is_approx: Set precision as was proposed in eigenpy

Author: Lucas-Haubert

tests/test_complex_schur.py

@@ -12,8 +12,8 @@
 T = cs.matrixT()
 
 A_complex = A.astype(complex)
-assert nanoeigenpy.is_approx(A_complex, U @ T @ U.conj().T, 1e-10)
-assert nanoeigenpy.is_approx(U @ U.conj().T, np.eye(dim), 1e-10)
+assert nanoeigenpy.is_approx(A_complex, U @ T @ U.conj().T)
+assert nanoeigenpy.is_approx(U @ U.conj().T, np.eye(dim))
 
 for row in range(1, dim):
     for col in range(row):
@@ -32,20 +32,20 @@
 T2 = cs2.matrixT()
 U2 = cs2.matrixU()
 
-assert nanoeigenpy.is_approx(T1, T2, 1e-12)
-assert nanoeigenpy.is_approx(U1, U2, 1e-12)
+assert nanoeigenpy.is_approx(T1, T2)
+assert nanoeigenpy.is_approx(U1, U2)
 
 cs_no_u = nanoeigenpy.ComplexSchur(A, False)
 assert cs_no_u.info() == nanoeigenpy.ComputationInfo.Success
 T_no_u = cs_no_u.matrixT()
 
-assert nanoeigenpy.is_approx(T, T_no_u, 1e-12)
+assert nanoeigenpy.is_approx(T, T_no_u)
 
 cs_compute_no_u = nanoeigenpy.ComplexSchur(dim)
 result_no_u = cs_compute_no_u.compute(A, False)
 assert result_no_u.info() == nanoeigenpy.ComputationInfo.Success
 T_compute_no_u = cs_compute_no_u.matrixT()
-assert nanoeigenpy.is_approx(T, T_compute_no_u, 1e-12)
+assert nanoeigenpy.is_approx(T, T_compute_no_u)
 
 cs_iter = nanoeigenpy.ComplexSchur(dim)
 cs_iter.setMaxIterations(30 * dim)  # m_maxIterationsPerRow * size
@@ -55,8 +55,8 @@
 
 T_iter = cs_iter.matrixT()
 U_iter = cs_iter.matrixU()
-assert nanoeigenpy.is_approx(T, T_iter, 1e-12)
-assert nanoeigenpy.is_approx(U, U_iter, 1e-12)
+assert nanoeigenpy.is_approx(T, T_iter)
+assert nanoeigenpy.is_approx(U, U_iter)
 
 cs_few_iter = nanoeigenpy.ComplexSchur(dim)
 cs_few_iter.setMaxIterations(1)
@@ -73,8 +73,8 @@
 U_triangular = cs_triangular.matrixU()
 
 A_triangular_complex = A_triangular.astype(complex)
-assert nanoeigenpy.is_approx(T_triangular, A_triangular_complex, 1e-10)
-assert nanoeigenpy.is_approx(U_triangular, np.eye(dim, dtype=complex), 1e-10)
+assert nanoeigenpy.is_approx(T_triangular, A_triangular_complex)
+assert nanoeigenpy.is_approx(U_triangular, np.eye(dim, dtype=complex))
 
 hess = nanoeigenpy.HessenbergDecomposition(A)
 H = hess.matrixH()
@@ -89,7 +89,7 @@
 
 A_complex = A.astype(complex)
 assert nanoeigenpy.is_approx(
-    A_complex, U_from_hess @ T_from_hess @ U_from_hess.conj().T, 1e-10
+    A_complex, U_from_hess @ T_from_hess @ U_from_hess.conj().T
 )
 
 cs1_id = nanoeigenpy.ComplexSchur(dim)

tests/test_full_piv_lu.py

@@ -57,7 +57,7 @@
 kernel = fullpivlu.kernel()
 image = fullpivlu.image(A)
 assert kernel.shape[1] == 1
-assert nanoeigenpy.is_approx(A @ kernel, np.zeros((dim, 1)), 1e-10)
+assert nanoeigenpy.is_approx(A @ kernel, np.zeros((dim, 1)))
 assert image.shape[1] == rank
 
 inverse = fullpivlu.inverse()

