: vec_z = nm.zeros_like(vec_x) vec_z[n_s+iz] = 1.0 mtx_a_z = mtx_a[iz] mtx_b_z = mtx_b[iz] sqrt_ab = nm.empty((iz.shape[0],), dtype=vec_a_r.dtype) for ir in range(len(iz)): row_a_z = mtx_a_z[ir] row_b_z = mtx_b_z[ir] sqrt_ab[ir] = nm.sqrt((row_a_z * row_a_z.T).todense() + (row_b_z * row_b_z.T).todense()) mul_a[iz] = ((mtx_a_z * vec_z) / sqrt_ab) - 1.0 mul_b[iz] = ((mtx_b_z * vec_z) / sqrt_ab) - 1.0 else: iz = nm.where(vec_a_r > vec_b_r)[0] mul_a = nm.zeros_like(vec_a_r) mul_b = nm.ones_like(mul_a) mul_a[iz] = 1.0 mul_b[iz] = 0.0 mtx_ns = sp.spdiags(mul_a, 0, n_ns, n_ns) * mtx_a \ + sp.spdiags(mul_b, 0, n_ns, n_ns) * mtx_b mtx_jac = compose_sparse([[mtx_s], [mtx_ns]]).tocsr() mtx_jac.sort_indices() return mtx_jac