Linear Least Squares

The linear least squares subroutines provide least squares solutions to linear systems of equations for general matrices using a QR factorization or a singular value decomposition. Some of these subroutines correspond to the LAPACK routines described in reference [9].

Table 1. List of LAPACK Linear Least Squares Subroutines
Short-Precision Subroutine	Long-Precision Subroutine	Descriptive Name and Location
SGESVD^Δ CGESVD^Δ SGESDD^Δ CGESDD^Δ LAPACKE_sgesvd^Δ LAPACKE_cgesvd^Δ LAPACKE_sgesdd^Δ LAPACKE_cgesdd^Δ	DGESVD^Δ ZGESVD^Δ DGESDD^Δ ZGESDD^Δ LAPACKE_dgesvd^Δ LAPACKE_zgesvd^Δ LAPACKE_dgesdd^Δ LAPACKE_zgesdd^Δ	SGESVD, DGESVD, CGESVD, ZGESVD, SGESDD, DGESDD, CGESDD, and ZGESDD (Singular Value Decomposition for a General Matrix)
SGEQRF^Δ^GPU CGEQRF^Δ^GPU LAPACKE_sgeqrf^Δ LAPACKE_cgeqrf^Δ	DGEQRF^Δ^GPU ZGEQRF^Δ^GPU LAPACKE_dgeqrf^Δ LAPACKE_zgeqrf^Δ	SGEQRF, DGEQRF, CGEQRF, and ZGEQRF (General Matrix QR Factorization)
SGELS^Δ^GPU CGELS^Δ^GPU LAPACKE_sgels^Δ LAPACKE_cgels^Δ	DGELS^{Δ ^GPU} ZGELS^Δ^GPU LAPACKE_dgels^Δ LAPACKE_zgels^Δ	SGELS, DGELS, CGELS, and ZGELS (Linear Least Squares Solution for a General Matrix)
SGELSD^Δ CGELSD^Δ LAPACKE_sgelsd^Δ LAPACKE_cgelsd^Δ	DGELSD^Δ ZGELSD^Δ LAPACKE_dgelsd^Δ LAPACKE_zgelsd^Δ	SGELSD, DGELSD, CGELSD, and ZGELSD (Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition)
^Δ LAPACK ^GPU This subroutine can offload computations to the GPUs when the ESSL SMP CUDA Library is used.

Table 2. List of Non–LAPACK Linear Least Squares Subroutines
Short-Precision Subroutine	Long-Precision Subroutine	Descriptive Name and Location
SGESVF^§	DGESVF^§	SGESVF and DGESVF (Singular Value Decomposition for a General Matrix)
SGESVS^§	DGESVS^§	SGESVS and DGESVS (Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition)
SGELLS^§	DGELLS^§	SGELLS and DGELLS (Linear Least Squares Solution for a General Matrix with Column Pivoting)
^§ This subroutine is provided only for migration from earlier releases of ESSL and is not intended for use in new programs.