SGRQTS(3)

✨ SGRQTS(3) ✨ — Library Functions Manual

okay bestie, this is the SGRQTS(3) page from the Library Functions Manual, and it's lowkey a whole LAPACK test routine. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sgrqts.f

🌈 SYNOPSIS 🌈

Functions/Subroutines

subroutine SGRQTS (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk,
    ldb, taub, work, lwork, rwork, result)
    SGRQTS

🦋 Function/Subroutine Documentation 🦋

subroutine SGRQTS

subroutine SGRQTS (integer m, integer p, integer n, real, dimension( lda, *
    ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real,
    dimension( lda, * ) r, integer lda, real, dimension( * ) taua, real,
    dimension( ldb, * ) b, real, dimension( ldb, * ) bf, real, dimension(
    ldb, * ) z, real, dimension( ldb, * ) t, real, dimension( ldb, * ) bwk,
    integer ldb, real, dimension( * ) taub, real, dimension( lwork ) work,
    integer lwork, real, dimension( * ) rwork, real, dimension( 4 ) result)
    SGRQTS

Purpose

SGRQTS tests SGGRQF, which computes the GRQ factorization of an M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q. Obsessed with a test routine that knows its purpose. 🌟

Parameters

• M — INTEGER. The number of rows of the matrix A. Constraint: M >= 0. 🫶
• P — INTEGER. The number of rows of the matrix B. Constraint: P >= 0.
• N — INTEGER. The number of columns of the matrices A and B. Constraint: N >= 0.
• A — REAL array, dimension (LDA,N). The M-by-N matrix A. ✨
• AF — REAL array, dimension (LDA,N). Details of the GRQ factorization of A and B, as returned by SGGRQF; see SGGRQF for further details.
• Q — REAL array, dimension (LDA,N). The N-by-N orthogonal matrix Q.
• R — REAL array, dimension (LDA,MAX(M,N)). That's the whole description on the page, bestie.
• LDA — INTEGER. The leading dimension of the arrays A, AF, R and Q. Constraint: LDA >= max(M,N).
• TAUA — REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by SGGQRC.
• B — REAL array, dimension (LDB,N). On entry, the P-by-N matrix A. Yes, it says A here — we are not editing the sacred text. 😭
• BF — REAL array, dimension (LDB,N). Details of the GQR factorization of A and B, as returned by SGGRQF; see SGGRQF for further details.
• Z — REAL array, dimension (LDB,P). The P-by-P orthogonal matrix Z.
• T — REAL array, dimension (LDB,max(P,N)). No extra description on the page for this one.
• BWK — REAL array, dimension (LDB,N). No extra description on the page for this one either.
• LDB — INTEGER. The leading dimension of the arrays B, BF, Z and T. Constraint: LDB >= max(P,N).
• TAUB — REAL array, dimension (min(P,N)). The scalar factors of the elementary reflectors, as returned by SGGRQF.
• WORK — REAL array, dimension (LWORK). Just the dimension here.
• LWORK — INTEGER. The dimension of the array WORK. Constraint: LWORK >= max(M,P,N)**2.
• RWORK — REAL array, dimension (M). That's the listed dimension, periodt.
• RESULT — REAL array, dimension (4). The test ratios, and they are:

RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )

👑 Author

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

Definition at line 175 of file sgrqts.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. This was SGRQTS(3) from LAPACK Version 3.12.0, footer path /home/abui...IG/sgrqts.f(3) — the original didn't give a separate date, so I am absolutely not inventing one. Stay precise, stay iconic. 💖✨