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
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
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
