def test_pinvarray_in_functions(self, arrays):
m_sb, high, m_bs = view_as(*arrays)
# hy.assume(hn.tall(m_bs))
hy.assume(hn.all_well_behaved(m_bs))
cond = np.linalg.cond(m_bs).max()
self.assertArrayAllClose(gf.matmul(m_bs.pinv, high),
gf.lstsq(m_bs, high),
cond=cond)
self.assertArrayAllClose(gf.matmul(m_sb, m_bs.pinv.t),
gf.rlstsq(m_sb, m_bs.t),
cond=cond)
xpout = la.pinvarray(np.empty_like(m_bs))
m_bs_p = np.multiply(m_bs.pinv, 2, out=xpout)
self.assertArrayAllClose(m_bs_p.pinv, xpout.pinv)
self.assertArrayAllClose(m_bs_p.pinv, m_bs / 2)
with self.assertRaises(TypeError):
gf.matmul(m_bs.pinv, m_sb.pinv)
self.assertArrayAllClose(gf.lstsq(m_sb.pinv, high),
gf.matmul(m_sb, high))
with self.assertRaises(TypeError):
gf.lstsq(high, m_sb.pinv)
self.assertArrayAllClose(gf.rlstsq(high.t, m_sb.t.pinv),
gf.matmul(high.t, m_sb.t))
with self.assertRaises(TypeError):
gf.rlstsq(m_sb.t.pinv, high.t)
with self.assertRaises(TypeError):
gf.rmatmul(m_sb.pinv, m_bs.pinv)
with self.assertRaises(TypeError):
gf.solve(m_sb.pinv, high)
with self.assertRaises(TypeError):
gf.rsolve(m_sb, m_bs.pinv)
def test_invarray_operators(self, arrays):
m_ss, m_bs, m_sb, mini, scal = view_as(*arrays)
scal[np.abs(scal) < 1e-5] += 1.
scal = scal.s
# hy.assume(hn.tall(m_bs))
hy.assume(hn.all_well_behaved(m_ss, mini))
cond = np.linalg.cond(m_ss).max()
self.assertArrayAllClose(m_ss.inv @ m_sb,
gf.solve(m_ss, m_sb),
cond=cond)
self.assertArrayAllClose(m_ss.inv() @ m_sb,
gf.solve(m_ss, m_sb),
cond=cond)
self.assertArrayAllClose(m_bs @ m_ss.inv,
gf.rsolve(m_bs, m_ss),
cond=cond)
self.assertArrayAllClose((m_ss.inv @ mini.inv).inv, mini @ m_ss)
self.assertArrayAllClose((m_ss.inv * 3.5).inv, m_ss / 3.5)
self.assertArrayAllClose((2.4 * m_ss.inv).inv, m_ss / 2.4)
self.assertArrayAllClose((m_ss.inv / 3.564).inv, m_ss * 3.564)
with self.assertRaises(TypeError):
45.564 / m_ss.inv # pylint: disable=pointless-statement
self.assertArrayAllClose((mini.inv * scal).inv, mini / scal)
self.assertArrayAllClose((scal * mini.inv).inv, mini / scal)
self.assertArrayAllClose((mini.inv / scal).inv, mini * scal)
with self.assertRaises(TypeError):
scal / mini.inv # pylint: disable=pointless-statement
with self.assertRaises(TypeError):
scal.inv * mini.inv # pylint: disable=pointless-statement
with self.assertRaises(TypeError):
m_ss + mini.inv # pylint: disable=pointless-statement
mini_ss = m_ss @ mini
mini_i = mini.inv
mini_i @= m_ss.inv
self.assertArrayAllClose(mini, mini_ss)
def test_functions_solve(self, arrays):
m_ss, m_sb, m_bs = arrays
hy.assume(hn.all_well_behaved(m_ss))
cond = np.linalg.cond(m_ss).max()
# with self.subTest('solve'):
self.assertArrayAllClose(la.solve(m_ss, m_sb),
gf.solve(m_ss, m_sb),
cond=cond)
slv_sh = utn.array_return_shape('(a,a),(a,b)->(a,b)', m_ss, m_sb)
slv_out = np.empty(slv_sh, m_ss.dtype)
slv_r = la.solve(m_ss, m_sb, out=slv_out)
self.assertArrayAllClose(slv_out, slv_r)
# with self.subTest('rsolve'):
self.assertArrayAllClose(la.rsolve(m_bs, m_ss),
