Add matrix inversion sfg generator

.gitignore

@@ -116,6 +116,7 @@ TODO.txt
 b_asic/_version.py
 docs_sphinx/_build/
 docs_sphinx/examples
+docs_sphinx/sg_execution_times.rst
 result_images/
 .coverage
 Digraph.gv

b_asic/core_operations.py

@@ -1099,6 +1099,108 @@ class MAD(AbstractOperation):
             p._index = i
 
 
+class MADS(AbstractOperation):
+    __slots__ = (
+        "_is_add",
+        "_override_zero_on_src0",
+        "_src0",
+        "_src1",
+        "_src2",
+        "_name",
+        "_latency",
+        "_latency_offsets",
+        "_execution_time",
+    )
+    _is_add: Optional[bool]
+    _override_zero_on_src0: Optional[bool]
+    _src0: Optional[SignalSourceProvider]
+    _src1: Optional[SignalSourceProvider]
+    _src2: Optional[SignalSourceProvider]
+    _name: Name
+    _latency: Optional[int]
+    _latency_offsets: Optional[Dict[str, int]]
+    _execution_time: Optional[int]
+
+    is_swappable = True
+
+    def __init__(
+        self,
+        is_add: Optional[bool] = True,
+        override_zero_on_src0: Optional[bool] = False,
+        src0: Optional[SignalSourceProvider] = None,
+        src1: Optional[SignalSourceProvider] = None,
+        src2: Optional[SignalSourceProvider] = None,
+        name: Name = Name(""),
+        latency: Optional[int] = None,
+        latency_offsets: Optional[Dict[str, int]] = None,
+        execution_time: Optional[int] = None,
+    ):
+        """Construct a MADS operation."""
+        super().__init__(
+            input_count=3,
+            output_count=1,
+            name=Name(name),
+            input_sources=[src0, src1, src2],
+            latency=latency,
+            latency_offsets=latency_offsets,
+            execution_time=execution_time,
+        )
+        self.set_param("is_add", is_add)
+        self.set_param("override_zero_on_src0", override_zero_on_src0)
+
+    @classmethod
+    def type_name(cls) -> TypeName:
+        return TypeName("mads")
+
+    def evaluate(self, a, b, c):
+        if self.is_add:
+            if self.override_zero_on_src0:
+                return b * c
+            else:
+                return a + b * c
+        else:
+            if self.override_zero_on_src0:
+                return -b * c
+            else:
+                return a - b * c
+
+    @property
+    def is_add(self) -> bool:
+        """Get if operation is an addition."""
+        return self.param("is_add")
+
+    @is_add.setter
+    def is_add(self, is_add: bool) -> None:
+        """Set if operation is an addition."""
+        self.set_param("is_add", is_add)
+
+    @property
+    def override_zero_on_src0(self) -> bool:
+        """Get if operation is overriding a zero on port src0."""
+        return self.param("override_zero_on_src0")
+
+    @override_zero_on_src0.setter
+    def override_zero_on_src0(self, override_zero_on_src0: bool) -> None:
+        """Set if operation is overriding a zero on port src0."""
+        self.set_param("override_zero_on_src0", override_zero_on_src0)
+
+    @property
+    def is_linear(self) -> bool:
+        return (
+            self.input(1).connected_source.operation.is_constant
+            or self.input(2).connected_source.operation.is_constant
+        )
+
+    def swap_io(self) -> None:
+        self._input_ports = [
+            self._input_ports[0],
+            self._input_ports[2],
+            self._input_ports[1],
+        ]
+        for i, p in enumerate(self._input_ports):
+            p._index = i
+
+
 class SymmetricTwoportAdaptor(AbstractOperation):
     r"""
     Wave digital filter symmetric twoport-adaptor operation.
@@ -1519,6 +1621,51 @@ class Shift(AbstractOperation):
         self.set_param("value", value)
 
 
+class DontCare(AbstractOperation):
+    r"""
+    Dont-care operation
+
+    Used for ignoring the input to another operation and thus avoiding dangling input nodes.
+
+    Parameters
+    ----------
+    name : Name, optional
+        Operation name.
+
+    """
+
+    __slots__ = "_name"
+    _name: Name
+
+    is_linear = True
+
+    def __init__(self, name: Name = ""):
+        """Construct a DontCare operation."""
+        super().__init__(
+            input_count=0,
+            output_count=1,
+            name=name,
+            latency_offsets={"out0": 0},
+        )
+
+    @classmethod
+    def type_name(cls) -> TypeName:
+        return TypeName("dontcare")
+
+    def evaluate(self):
+        return 0
+
+    @property
+    def latency(self) -> int:
+        return self.latency_offsets["out0"]
+
+    def __repr__(self) -> str:
+        return "DontCare()"
+
+    def __str__(self) -> str:
+        return "dontcare"
+
+
 class Sink(AbstractOperation):
     r"""
     Sink operation.

