SRC/sgeqrfp.f(3)

okay so bestie, this is the SRC/sgeqrfp.f(3) page from the Library Functions Manual, and it's literally all about SGEQRFP. it's giving LAPACK, it's giving QR factorization, it's giving main character energy. 🎀✨

✨ NAME ✨

SRC/sgeqrfp.f — that's it, that's the name section. 💖

🦋 SYNOPSIS 🦋

💅 Functions/Subroutines 💅

• subroutine sgeqrfp (m, n, a, lda, tau, work, lwork, info) — SGEQRFP

🌸 Function/Subroutine Documentation 🌸

🫶 subroutine sgeqrfp 🫶

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

👑 SGEQRFP 👑

💅 Purpose: 💅

okay so the page literally says this, and we're keeping every word:

!>
!> SGEQR2P computes a QR factorization of a real M-by-N matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a M-by-M orthogonal matrix;
!>    R is an upper-triangular N-by-N matrix with nonnegative diagonal
!>    entries;
!>    0 is a (M-N)-by-N zero matrix, if M > N.
!>
!>

🎀 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, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative; the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) 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(1) H(2) . . . H(k), 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
!>  and tau in TAU(i).
!>
!> See Lapack Working Note 203 for details
!>

📍 Definition at line 149 of file sgeqrfp.f. 📍

Definition at line 149 of file sgeqrfp.f.

🫶 Author 🫶

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✨ and that's the whole page, bestie — footer vibes: LAPACK Version 3.12.0, from SRC/sgeqrfp.f(3) (no date shown, just those). 🎀💖