Returns:
The one-particle reduced density matrix of the Slater determinant.
"""
- # TODO figure out why mypy complains about this line with
- # error: Need type annotation for "one_rdm" [var-annotated]
- one_rdm = np.zeros((2 * norb, 2 * norb), dtype=complex) # type: ignore
+ one_rdm = np.zeros((2 * norb, 2 * norb), dtype=complex)
alpha_orbitals = np.array(occupied_orbitals[0])
beta_orbitals = np.array(occupied_orbitals[1]) + norb
one_rdm[(alpha_orbitals, alpha_orbitals)] = 1
diff --git a/searchindex.js b/searchindex.js
index 8c146e16d..d2795f920 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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(ffsim.doublefactorizedhamiltonian property)": [[0, "ffsim.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.norb"]], "norb (ffsim.molecularhamiltonian property)": [[0, "ffsim.MolecularHamiltonian.norb"]], "norb (ffsim.ucjoperator property)": [[0, "ffsim.UCJOperator.norb"]], "normal_ordered() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.normal_ordered"]], "one_body_tensor (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.one_body_tensor"]], "one_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.one_body_tensor"]], "one_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.one_body_tensor"]], "one_hot() (in module ffsim)": [[0, "ffsim.one_hot"]], "orb (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.orb"]], "orbital_rotations (ffsim.doublefactorizedhamiltonian attribute)": [[0, 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"one_body_linop() (in module ffsim.contract)": [[1, "ffsim.contract.one_body_linop"]], "apply_matrix_to_slices() (in module ffsim.linalg)": [[2, "ffsim.linalg.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg)": [[2, "ffsim.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[2, "module-ffsim.linalg"]], "givens_decomposition() (in module ffsim.linalg)": [[2, "ffsim.linalg.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_unitary"]], "lup() (in module ffsim.linalg)": [[2, "ffsim.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg)": [[2, "ffsim.linalg.modified_cholesky"]], "reduced_matrix() (in module ffsim.linalg)": [[2, "ffsim.linalg.reduced_matrix"]], "ffsim.random": [[3, "module-ffsim.random"]], "random_antihermitian() (in module ffsim.random)": [[3, "ffsim.random.random_antihermitian"]], "random_hermitian() (in module ffsim.random)": [[3, "ffsim.random.random_hermitian"]], "random_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_orthogonal"]], "random_real_symmetric_matrix() (in module ffsim.random)": [[3, "ffsim.random.random_real_symmetric_matrix"]], "random_special_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_special_orthogonal"]], "random_statevector() (in module ffsim.random)": [[3, "ffsim.random.random_statevector"]], "random_t2_amplitudes() (in module ffsim.random)": [[3, "ffsim.random.random_t2_amplitudes"]], "random_two_body_tensor_real() (in module ffsim.random)": [[3, "ffsim.random.random_two_body_tensor_real"]], "random_unitary() (in module ffsim.random)": [[3, "ffsim.random.random_unitary"]], "ffsim.testing": [[4, "module-ffsim.testing"]], "random_nelec() (in module ffsim.testing)": [[4, "ffsim.testing.random_nelec"]], "random_occupied_orbitals() (in module ffsim.testing)": [[4, "ffsim.testing.random_occupied_orbitals"]]}})
\ No newline at end of file
+Search.setIndex({"docnames": ["api/ffsim", "api/ffsim.contract", "api/ffsim.linalg", "api/ffsim.random", "api/ffsim.testing", "index", "tutorials/01-introduction", "tutorials/02-orbital-rotation", "tutorials/03-double-factorized", "tutorials/04-lucj", "tutorials/05-entanglement-forging", "tutorials/06-fermion-operator"], "filenames": ["api/ffsim.rst", "api/ffsim.contract.rst", "api/ffsim.linalg.rst", "api/ffsim.random.rst", "api/ffsim.testing.rst", "index.rst", "tutorials/01-introduction.ipynb", "tutorials/02-orbital-rotation.ipynb", "tutorials/03-double-factorized.ipynb", "tutorials/04-lucj.ipynb", "tutorials/05-entanglement-forging.ipynb", "tutorials/06-fermion-operator.ipynb"], "titles": ["ffsim", "ffsim.contract", "ffsim.linalg", "ffsim.random", "ffsim.testing", "Welcome to ffsim\u2019s documentation!", "Introduction to ffsim", "Orbital rotations and quadratic Hamiltonians", "Diagonal Coulomb operators and double-factorized Trotter simulation", "The local unitary cluster Jastrow 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\ No newline at end of file
diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb
index d47f2cc0e..f1cb415c1 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
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+ "shell.execute_reply": "2023-10-25T21:08:37.728661Z"
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@@ -62,10 +62,10 @@