b_asic/sfg_generators.py

@@ -9,10 +9,13 @@ from typing import TYPE_CHECKING, Dict, Optional, Sequence, Union
 import numpy as np
 
 from b_asic.core_operations import (
+    MADS,
     Addition,
     Butterfly,
     ConstantMultiplication,
+    DontCare,
     Name,
+    Reciprocal,
     SymmetricTwoportAdaptor,
 )
 from b_asic.signal import Signal
@@ -432,6 +435,82 @@ def radix_2_dif_fft(points: int) -> SFG:
     return SFG(inputs=inputs, outputs=outputs)
 
 
+def ldlt_matrix_inverse(N: int) -> SFG:
+    """Generates an SFG for the LDLT matrix inverse algorithm.
+
+    Parameters
+    ----------
+    N : int
+        Dimension of the square input matrix.
+
+    Returns
+    -------
+    SFG
+        Signal Flow Graph
+    """
+    inputs = []
+    A = [[None for _ in range(N)] for _ in range(N)]
+    for i in range(N):
+        for j in range(i, N):
+            in_op = Input()
+            A[i][j] = in_op
+            inputs.append(in_op)
+
+    D = [None for _ in range(N)]
+    for i in range(N):
+        D[i] = A[i][i]
+
+    D_inv = [None for _ in range(N)]
+
+    R = [[None for _ in range(N)] for _ in range(N)]
+    M = [[None for _ in range(N)] for _ in range(N)]
+
+    # R*di*R^T factorization
+    for i in range(N):
+        for k in range(i):
+            D[i] = MADS(False, False, D[i], M[k][i], R[k][i])
+
+        D_inv[i] = Reciprocal(D[i])
+
+        for j in range(i + 1, N):
+            R[i][j] = A[i][j]
+
+            for k in range(i):
+                R[i][j] = MADS(False, False, R[i][j], M[k][i], R[k][j])
+
+            # if is_complex:
+            #     M[i][j] = ComplexConjugate(R[i][j])
+            # else:
+            M[i][j] = R[i][j]
+
+            R[i][j] = MADS(True, True, DontCare(), R[i][j], D_inv[i])
+
+    # back substitution
+    A_inv = [[None for _ in range(N)] for _ in range(N)]
+    for i in reversed(range(N)):
+        A_inv[i][i] = D_inv[i]
+        for j in reversed(range(i + 1)):
+            for k in reversed(range(j + 1, N)):
+                if k == N - 1 and i != j:
+                    A_inv[j][i] = MADS(False, True, DontCare(), R[j][k], A_inv[i][k])
+                else:
+                    if A_inv[i][k]:
+                        A_inv[j][i] = MADS(
+                            False, False, A_inv[j][i], R[j][k], A_inv[i][k]
+                        )
+                    else:
+                        A_inv[j][i] = MADS(
+                            False, False, A_inv[j][i], R[j][k], A_inv[k][i]
+                        )
+
+    outputs = []
+    for i in range(N):
+        for j in range(i, N):
+            outputs.append(Output(A_inv[i][j]))
+
+    return SFG(inputs, outputs)
+
+
 def _construct_dif_fft_stage(
     ports_from_previous_stage: list["OutputPort"],
     number_of_stages: int,

test/test_core_operations.py

@@ -3,6 +3,9 @@
 import pytest
 
 from b_asic import (
+    MAD,
+    MADS,
+    SFG,
     Absolute,
     Addition,
     AddSub,
@@ -11,10 +14,13 @@ from b_asic import (
     Constant,
     ConstantMultiplication,
     Division,
+    DontCare,
+    Input,
     LeftShift,
     Max,
     Min,
     Multiplication,
+    Output,
     Reciprocal,
     RightShift,
     Shift,
@@ -47,6 +53,14 @@ class TestConstant:
         test_operation.value = 4
         assert test_operation.value == 4
 
+    def test_constant_repr(self):
+        test_operation = Constant(3)
+        assert repr(test_operation) == "Constant(3)"
+
+    def test_constant_str(self):
+        test_operation = Constant(3)
+        assert str(test_operation) == "3"
+
 
 class TestAddition:
     """Tests for Addition class."""
@@ -83,16 +97,16 @@ class TestSubtraction:
 class TestAddSub:
     """Tests for AddSub class."""
 
