SRC/dgelss.f(3)

SRC/dgelss.f(3) 🎀 — Library Functions Manual ✨

okay bestie, welcome to the SRC/dgelss.f page. The manual name is Library Functions Manual and this whole thing is very “linear algebra but make it main character energy.” 💅

NAME 🦋

SRC/dgelss.f — that's the name, bestie. Periodt. ✨

SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine dgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work,
    lwork, info)

DGELSS solves overdetermined or underdetermined systems for GE matrices. Slay. 🫶

Function/Subroutine Documentation 💖

Here's the full signature flex:

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

DGELSS solves overdetermined or underdetermined systems for GE matrices. 🦋

Purpose 🌟

okay so DGELSS 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. Not me loving a rank-deficient icon. 😭

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. Vibe check: passed. ✨

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Parameters 🍓

• M — INTEGER. The number of rows of the matrix A. M >= 0.
• N — INTEGER. The number of columns of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• A — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,max(M,N)).
• S — DOUBLE PRECISION 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 — DOUBLE PRECISION. 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 — INTEGER. The effective rank of A, i.e., the number of singular values which are greater than RCOND*S(1).
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — 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 — 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.

Bestie, pay attention to those INFO codes. They are literally telling you what happened. No cap. 👑

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Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 170 of file dgelss.f. 🎀

Author (auto-generated) 💅

Generated automatically by Doxygen for LAPACK from the source code.

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💖 and that's the whole page, bestie — source/version: LAPACK Version 3.12.0, file SRC/dgelss.f(3). periodt. 💖