SRC/sgelss.f(3)

🎀 SRC/sgelss.f(3) 🎀 LAPACK Library Functions Manual

💖 NAME 💖

SRC/sgelss.f — bestie, this is the page for the sgelss subroutine, and it is lowkey iconic with main character energy. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine sgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, info) — SGELSS solves overdetermined or underdetermined systems for GE matrices. ✨

🧚 Function/Subroutine Documentation 🧚

subroutine sgelss (integer m, integer n, integer nrhs, real, dimension( lda,
* ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
dimension( * ) s, real rcond, integer rank, real, dimension( * ) work,
integer lwork, integer info)

SGELSS solves overdetermined or underdetermined systems for GE matrices. 🔥

🌸 Purpose 🌸

Okay so SGELSS computes the minimum norm solution to a real linear least squares problem: 💖

Minimize 2-norm(| b - A*x |).

It does this using the singular value decomposition (SVD) of A. A is an M-by-N matrix which may be rank-deficient. It’s giving SVD excellence. 👑

Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. 🫶

The effective rank of A is determined by treating as zero those singular values which are less than RCOND times the largest singular value. Periodt. 💅

🎀 Parameters 🎀

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. 💖
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. 🌸
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. ✨
• A — A is REAL array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the first min(m,n) rows of A are overwritten with its right singular vectors, stored rowwise. 👑
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). 💅
• B — B is REAL array, dimension (LDB,NRHS). On entry, the M-by-NRHS right hand side matrix B. On exit, B is overwritten by the N-by-NRHS solution matrix X. If m >= n and RANK = n, the residual sum-of-squares for the solution in the i-th column is given by the sum of squares of elements n+1:m in that column. 😭🔥
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,max(M,N)). 🫶
• S — S is REAL array, dimension (min(M,N)). The singular values of A in decreasing order. The condition number of A in the 2-norm = S(1)/S(min(m,n)). ⭐
• RCOND — RCOND is REAL. RCOND is used to determine the effective rank of A. Singular values S(i) <= RCOND*S(1) are treated as zero. If RCOND < 0, machine precision is used instead. 🧚
• RANK — RANK is INTEGER. The effective rank of A, i.e., the number of singular values which are greater than RCOND*S(1). 👑
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 💖
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1, and also: LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ). For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🚨
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: the algorithm for computing the SVD failed to converge; if INFO = i, i off-diagonal elements of an intermediate bidiagonal form did not converge to zero. 💀

💖 Author 💖

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 170 of file sgelss.f. 📍

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. 🤖

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That’s the whole page, bestie — signed off with LAPACK Version 3.12.0 for SRC/sgelss.f(3) and generated automatically by Doxygen for LAPACK from the source code. Byeee! 🫶💅✨