-    def test_addition_positive(self):
+    def test_addsub_positive(self):
         test_operation = AddSub(is_add=True)
         assert test_operation.evaluate_output(0, [3, 5]) == 8
 
-    def test_addition_negative(self):
+    def test_addsub_negative(self):
         test_operation = AddSub(is_add=True)
         assert test_operation.evaluate_output(0, [-3, -5]) == -8
         assert test_operation.is_add
 
-    def test_addition_complex(self):
+    def test_addsub_complex(self):
         test_operation = AddSub(is_add=True)
         assert test_operation.evaluate_output(0, [3 + 5j, 4 + 6j]) == 7 + 11j
 
@@ -116,6 +130,22 @@ class TestAddSub:
         test_operation = AddSub(is_add=True)
         assert test_operation.is_swappable
 
+    def test_addsub_is_add_getter(self):
+        test_operation = AddSub(is_add=False)
+        assert not test_operation.is_add
+
+        test_operation = AddSub(is_add=True)
+        assert test_operation.is_add
+
+    def test_addsub_is_add_setter(self):
+        test_operation = AddSub(is_add=False)
+        test_operation.is_add = True
+        assert test_operation.is_add
+
+        test_operation = AddSub(is_add=True)
+        test_operation.is_add = False
+        assert not test_operation.is_add
+
 
 class TestMultiplication:
     """Tests for Multiplication class."""
@@ -148,6 +178,13 @@ class TestDivision:
         test_operation = Division()
         assert test_operation.evaluate_output(0, [60 + 40j, 10 + 20j]) == 2.8 - 1.6j
 
+    def test_mads_is_linear(self):
+        test_operation = Division(Constant(3), Addition(Input(), Constant(3)))
+        assert not test_operation.is_linear
+
+        test_operation = Division(Addition(Input(), Constant(3)), Constant(3))
+        assert test_operation.is_linear
+
 
 class TestSquareRoot:
     """Tests for SquareRoot class."""
@@ -200,6 +237,13 @@ class TestMin:
         test_operation = Min()
         assert test_operation.evaluate_output(0, [-30, -5]) == -30
 
+    def test_min_complex(self):
+        test_operation = Min()
+        with pytest.raises(
+            ValueError, match="core_operations.Min does not support complex numbers."
+        ):
+            test_operation.evaluate_output(0, [-1 - 1j, 2 + 2j])
+
 
 class TestAbsolute:
     """Tests for Absolute class."""
@@ -216,6 +260,13 @@ class TestAbsolute:
         test_operation = Absolute()
         assert test_operation.evaluate_output(0, [3 + 4j]) == 5.0
 
+    def test_max_complex(self):
+        test_operation = Max()
+        with pytest.raises(
+            ValueError, match="core_operations.Max does not support complex numbers."
+        ):
+            test_operation.evaluate_output(0, [-1 - 1j, 2 + 2j])
+
 
 class TestConstantMultiplication:
     """Tests for ConstantMultiplication class."""
@@ -234,6 +285,136 @@ class TestConstantMultiplication:
         assert test_operation.evaluate_output(0, [3 + 4j]) == 1 + 18j
 
