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Simplify logic in Diagonal-Tridiagonal multiplication #1338

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May 8, 2025
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Simplify logic in Diagonal-Tridiagonal multiplication #1338

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32 changes: 10 additions & 22 deletions src/bidiag.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1186,39 +1186,27 @@ function _dibimul!(C, A, B, _add)
end
function _dibimul_nonzeroalpha!(C, A, B, _add)
n = size(A,1)
if n <= 3
# For simplicity, use a naive multiplication for small matrices
# that loops over all elements.
for I in CartesianIndices(C)
C[I] += _add(A.diag[I[1]] * B[I[1], I[2]])
end
return C
end
Ad = A.diag
Bl = _diag(B, -1)
Bd = _diag(B, 0)
Bu = _diag(B, 1)
@inbounds begin
# first row of C
C[1,1] += _add(A[1,1]*B[1,1])
C[1,2] += _add(A[1,1]*B[1,2])
# second row of C
C[2,1] += _add(A[2,2]*B[2,1])
C[2,2] += _add(A[2,2]*B[2,2])
C[2,3] += _add(A[2,2]*B[2,3])
for j in 3:n-2
C[1,1] += _add(Ad[1]*Bd[1])
if n >= 2
C[1,2] += _add(Ad[1]*Bu[1])
end
for j in 2:n-1
Ajj = Ad[j]
C[j, j-1] += _add(Ajj*Bl[j-1])
C[j, j ] += _add(Ajj*Bd[j])
C[j, j+1] += _add(Ajj*Bu[j])
end
# row before last of C
C[n-1,n-2] += _add(A[n-1,n-1]*B[n-1,n-2])
C[n-1,n-1] += _add(A[n-1,n-1]*B[n-1,n-1])
C[n-1,n ] += _add(A[n-1,n-1]*B[n-1,n ])
# last row of C
C[n,n-1] += _add(A[n,n]*B[n,n-1])
C[n,n ] += _add(A[n,n]*B[n,n ])
if n >= 2
# last row of C
C[n,n-1] += _add(Ad[n]*Bl[n-1])
C[n,n ] += _add(Ad[n]*Bd[n])
end
end # inbounds
C
end
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