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⚡ Bolt: [Optimization in static_susceptibility to avoid O(N^3) matmul] #77

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⚡ Bolt: [Optimization in static_susceptibility to avoid O(N^3) matmul] #77

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3 changes: 3 additions & 0 deletions .jules/bolt.md
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## 2025-11-01 - [Avoid Temporary Array Allocations in Reductions]
**Learning:** In loops over parameters like temperature (`thermal_scan`), doing `np.sum(arr1 * arr2)` where array sizes match the system Hilbert space creates huge temporary arrays per loop iteration. Memory allocation dominates execution time.
**Action:** Use `np.dot(arr1, arr2)` instead of `np.sum(arr1 * arr2)` for 1D arrays to evaluate reductions in C-level BLAS/NumPy functions, bypassing Python/NumPy array allocations and boosting performance significantly with less peak memory.
## 2025-11-01 - [Avoid O(N^3) Full Matrix Multiplication when Only the Diagonal is Needed]
**Learning:** In computing expectation values of squared operators (like $A^2$ in finite temperature static susceptibility calculations), using `A @ A` computes the entire full matrix which has an $O(N^3)$ computational cost and $O(N^2)$ memory allocation cost, only for `np.diag(A @ A)` to discard everything but the diagonal elements.
**Action:** Replace `np.diag(A @ A)` with `np.einsum('ij,ji->i', A, A, optimize=True)`. This computes only the diagonal elements mathematically taking $O(N^2)$ operations and zero intermediate $O(N^2)$ allocations, dramatically speeding up calculations for large dimensions (e.g. from 20s to <1s for large N).
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