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toeplitz_matvec

Function toeplitz_matvec 

Source
pub fn toeplitz_matvec<T: Float>(kernel: &[T], x: &[T]) -> Vec<T>
Expand description

Causal Toeplitz matrix-vector product — the convolutional view of an SSM. Implicitly applies the lower-triangular matrix M[i][j] = kernel[i - j] for j <= i, 0 otherwise to x, i.e. computes the causal convolution: y[i] = sum_{j=0}^{i} kernel[i - j] * x[j]

kernel and x must be the same length n; cost is O(n^2). This is the direct reference implementation — fft_conv computes the exact same quantity in O(n log n) and is tested against this function.