 
+class TestMAD:
+    def test_mad_positive(self):
+        test_operation = MAD()
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == 5
+
+    def test_mad_negative(self):
+        test_operation = MAD()
+        assert test_operation.evaluate_output(0, [-3, -5, -8]) == 7
+
+    def test_mad_complex(self):
+        test_operation = MAD()
+        assert test_operation.evaluate_output(0, [3 + 6j, 2 + 6j, 1 + 1j]) == -29 + 31j
+
+    def test_mad_is_linear(self):
+        test_operation = MAD(
+            Constant(3), Addition(Input(), Constant(3)), Addition(Input(), Constant(3))
+        )
+        assert test_operation.is_linear
+
+        test_operation = MAD(
+            Addition(Input(), Constant(3)), Constant(3), Addition(Input(), Constant(3))
+        )
+        assert test_operation.is_linear
+
+        test_operation = MAD(
+            Addition(Input(), Constant(3)), Addition(Input(), Constant(3)), Constant(3)
+        )
+        assert not test_operation.is_linear
+
+    def test_mad_swap_io(self):
+        test_operation = MAD()
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == 5
+        test_operation.swap_io()
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == 5
+
+
+class TestMADS:
+    def test_mads_positive(self):
+        test_operation = MADS(is_add=False)
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == -5
+
+    def test_mads_negative(self):
+        test_operation = MADS(is_add=False)
+        assert test_operation.evaluate_output(0, [-3, -5, -8]) == -43
+
+    def test_mads_complex(self):
+        test_operation = MADS(is_add=False)
+        assert test_operation.evaluate_output(0, [3 + 6j, 2 + 6j, 1 + 1j]) == 7 - 2j
+
+    def test_mads_positive_add(self):
+        test_operation = MADS(is_add=True)
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == 7
+
+    def test_mads_negative_add(self):
+        test_operation = MADS(is_add=True)
+        assert test_operation.evaluate_output(0, [-3, -5, -8]) == 37
+
+    def test_mads_complex_add(self):
+        test_operation = MADS(is_add=True)
+        assert test_operation.evaluate_output(0, [3 + 6j, 2 + 6j, 1 + 1j]) == -1 + 14j
+
+    def test_mads_zero_override(self):
+        test_operation = MADS(is_add=True, override_zero_on_src0=True)
+        assert test_operation.evaluate_output(0, [1, 1, 1]) == 1
+
+    def test_mads_sub_zero_override(self):
+        test_operation = MADS(is_add=False, override_zero_on_src0=True)
+        assert test_operation.evaluate_output(0, [1, 1, 1]) == -1
+
+    def test_mads_is_linear(self):
+        test_operation = MADS(
+            src0=Constant(3),
+            src1=Addition(Input(), Constant(3)),
+            src2=Addition(Input(), Constant(3)),
+        )
+        assert not test_operation.is_linear
+
+        test_operation = MADS(
+            src0=Addition(Input(), Constant(3)),
+            src1=Constant(3),
+            src2=Addition(Input(), Constant(3)),
+        )
+        assert test_operation.is_linear
+
+        test_operation = MADS(
+            src0=Addition(Input(), Constant(3)),
+            src1=Addition(Input(), Constant(3)),
+            src2=Constant(3),
+        )
+        assert test_operation.is_linear
+
+    def test_mads_swap_io(self):
+        test_operation = MADS(is_add=False)
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == -5
+        test_operation.swap_io()
+        assert test_operation.evaluate_output(0, [1, 2, 3]) == -5
+
+    def test_mads_is_add_getter(self):
+        test_operation = MADS(is_add=False)
+        assert not test_operation.is_add
+
+        test_operation = MADS(is_add=True)
+        assert test_operation.is_add
+
+    def test_mads_is_add_setter(self):
+        test_operation = MADS(is_add=False)
+        test_operation.is_add = True
+        assert test_operation.is_add
+
+        test_operation = MADS(is_add=True)
+        test_operation.is_add = False
+        assert not test_operation.is_add
+
+    def test_mads_override_zero_on_src0_getter(self):
+        test_operation = MADS(override_zero_on_src0=False)
+        assert not test_operation.override_zero_on_src0
+
+        test_operation = MADS(override_zero_on_src0=True)
+        assert test_operation.override_zero_on_src0
+
+    def test_mads_override_zero_on_src0_setter(self):
+        test_operation = MADS(override_zero_on_src0=False)
+        test_operation.override_zero_on_src0 = True
+        assert test_operation.override_zero_on_src0
+
+        test_operation = MADS(override_zero_on_src0=True)
+        test_operation.override_zero_on_src0 = False
+        assert not test_operation.override_zero_on_src0
+
+
 class TestRightShift:
     """Tests for RightShift class."""
 
