Add SimpleArray::pow() for matrix power#844
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Add SimpleArray::pow(n) computing A^n for a square matrix and a non-negative integer exponent via exponentiation by squaring (O(log n) matmuls). A^0 returns the identity; negative exponents are rejected since they require matrix inversion (tracked in issue solvcon#719). Include Float32/Float64 tests covering exponent values, identity invariance, a numpy cross-check over fixed fixtures, and the non-square and non-2D (1D/3D/4D) error cases. For issue solvcon#821.
yungyuc
commented
May 30, 2026
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| // Exponentiation by squaring. n is non-negative here, so scanning its | ||
| // bits is well-defined. | ||
| A base = *athis; |
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Squaring (O(ln n) complexity) needs two arrays.
| A SimpleArrayMixinMatrix<A, T>::pow(ssize_t n) const | ||
| { | ||
| auto const * athis = static_cast<A const *>(this); | ||
| validate_square("pow"); |
| def test_matrix_dim_to_5(self): | ||
| """A^n matches numpy across several square matrices and exponents""" | ||
| fixtures = [ | ||
| [[-3]], |
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Test with 1x1, 2x2, 3x3, and 5x5 matrices.
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| def test_non_square_error(self): | ||
| """A non-square matrix cannot be raised to a power""" | ||
| mat_data = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], |
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Power requires square matrices.
| """A non-2D SimpleArray cannot be raised to a power""" | ||
| # 1D, 3D, and 4D arrays must all be rejected, and the error must | ||
| # report the offending dimensionality. | ||
| shapes = [(3,), (2, 2, 2), (2, 2, 2, 2)] |
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Matrices must be 2D arrays.
yungyuc
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SimpleArray::pow() for matrix power
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@ThreeMonth03 @tigercosmos @KHLee529 please help take a look. All PRs have CI false alarms, so does this one. We have to inspect and then ignore them before coming up with a solution. |
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Add$$A^n$$ for a square matrix and a non-negative integer exponent via exponentiation by squaring (O(log n) matmuls). $$A^0$$ returns the identity; negative exponents are rejected since they require matrix inversion (tracked in issue #719).
SimpleArray::pow(n)computingInclude Float32/Float64 tests covering exponent values, identity invariance, a numpy cross-check over fixed fixtures, and the non-square and non-2D (1D/3D/4D) error cases.
For issue #821.