SGEQLF(3)

🌸 NAME 🌸

Okay so this page is SGEQLF(3) from the Library Functions Manual — and the header path is /home/abui...RC/sgeqlf.f(3) (the source header literally has that path on both sides of the manual name, iykyk). The NAME entry itself points at:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeqlf.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

💅 Function/Subroutine Documentation 💅

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

🎯 Purpose 🎯

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

A = Q * L

That’s the whole vibe, bestie. ✨

🎀 Parameters 🎀

• M — M is INTEGER. It’s the number of rows of the matrix A. M >= 0.
• N — N is INTEGER. It’s 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. It’s the leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is REAL array, dimension (min(M,N)). These are 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. It’s the dimension of the array WORK. LWORK >= max(1,N). 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 137 of file sgeqlf.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie — bye! 💖 LAPACK, Version 3.12.0, footer path /home/abui...RC/sgeqlf.f(3) — periodt. 💅