@@ -408,6 +589,33 @@ class TestDepends:
         assert set(bfly1.inputs_required_for_output(1)) == {0, 1}
 
 
+class TestDontCare:
+    def test_create_sfg_with_dontcare(self):
+        i1 = Input()
+        dc = DontCare()
+        a = Addition(i1, dc)
+        o = Output(a)
+        sfg = SFG([i1], [o])
+
+        assert sfg.output_count == 1
+        assert sfg.input_count == 1
+
+        assert sfg.evaluate_output(0, [0]) == 0
+        assert sfg.evaluate_output(0, [1]) == 1
+
+    def test_dontcare_latency_getter(self):
+        test_operation = DontCare()
+        assert test_operation.latency == 0
+
+    def test_dontcare_repr(self):
+        test_operation = DontCare()
+        assert repr(test_operation) == "DontCare()"
+
+    def test_dontcare_str(self):
+        test_operation = DontCare()
+        assert str(test_operation) == "dontcare"
+
+
 class TestSink:
     def test_create_sfg_with_sink(self):
         bfly = Butterfly()
@@ -420,3 +628,15 @@ class TestSink:
             assert sfg1.input_count == 2
 
             assert sfg.evaluate_output(1, [0, 1]) == sfg1.evaluate_output(0, [0, 1])
+
+    def test_sink_latency_getter(self):
+        test_operation = Sink()
+        assert test_operation.latency == 0
+
+    def test_sink_repr(self):
+        test_operation = Sink()
+        assert repr(test_operation) == "Sink()"
+
+    def test_sink_str(self):
+        test_operation = Sink()
+        assert str(test_operation) == "sink"