tests/test_generalized_eigen_solver.py

@@ -34,8 +34,8 @@
 
     Av = A @ v
     lambda_Bv = lambda_k * (B @ v)
-    assert nanoeigenpy.is_approx(Av.real, lambda_Bv.real, 1e-10)
-    assert nanoeigenpy.is_approx(Av.imag, lambda_Bv.imag, 1e-10)
+    assert nanoeigenpy.is_approx(Av.real, lambda_Bv.real, 1e-6)
+    assert nanoeigenpy.is_approx(Av.imag, lambda_Bv.imag, 1e-6)
 
 for k in range(dim):
     v = eigenvectors[:, k]
@@ -44,8 +44,8 @@
 
     alpha_Bv = alpha * (B @ v)
     beta_Av = beta * (A @ v)
-    assert nanoeigenpy.is_approx(alpha_Bv.real, beta_Av.real, 1e-10)
-    assert nanoeigenpy.is_approx(alpha_Bv.imag, beta_Av.imag, 1e-10)
+    assert nanoeigenpy.is_approx(alpha_Bv.real, beta_Av.real, 1e-6)
+    assert nanoeigenpy.is_approx(alpha_Bv.imag, beta_Av.imag, 1e-6)
 
 for k in range(dim):
     if abs(betas[k]) > 1e-12:

tests/test_generalized_self_adjoint_eigen_solver.py

@@ -20,7 +20,7 @@
 
 @pytest.mark.parametrize("options", _options)
 def test_generalized_selfadjoint_eigensolver(options):
-    dim = 5
+    dim = 100
     rng = np.random.default_rng()
     A = rng.random((dim, dim))
     A = (A + A.T) * 0.5
@@ -49,10 +49,10 @@ def test_generalized_selfadjoint_eigensolver(options):
                 lam = D[i]
                 Av = A @ v
                 lam_Bv = lam * (B @ v)
-                assert nanoeigenpy.is_approx(Av, lam_Bv, 1e-10)
+                assert nanoeigenpy.is_approx(Av, lam_Bv, 1e-6)
 
             VT_B_V = V.T @ B @ V
-            assert nanoeigenpy.is_approx(VT_B_V, np.eye(dim), 1e-10)
+            assert nanoeigenpy.is_approx(VT_B_V, np.eye(dim), 1e-6)
 
         elif options & nanoeigenpy.DecompositionOptions.ABx_lx.value:
             AB = A @ B
@@ -61,7 +61,7 @@ def test_generalized_selfadjoint_eigensolver(options):
                 lam = D[i]
                 ABv = AB @ v
                 lam_v = lam * v
-                assert nanoeigenpy.is_approx(ABv, lam_v, 1e-10)
+                assert nanoeigenpy.is_approx(ABv, lam_v, 1e-6)
 
         elif options & nanoeigenpy.DecompositionOptions.BAx_lx.value:
             BA = B @ A
@@ -70,7 +70,7 @@ def test_generalized_selfadjoint_eigensolver(options):
                 lam = D[i]
                 BAv = BA @ v
                 lam_v = lam * v
-                assert nanoeigenpy.is_approx(BAv, lam_v, 1e-10)
+                assert nanoeigenpy.is_approx(BAv, lam_v, 1e-6)
 
     _gsaes_compute = gsaes.compute(A, B)
     _gsaes_compute_options = gsaes.compute(A, B, options)

tests/test_hessenberg_decomposition.py

@@ -14,7 +14,7 @@
     A_reconstructed = Q @ H @ Q.conj().T
 else:
     A_reconstructed = Q @ H @ Q.T
-assert nanoeigenpy.is_approx(A, A_reconstructed, 1e-10)
+assert nanoeigenpy.is_approx(A, A_reconstructed)
 
 for row in range(2, dim):
     for col in range(row - 1):
@@ -24,7 +24,7 @@
     QQ_conj = Q @ Q.conj().T
 else:
     QQ_conj = Q @ Q.T
-assert nanoeigenpy.is_approx(QQ_conj, np.eye(dim), 1e-10)
+assert nanoeigenpy.is_approx(QQ_conj, np.eye(dim))
 
