SRC/sgeqlf.f(3)

okay bestie, this is the SRC/sgeqlf.f page from the Library Functions Manual 💅✨. it’s giving main character energy for a LAPACK routine, and we’re doing a full vibe check with zero skips. no cap 🫶

✨ NAME ✨

SRC/sgeqlf.f — that’s the name, that’s the file, periodt 💖

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

here’s the synopsis exactly as she appears, because we do not play with signatures 🔥:

subroutine sgeqlf (m, n, a, lda, tau, work, lwork, info)
    SGEQLF

and the routine is literally called SGEQLF — iconic 👑.

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👑 Function/Subroutine Documentation 👑

full typed signature, copied with love and exact characters:

subroutine sgeqlf (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( * ) work,
    integer lwork, integer info)
    SGEQLF

SGEQLF again, because she said it twice and we respect it 💖.

🎯 Purpose 🎯

SGEQLF computes a QL factorization of a real M-by-N matrix A:

A = Q * L

🧮 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. 💖
• A — A is REAL array, dimension (LDA,N). on entry, the M-by-N matrix A. on exit:
  • if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
  • if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L;
  • the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). ✨
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M). 💅
• TAU — TAU is REAL array, dimension (min(M,N)). the scalar factors of the elementary reflectors (see Further Details). 🫶
• 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, if MIN(M,N) = 0, and LWORK >= N, otherwise. for optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. 💀

🌈 Author 🌈

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

🧚 Further Details 🧚

the matrix Q is represented as a product of elementary reflectors:

Q = H(k) . . . H(2) H(1), where k = min(m,n).

each H(i) has the form:

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real vector with v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i). 🦋

Definition at line 138 of file sgeqlf.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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k bye bestie 💖 this page is from LAPACK, Version 3.12.0, for SRC/sgeqlf.f(3) — slay, stay safe, and keep that QL factorization iconic ✨🫶