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- "shell.execute_reply": "2023-10-25T21:06:54.991423Z"
+ "iopub.execute_input": "2023-10-25T21:08:37.734177Z",
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+ "iopub.status.idle": "2023-10-25T21:08:37.738009Z",
+ "shell.execute_reply": "2023-10-25T21:08:37.737381Z"
}
},
"outputs": [],
@@ -93,10 +93,10 @@
"execution_count": 3,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:54.996114Z",
- "iopub.status.busy": "2023-10-25T21:06:54.995720Z",
- "iopub.status.idle": "2023-10-25T21:06:55.000745Z",
- "shell.execute_reply": "2023-10-25T21:06:54.999964Z"
+ "iopub.execute_input": "2023-10-25T21:08:37.741569Z",
+ "iopub.status.busy": "2023-10-25T21:08:37.741092Z",
+ "iopub.status.idle": "2023-10-25T21:08:37.744522Z",
+ "shell.execute_reply": "2023-10-25T21:08:37.743856Z"
}
},
"outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index 5094d123b..3235216ef 100644
--- a/tutorials/02-orbital-rotation.ipynb
+++ b/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
"execution_count": 1,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:57.080519Z",
- "iopub.status.busy": "2023-10-25T21:06:57.080023Z",
- "iopub.status.idle": "2023-10-25T21:06:57.466704Z",
- "shell.execute_reply": "2023-10-25T21:06:57.465754Z"
+ "iopub.execute_input": "2023-10-25T21:08:39.742918Z",
+ "iopub.status.busy": "2023-10-25T21:08:39.742349Z",
+ "iopub.status.idle": "2023-10-25T21:08:40.131149Z",
+ "shell.execute_reply": "2023-10-25T21:08:40.130262Z"
}
},
"outputs": [],
@@ -111,10 +111,10 @@
"execution_count": 2,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:57.471609Z",
- "iopub.status.busy": "2023-10-25T21:06:57.471207Z",
- "iopub.status.idle": "2023-10-25T21:06:57.509773Z",
- "shell.execute_reply": "2023-10-25T21:06:57.508635Z"
+ "iopub.execute_input": "2023-10-25T21:08:40.135978Z",
+ "iopub.status.busy": "2023-10-25T21:08:40.135513Z",
+ "iopub.status.idle": "2023-10-25T21:08:40.175106Z",
+ "shell.execute_reply": "2023-10-25T21:08:40.174099Z"
}
},
"outputs": [],
@@ -158,10 +158,10 @@
"execution_count": 3,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:57.513608Z",
- "iopub.status.busy": "2023-10-25T21:06:57.513367Z",
- "iopub.status.idle": "2023-10-25T21:06:57.535938Z",
- "shell.execute_reply": "2023-10-25T21:06:57.535161Z"
+ "iopub.execute_input": "2023-10-25T21:08:40.180565Z",
+ "iopub.status.busy": "2023-10-25T21:08:40.179394Z",
+ "iopub.status.idle": "2023-10-25T21:08:40.194618Z",
+ "shell.execute_reply": "2023-10-25T21:08:40.193830Z"
}
},
"outputs": [],
@@ -201,10 +201,10 @@
"execution_count": 4,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:57.539737Z",
- "iopub.status.busy": "2023-10-25T21:06:57.539509Z",
- "iopub.status.idle": "2023-10-25T21:06:57.546884Z",
- "shell.execute_reply": "2023-10-25T21:06:57.546144Z"
+ "iopub.execute_input": "2023-10-25T21:08:40.198998Z",
+ "iopub.status.busy": "2023-10-25T21:08:40.197895Z",
+ "iopub.status.idle": "2023-10-25T21:08:40.205019Z",
+ "shell.execute_reply": "2023-10-25T21:08:40.204228Z"
}
},
"outputs": [],
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index 53fcc317f..7cd5fa759 100644
--- a/tutorials/03-double-factorized.ipynb
+++ b/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
"execution_count": 1,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.408368Z",
- "iopub.status.busy": "2023-10-25T21:06:59.407942Z",
- "iopub.status.idle": "2023-10-25T21:06:59.914950Z",
- "shell.execute_reply": "2023-10-25T21:06:59.913923Z"
+ "iopub.execute_input": "2023-10-25T21:08:41.954783Z",
+ "iopub.status.busy": "2023-10-25T21:08:41.954389Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.447245Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.446529Z"
}
},
"outputs": [
@@ -92,10 +92,10 @@
"execution_count": 2,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.928012Z",
- "iopub.status.busy": "2023-10-25T21:06:59.927218Z",
- "iopub.status.idle": "2023-10-25T21:06:59.934847Z",
- "shell.execute_reply": "2023-10-25T21:06:59.934060Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.465427Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.465038Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.472055Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.471478Z"
}
},
"outputs": [
@@ -226,10 +226,10 @@
"execution_count": 3,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.938180Z",
- "iopub.status.busy": "2023-10-25T21:06:59.937705Z",
- "iopub.status.idle": "2023-10-25T21:06:59.943294Z",
- "shell.execute_reply": "2023-10-25T21:06:59.942655Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.475371Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.474914Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.480136Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.479530Z"
}
},
"outputs": [],