 A_test = rng.random((dim, dim))
 hess1 = nanoeigenpy.HessenbergDecomposition(dim)
@@ -36,8 +36,8 @@
 Q1 = hess1.matrixQ()
 Q2 = hess2.matrixQ()
 
-assert nanoeigenpy.is_approx(H1, H2, 1e-12)
-assert nanoeigenpy.is_approx(Q1, Q2, 1e-12)
+assert nanoeigenpy.is_approx(H1, H2)
+assert nanoeigenpy.is_approx(Q1, Q2)
 
 hCoeffs = hess.householderCoefficients()
 packed = hess.packedMatrix()

tests/test_real_qz.py

@@ -14,11 +14,11 @@
 Z = realqz.matrixZ()
 T = realqz.matrixT()
 
-assert nanoeigenpy.is_approx(A, Q @ S @ Z, 1e-10)
-assert nanoeigenpy.is_approx(B, Q @ T @ Z, 1e-10)
+assert nanoeigenpy.is_approx(A, Q @ S @ Z)
+assert nanoeigenpy.is_approx(B, Q @ T @ Z)
 
-assert nanoeigenpy.is_approx(Q @ Q.T, np.eye(dim), 1e-10)
-assert nanoeigenpy.is_approx(Z @ Z.T, np.eye(dim), 1e-10)
+assert nanoeigenpy.is_approx(Q @ Q.T, np.eye(dim))
+assert nanoeigenpy.is_approx(Z @ Z.T, np.eye(dim))
 
 for i in range(dim):
     for j in range(i):
@@ -61,8 +61,8 @@
 S_without = realqz_without_qz.matrixS()
 T_without = realqz_without_qz.matrixT()
 
-assert nanoeigenpy.is_approx(S_with, S_without, 1e-12)
-assert nanoeigenpy.is_approx(T_with, T_without, 1e-12)
+assert nanoeigenpy.is_approx(S_with, S_without)
+assert nanoeigenpy.is_approx(T_with, T_without)
 
 iterations = realqz.iterations()
 assert iterations >= 0

tests/test_real_schur.py

@@ -29,8 +29,8 @@ def verify_is_quasi_triangular(T):
 U = rs.matrixU()
 T = rs.matrixT()
 
-assert nanoeigenpy.is_approx(A, U @ T @ U.T, 1e-10)
-assert nanoeigenpy.is_approx(U @ U.T, np.eye(dim), 1e-10)
+assert nanoeigenpy.is_approx(A, U @ T @ U.T)
+assert nanoeigenpy.is_approx(U @ U.T, np.eye(dim))
 
 verify_is_quasi_triangular(T)
 
@@ -47,20 +47,20 @@ def verify_is_quasi_triangular(T):
 T2 = rs2.matrixT()
 U2 = rs2.matrixU()
 
-assert nanoeigenpy.is_approx(T1, T2, 1e-12)
-assert nanoeigenpy.is_approx(U1, U2, 1e-12)
+assert nanoeigenpy.is_approx(T1, T2)
+assert nanoeigenpy.is_approx(U1, U2)
 
 rs_no_u = nanoeigenpy.RealSchur(A, False)
 assert rs_no_u.info() == nanoeigenpy.ComputationInfo.Success
 T_no_u = rs_no_u.matrixT()
 
-assert nanoeigenpy.is_approx(T, T_no_u, 1e-12)
+assert nanoeigenpy.is_approx(T, T_no_u)
 
 rs_compute_no_u = nanoeigenpy.RealSchur(dim)
 result_no_u = rs_compute_no_u.compute(A, False)
 assert result_no_u.info() == nanoeigenpy.ComputationInfo.Success
 T_compute_no_u = rs_compute_no_u.matrixT()
-assert nanoeigenpy.is_approx(T, T_compute_no_u, 1e-12)
+assert nanoeigenpy.is_approx(T, T_compute_no_u)
 
 rs_iter = nanoeigenpy.RealSchur(dim)
 rs_iter.setMaxIterations(40 * dim)  # m_maxIterationsPerRow * size
@@ -70,8 +70,8 @@ def verify_is_quasi_triangular(T):
 
