SRC/dgelst.f(3)

💖 SRC/dgelst.f 💖

okay bestie, welcome to the Library Functions Manual glow-up for SRC/dgelst.f(3) — it’s giving Fortran subroutine realness, and we’re gonna go through every single deet so nobody gets left on read 💅✨

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🌸 NAME 🌸

• SRC/dgelst.f

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🦋 SYNOPSIS 🦋

💫 Functions/Subroutines 💫

subroutine dgelst (character trans, integer m, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q. periodt 💅

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✨ Function/Subroutine Documentation ✨

subroutine dgelst (character trans, integer m, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q. iconic behavior honestly 👑

🎀 Purpose 🎀

DGELST solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A with compact WY representation of Q. slay 💖

It is assumed that A has full rank, and only a rudimentary protection against rank-deficient matrices is provided. This subroutine only detects exact rank-deficiency, where a diagonal element of the triangular factor of A is exactly zero.

bestie warning 😭 this is not a vibe check for almost rank-deficient matrices — it only catches the exact-zero situation, okay?

It is conceivable for one (or more) of the diagonal elements of the triangular factor of A to be subnormally tiny numbers without this subroutine signalling an error. The solutions computed for such almost-rank-deficient matrices may be less accurate due to a loss of numerical precision. no cap, that’s the tea 🫖

The following options are provided:

1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

minimize || B - A*X ||.

2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.
3. If TRANS = 'T' and m >= n: find the minimum norm solution of an underdetermined system A**T * X = B.
4. If TRANS = 'T' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

minimize || B - A**T * X ||.

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. group-chat efficiency, we love to see it 💅

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🌈 Parameters 🌈

• TRANS — TRANS is CHARACTER*1
  • = 'N': the linear system involves A;
  • = 'T': the linear system involves A**T.
• 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 DOUBLE PRECISION array, dimension (LDA,N)
  • On entry, the M-by-N matrix A.
  • On exit:
    • if M >= N, A is overwritten by details of its QR factorization as returned by DGEQRT;
    • if M < N, A is overwritten by details of its LQ factorization as returned by DGELQT.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS)
  • On entry, the matrix B of right hand side vectors, stored columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS if TRANS = 'T'.
  • On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise:
    • if TRANS = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements N+1 to M in that column;
    • if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors;
    • if TRANS = 'T' and m >= n, rows 1 to M of B contain the minimum norm solution vectors;
    • if TRANS = 'T' and m < n, rows 1 to M of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements M+1 to N in that column.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= MAX(1,M,N).
• WORK — WORK is DOUBLE PRECISION 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 >= max( 1, MN + max( MN, NRHS ) ). For optimal performance, LWORK >= max( 1, (MN + max( MN, NRHS ))*NB ). where MN = min(M,N) and NB is the optimum block size.
  • 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: if INFO = i, the i-th diagonal element of the triangular factor of A is exactly zero, so that A does not have full rank; the least squares solution could not be computed.

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👑 Author 👑

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

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🧚 Contributors 🧚

• November 2022, Igor Kozachenko,
  • Computer Science Division,
  • University of California, Berkeley

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Definition at line 201 of file dgelst.f.

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🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie — signed off from SRC/dgelst.f(3) with LAPACK Version 3.12.0 💜 the footer didn’t hand us a date, so no made-up date energy here 🫶 mwah 💋✨