@@ -284,10 +284,10 @@
"execution_count": 4,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.946847Z",
- "iopub.status.busy": "2023-10-25T21:06:59.946279Z",
- "iopub.status.idle": "2023-10-25T21:06:59.950923Z",
- "shell.execute_reply": "2023-10-25T21:06:59.950186Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.483229Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.482635Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.487395Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.486648Z"
}
},
"outputs": [],
@@ -324,10 +324,10 @@
"execution_count": 5,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.954158Z",
- "iopub.status.busy": "2023-10-25T21:06:59.953707Z",
- "iopub.status.idle": "2023-10-25T21:06:59.959974Z",
- "shell.execute_reply": "2023-10-25T21:06:59.959325Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.490423Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.490047Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.496121Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.495452Z"
}
},
"outputs": [
@@ -366,10 +366,10 @@
"execution_count": 6,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.963539Z",
- "iopub.status.busy": "2023-10-25T21:06:59.962917Z",
- "iopub.status.idle": "2023-10-25T21:06:59.978690Z",
- "shell.execute_reply": "2023-10-25T21:06:59.977952Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.499169Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.498798Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.513602Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.512833Z"
}
},
"outputs": [
@@ -408,10 +408,10 @@
"execution_count": 7,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.982423Z",
- "iopub.status.busy": "2023-10-25T21:06:59.982004Z",
- "iopub.status.idle": "2023-10-25T21:06:59.992865Z",
- "shell.execute_reply": "2023-10-25T21:06:59.992152Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.517185Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.516593Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.526898Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.526265Z"
}
},
"outputs": [
@@ -449,10 +449,10 @@
"execution_count": 8,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:06:59.995810Z",
- "iopub.status.busy": "2023-10-25T21:06:59.995534Z",
- "iopub.status.idle": "2023-10-25T21:07:00.054646Z",
- "shell.execute_reply": "2023-10-25T21:07:00.053963Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.529939Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.529675Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.591076Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.589087Z"
}
},
"outputs": [
@@ -492,10 +492,10 @@
"execution_count": 9,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:07:00.058808Z",
- "iopub.status.busy": "2023-10-25T21:07:00.057468Z",
- "iopub.status.idle": "2023-10-25T21:07:00.098846Z",
- "shell.execute_reply": "2023-10-25T21:07:00.098143Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.595003Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.594745Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.634491Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.632865Z"
}
},
"outputs": [
@@ -534,10 +534,10 @@
"execution_count": 10,
"metadata": {
"execution": {
- "iopub.execute_input": "2023-10-25T21:07:00.104116Z",
- "iopub.status.busy": "2023-10-25T21:07:00.102927Z",
- "iopub.status.idle": "2023-10-25T21:07:00.127804Z",
- "shell.execute_reply": "2023-10-25T21:07:00.127092Z"
+ "iopub.execute_input": "2023-10-25T21:08:42.637571Z",
+ "iopub.status.busy": "2023-10-25T21:08:42.637290Z",
+ "iopub.status.idle": "2023-10-25T21:08:42.656002Z",
+ "shell.execute_reply": "2023-10-25T21:08:42.655099Z"
}
},
"outputs": [
diff --git a/tutorials/04-lucj.html b/tutorials/04-lucj.html
index 6e0a4d8ec..ea5d845ba 100644
--- a/tutorials/04-lucj.html
+++ b/tutorials/04-lucj.html
@@ -96,7 +96,7 @@ The local unitary cluster Jastrow (LUCJ) ansatz
converged SCF energy = -77.4456267643962
-CASCI E = -77.6290254326716 E(CI) = -3.57322412553862 S^2 = 0.0000000
+CASCI E = -77.6290254326717 E(CI) = -3.57322412553862 S^2 = 0.0000000
-E(CCSD) = -77.49387212754471 E_corr = -0.04824536314851433
-Energy at initialialization: -77.4697560002168
+E(CCSD) = -77.49387212754471 E_corr = -0.04824536314851303
+Energy at initialialization: -77.46975600021699
To facilitate variational optimization of the ansatz, UCJOperator implements methods for conversion to and from a vector of real-valued parameters. The precise relation between a parameter vector and the matrices of the UCJ operator is somewhat complicated. In short, the parameter vector stores the entries of the UCJ matrices in a non-redundant way (for the orbital rotations, the parameter vector actually stores the entries of their generators.)
