Compute Derivative of \(\textbf{U}\textbf{G}\textbf{X}^{T}\textbf{y}\) with Respect to Lambda
compute_dG_u_dlambda_xy(
AGAInv_AGXy,
AGAInv,
G,
A,
dG_dlambda,
nc,
nca,
K,
Xy,
Ghalf,
dGhalf,
GhalfXy_temp,
parallel,
cl,
chunk_size,
num_chunks,
rem_chunks
)Vector of derivatives
Product of \((\textbf{A}^{T}\textbf{G}\textbf{A})^{-1}\) and \(\textbf{A}^{T}\textbf{G}\textbf{X}^{T}\textbf{y}\)
Inverse of \(\textbf{A}^{T}\textbf{G}\textbf{A}\)
List of \(\textbf{G}\) matrices
Constraint matrix \(\textbf{A}\)
List of \(d\textbf{G}/d\lambda\) matrices
Number of columns
Number of constraint columns
Number of partitions minus 1 (\(K\))
List of \(\textbf{X}^{T}\textbf{y}\) products
List of \(\textbf{G}^{1/2}\) matrices
List of \(d\textbf{G}^{1/2}/d\lambda\) matrices
Temporary storage for \(\textbf{G}^{1/2}\textbf{X}^{T}\textbf{y}\)
Use parallel processing
Cluster object
Size of parallel chunks
Number of chunks
Remaining chunks
Computes \(d(\textbf{U}\textbf{G}\textbf{X}^{T}\textbf{y})/d\lambda\). Uses efficient implementation avoiding large matrix construction. For large problems (\(K \ge 10\), \(nc > 4\)), uses chunked parallel processing. For smaller problems, uses simpler least squares approach based on \(\textbf{G}^{1/2}\).