gf.rsolve(m_bs, m_ss),
cond=cond)
def test_functions_matldiv(self, arrays):
m_ss, m_sb, m_bb, m_bs = arrays
hy.assume(hn.all_well_behaved(m_ss))
hy.assume(hn.wide(m_sb))
# with self.subTest('solve'):
self.assertArrayAllClose(la.matldiv(m_ss, m_sb), gf.solve(m_ss, m_sb))
slv_sh = utn.array_return_shape('(a,a),(a,b)->(a,b)', m_ss, m_sb)
slv_out = np.empty(slv_sh, m_ss.dtype)
slv_r = la.matldiv(m_ss, m_sb, out=slv_out)
cond = np.linalg.cond(m_ss).max()
self.assertArrayAllClose(slv_out, slv_r, cond=cond)
# with self.subTest('lstsq'):
cond = np.linalg.cond(m_bs).max()
self.assertArrayAllClose(la.matldiv(m_bs, m_bb),
gf.lstsq(m_bs, m_bb),
cond=cond)
cond = np.linalg.cond(m_sb).max()
self.assertArrayAllClose(la.matldiv(m_sb, m_ss),
gf.lstsq(m_sb, m_ss),
cond=cond)
def test_lnarray_operations_return_expected_values(self, arrays):
m_bs, m_ss, vec = view_as(*arrays)
m_bs_m = hn.core_only(m_bs)
vec = hn.core_only(vec, dims=1)
hy.assume(hn.tall(m_bs))
hy.assume(m_ss.ndim != 3) # causes np..solve's broadcasting issue
hy.assume(hn.all_well_behaved(m_ss, m_bs_m))
expect = utn.array_return_shape('(a,b),(b,c)->(a,c)', m_bs, m_ss)
ts_o = np.empty(expect, m_ss.dtype)
ts_r = la.matmul(m_bs, m_ss, ts_o)
self.assertArrayAllClose(ts_r, ts_o)
self.assertArrayAllClose(m_bs @ m_ss, np.matmul(m_bs, m_ss))
self.assertArrayAllClose(m_bs @ m_ss, np.matmul(m_bs, m_ss))
self.assertArrayAllClose(m_bs @ vec, np.matmul(m_bs, vec))
cond = np.linalg.cond(m_ss).max()
self.assertArrayAllClose(gf.solve(m_ss, vec),
nl.solve(m_ss, vec.c).uc,
cond=cond)
cond = np.linalg.cond(m_bs_m).max()
self.assertArrayAllClose(gf.lstsq(m_bs_m.t, vec),
nl.lstsq(m_bs_m.t, vec, rcond=None)[0],
cond=cond)
self.assertArrayAllClose(gf.rmatmul(m_ss, m_bs), np.matmul(m_bs, m_ss))
def test_invarray_in_functions(self, arrays):
m_ss, m_bs, m_sb, mini = view_as(*arrays)
# hy.assume(hn.tall(m_bs))
hy.assume(hn.all_well_behaved(m_ss, mini))
cond = np.linalg.cond(m_ss).max()
self.assertArrayAllClose(gf.matmul(m_ss.inv, m_sb),
gf.solve(m_ss, m_sb),
cond=cond)
self.assertArrayAllClose(gf.matmul(m_bs, m_ss.inv),
gf.rsolve(m_bs, m_ss),
cond=cond)
self.assertArrayAllClose(
gf.matmul(m_ss.inv, mini.inv).inv, mini @ m_ss)
self.assertArrayAllClose(gf.solve(m_ss.inv, m_sb),
gf.matmul(m_ss, m_sb))
self.assertArrayAllClose(
gf.solve(mini, m_ss.inv).inv, gf.matmul(m_ss, mini))
self.assertArrayAllClose(gf.solve(mini.inv, m_ss.inv),
gf.rsolve(mini, m_ss),
cond=cond)
self.assertArrayAllClose(gf.rsolve(m_ss, mini.inv),
gf.matmul(m_ss, mini))
self.assertArrayAllClose(
gf.rsolve(mini.inv, m_ss).inv, gf.matmul(m_ss, mini))
cond = np.linalg.cond(mini).max()
self.assertArrayAllClose(gf.rsolve(mini.inv, m_ss.inv),
gf.solve(mini, m_ss),
cond=cond)
self.assertArrayAllClose(gf.rmatmul(m_ss, mini.inv),
gf.solve(mini, m_ss),
cond=cond)
self.assertArrayAllClose(gf.rmatmul(mini.inv, m_ss),
gf.rsolve(m_ss, mini),
cond=cond)
self.assertArrayAllClose(
gf.rmatmul(mini.inv, m_ss.inv).inv, mini @ m_ss)