-Energy at initialialization: -75.6836617444762
+Energy at initialialization: -75.68366174447624
FermionOperator({
- (cre_a(0), des_a(3)): 0.5,
+ (cre_b(1), des_b(5), cre_a(4)): 1+1j,
(cre_a(3), des_a(0)): -0.25,
- (cre_b(1), des_b(5), cre_a(4)): 1+1j
+ (cre_a(0), des_a(3)): 0.5
})
-'FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})'
+'FermionOperator({((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j})'
FermionOperators support arithmetic operations. Note that when multiplying a FermionOperator by a scalar, the scalar must go on the left, i.e. 2 * op and not op * 2.
FermionOperator({
- (cre_a(3), des_a(0)): -0.5,
- (cre_a(0), des_a(3)): 1,
- (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
- (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
(cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
- (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
(cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
+ (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
+ (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
+ (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
+ (cre_b(2)): 0-0.25j,
+ (cre_a(0), des_a(3)): 1,
(cre_b(1), des_b(5), cre_a(4)): 2+2j,
(des_a(3), des_b(3)): 0.0625,
- (cre_b(2)): 0-0.25j,
- (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625
+ (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
+ (cre_a(3), des_a(0)): -0.5
})
FermionOperator({
- (cre_a(3), des_a(0)): 0+3j,
- (cre_a(0), des_a(3)): 0-6j,
- (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
- (cre_a(0), des_a(3), cre_b(2)): 2,
(cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
- (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
(cre_a(3), des_a(0), cre_b(2)): -1,
+ (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,
+ (cre_a(0), des_a(3), cre_b(2)): 2,
+ (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
+ (cre_b(2)): -5,
+ (cre_a(0), des_a(3)): 0-6j,
(cre_b(1), des_b(5), cre_a(4)): 12-12j,
(des_a(3), des_b(3)): 0-1.25j,
- (cre_b(2)): -5,
- (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j
+ (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
+ (cre_a(3), des_a(0)): 0+3j
})
FermionOperator({
+ (des_b(3), des_a(3)): 0+1.25j,
(cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,
- (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
- (cre_b(1), cre_a(4), des_b(5)): -12+12j,
- (cre_b(2)): -5,
- (cre_a(0), des_a(3)): 0-6j,
(cre_a(3), des_a(0)): 0+3j,
- (cre_b(2), cre_a(3), des_a(0)): -1,
(cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
- (des_b(3), des_a(3)): 0+1.25j,
- (cre_b(2), cre_a(0), des_a(3)): 2
+ (cre_b(2), cre_a(0), des_a(3)): 2,
+ (cre_a(0), des_a(3)): 0-6j,
+ (cre_b(2), cre_a(3), des_a(0)): -1,
+ (cre_b(1), cre_a(4), des_b(5)): -12+12j,
+ (cre_b(2)): -5,
+ (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j
})
-array([ 0. +0.j , 0. +0.j ,
- 0. +0.j , 0. +0.j ,
- -0.15725357-0.17502038j, 0. +0.j ,
- 0. +0.j , 0. +0.j ,
- 0. +0.j ])
+array([0. +0.j , 0. +0.j ,
+ 0. +0.j , 0. +0.j ,
+ 0.05261902-0.11277367j, 0. +0.j ,
+ 0. +0.j , 0. +0.j ,
+ 0. +0.j ])
It can also be passed into most linear algebra routines in scipy.sparse.linalg.