test/test_sfg_generators.py

@@ -3,15 +3,18 @@ import pytest
 from scipy import signal
 
 from b_asic.core_operations import (
+    MADS,
     Addition,
     Butterfly,
     ConstantMultiplication,
+    Reciprocal,
     SymmetricTwoportAdaptor,
 )
 from b_asic.sfg_generators import (
     direct_form_1_iir,
     direct_form_2_iir,
     direct_form_fir,
+    ldlt_matrix_inverse,
     radix_2_dif_fft,
     transposed_direct_form_fir,
     wdf_allpass,
@@ -637,3 +640,176 @@ class TestRadix2FFT:
         POINTS = 5
         with pytest.raises(ValueError, match="Points must be a power of two."):
             radix_2_dif_fft(points=POINTS)
+
+
+class TestLdltMatrixInverse:
+    def test_1x1(self):
+        sfg = ldlt_matrix_inverse(N=1)
+
+        assert len(sfg.inputs) == 1
+        assert len(sfg.outputs) == 1
+
+        assert len(sfg.find_by_type_name(MADS.type_name())) == 0
+        assert len(sfg.find_by_type_name(Reciprocal.type_name())) == 1
+
+        A_input = [Constant(5)]
+
+        sim = Simulation(sfg, A_input)
+        sim.run_for(1)
+
+        res = sim.results
+        assert np.isclose(res["0"], 0.2)
+
+    def test_2x2_simple_spd(self):
+        sfg = ldlt_matrix_inverse(N=2)
+
+        assert len(sfg.inputs) == 3
+        assert len(sfg.outputs) == 3
+
+        assert len(sfg.find_by_type_name(MADS.type_name())) == 4
+        assert len(sfg.find_by_type_name(Reciprocal.type_name())) == 2
+
+        A = np.array([[1, 2], [2, 1]])
+        A_input = [Constant(1), Constant(2), Constant(1)]
+
+        A_inv = np.linalg.inv(A)
+
+        sim = Simulation(sfg, A_input)
+        sim.run_for(1)
+
+        res = sim.results
+        assert np.isclose(res["0"], A_inv[0, 0])
+        assert np.isclose(res["1"], A_inv[0, 1])
+        assert np.isclose(res["2"], A_inv[1, 1])
+
+    def test_3x3_simple_spd(self):
+        sfg = ldlt_matrix_inverse(N=3)
+
+        assert len(sfg.inputs) == 6
+        assert len(sfg.outputs) == 6
+
+        assert len(sfg.find_by_type_name(MADS.type_name())) == 15
+        assert len(sfg.find_by_type_name(Reciprocal.type_name())) == 3
+
+        A = np.array([[2, -1, 0], [-1, 3, -1], [0, -1, 2]])
+        A_input = [
+            Constant(2),
+            Constant(-1),
+            Constant(0),
+            Constant(3),
+            Constant(-1),
+            Constant(2),
+        ]
+
+        A_inv = np.linalg.inv(A)
+
+        sim = Simulation(sfg, A_input)
+        sim.run_for(1)
+
+        res = sim.results
+        assert np.isclose(res["0"], A_inv[0, 0])
+        assert np.isclose(res["1"], A_inv[0, 1])
+        assert np.isclose(res["2"], A_inv[0, 2])
+        assert np.isclose(res["3"], A_inv[1, 1])
+        assert np.isclose(res["4"], A_inv[1, 2])
+        assert np.isclose(res["5"], A_inv[2, 2])
+
+    def test_5x5_random_spd(self):
+        N = 5
+
+        sfg = ldlt_matrix_inverse(N=N)
+
+        assert len(sfg.inputs) == 15
+        assert len(sfg.outputs) == 15
+
+        assert len(sfg.find_by_type_name(MADS.type_name())) == 70
+        assert len(sfg.find_by_type_name(Reciprocal.type_name())) == N
+
+        A = self._generate_random_spd_matrix(N)
+
+        upper_tridiag = A[np.triu_indices_from(A)]
+
+        A_input = [Constant(num) for num in upper_tridiag]
+        A_inv = np.linalg.inv(A)
+
+        sim = Simulation(sfg, A_input)
+        sim.run_for(1)
+        res = sim.results
+
+        row_indices, col_indices = np.triu_indices(N)
+        expected_values = A_inv[row_indices, col_indices]
+        actual_values = [res[str(i)] for i in range(len(expected_values))]
+
+        for i in range(len(expected_values)):
+            assert np.isclose(actual_values[i], expected_values[i])
+
+    def test_20x20_random_spd(self):
+        N = 20
+
+        sfg = ldlt_matrix_inverse(N=N)
+
+        A = self._generate_random_spd_matrix(N)
+
+        assert len(sfg.inputs) == len(A[np.triu_indices_from(A)])
+        assert len(sfg.outputs) == len(A[np.triu_indices_from(A)])
+
+        assert len(sfg.find_by_type_name(Reciprocal.type_name())) == N
+
+        upper_tridiag = A[np.triu_indices_from(A)]
+
+        A_input = [Constant(num) for num in upper_tridiag]
+        A_inv = np.linalg.inv(A)
+
+        sim = Simulation(sfg, A_input)
+        sim.run_for(1)
+        res = sim.results
+
+        row_indices, col_indices = np.triu_indices(N)
+        expected_values = A_inv[row_indices, col_indices]
+        actual_values = [res[str(i)] for i in range(len(expected_values))]
+
+        for i in range(len(expected_values)):
+            assert np.isclose(actual_values[i], expected_values[i])
+
+    # def test_2x2_random_complex_spd(self):
+    #     N = 2
+
+    #     sfg = ldlt_matrix_inverse(N=N, is_complex=True)
+
+    #     # A = self._generate_random_complex_spd_matrix(N)
+    #     A = np.array([[2, 1+1j],[1-1j, 3]])
+
+    #     assert len(sfg.inputs) == len(A[np.triu_indices_from(A)])
+    #     assert len(sfg.outputs) == len(A[np.triu_indices_from(A)])
+
+    #     assert len(sfg.find_by_type_name(Reciprocal.type_name())) == N
+
+    #     upper_tridiag = A[np.triu_indices_from(A)]
+
+    #     A_input = [Constant(num) for num in upper_tridiag]
+    #     A_inv = np.linalg.inv(A)
+
+    #     sim = Simulation(sfg, A_input)
+    #     sim.run_for(1)
+    #     res = sim.results
+
+    #     row_indices, col_indices = np.triu_indices(N)
+    #     expected_values = A_inv[row_indices, col_indices]
+    #     actual_values = [res[str(i)] for i in range(len(expected_values))]
+
+    #     for i in range(len(expected_values)):
+    #         assert np.isclose(actual_values[i], expected_values[i])
+
+    def _generate_random_spd_matrix(self, N: int) -> np.ndarray:
+        A = np.random.rand(N, N)
+        A = (A + A.T) / 2  # ensure symmetric
+        min_eig = np.min(np.linalg.eigvals(A))
+        A += (np.abs(min_eig) + 0.1) * np.eye(N)  # ensure positive definiteness
+        return A
+
+    # def _generate_random_complex_spd_matrix(self, N: int) -> np.ndarray:
+    #     A = np.random.randn(N, N) + 1j * np.random.randn(N, N)
+    #     A = (A + A.conj().T) / 2  # ensure symmetric
+    #     min_eig = np.min(np.linalg.eigvals(A))
+    #     A += (np.abs(min_eig) + 0.1) * np.eye(N)  # ensure positive definiteness
+    #     return A