 T_iter = rs_iter.matrixT()
 U_iter = rs_iter.matrixU()
-assert nanoeigenpy.is_approx(T, T_iter, 1e-12)
-assert nanoeigenpy.is_approx(U, U_iter, 1e-12)
+assert nanoeigenpy.is_approx(T, T_iter)
+assert nanoeigenpy.is_approx(U, U_iter)
 
 if dim > 2:
     rs_few_iter = nanoeigenpy.RealSchur(dim)
@@ -88,8 +88,8 @@ def verify_is_quasi_triangular(T):
 T_triangular = rs_triangular.matrixT()
 U_triangular = rs_triangular.matrixU()
 
-assert nanoeigenpy.is_approx(T_triangular, A_triangular, 1e-10)
-assert nanoeigenpy.is_approx(U_triangular, np.eye(dim), 1e-10)
+assert nanoeigenpy.is_approx(T_triangular, A_triangular)
+assert nanoeigenpy.is_approx(U_triangular, np.eye(dim))
 
 hess = nanoeigenpy.HessenbergDecomposition(A)
 H = hess.matrixH()
@@ -102,7 +102,7 @@ def verify_is_quasi_triangular(T):
 T_from_hess = rs_from_hess.matrixT()
 U_from_hess = rs_from_hess.matrixU()
 
-assert nanoeigenpy.is_approx(A, U_from_hess @ T_from_hess @ U_from_hess.T, 1e-10)
+assert nanoeigenpy.is_approx(A, U_from_hess @ T_from_hess @ U_from_hess.T)
 
 rs1_id = nanoeigenpy.RealSchur(dim)
 rs2_id = nanoeigenpy.RealSchur(dim)

tests/test_self_adjoint_eigen_solver.py

@@ -17,4 +17,4 @@
 AdotV = A @ V
 VdotD = V @ np.diag(D)
 
-assert nanoeigenpy.is_approx(AdotV, VdotD, 1e-10)
+assert nanoeigenpy.is_approx(AdotV, VdotD, 1e-6)

tests/test_tridiagonalization.py

@@ -11,15 +11,15 @@
 Q = tri.matrixQ()
 T = tri.matrixT()
 
-assert nanoeigenpy.is_approx(A, Q @ T @ Q.T, 1e-10)
-assert nanoeigenpy.is_approx(Q @ Q.T, np.eye(dim), 1e-10)
+assert nanoeigenpy.is_approx(A, Q @ T @ Q.T)
+assert nanoeigenpy.is_approx(Q @ Q.T, np.eye(dim))
 
 for i in range(dim):
     for j in range(dim):
         if abs(i - j) > 1:
             assert abs(T[i, j]) < 1e-12
 
-assert nanoeigenpy.is_approx(T, T.T, 1e-12)
+assert nanoeigenpy.is_approx(T, T.T)
 
 diag = tri.diagonal()
 sub_diag = tri.subDiagonal()
@@ -42,8 +42,8 @@
 Q2 = tri2.matrixQ()
 T2 = tri2.matrixT()
 
-assert nanoeigenpy.is_approx(Q1, Q2, 1e-12)
-assert nanoeigenpy.is_approx(T1, T2, 1e-12)
+assert nanoeigenpy.is_approx(Q1, Q2)
+assert nanoeigenpy.is_approx(T1, T2)
 
 h_coeffs = tri.householderCoefficients()
 packed = tri.packedMatrix()
@@ -65,7 +65,7 @@
 Q_diag = tri_diag.matrixQ()
 T_diag = tri_diag.matrixT()
 
-assert nanoeigenpy.is_approx(A_diag, Q_diag @ T_diag @ Q_diag.T, 1e-10)
+assert nanoeigenpy.is_approx(A_diag, Q_diag @ T_diag @ Q_diag.T)
 for i in range(dim):
     for j in range(dim):
         if i != j:
@@ -83,7 +83,7 @@
 Q_tridiag = tri_tridiag.matrixQ()
 T_tridiag = tri_tridiag.matrixT()
 
-assert nanoeigenpy.is_approx(A_tridiag, Q_tridiag @ T_tridiag @ Q_tridiag.T, 1e-10)
+assert nanoeigenpy.is_approx(A_tridiag, Q_tridiag @ T_tridiag @ Q_tridiag.T)
 
 
 tri1_id = nanoeigenpy.Tridiagonalization(dim)