SGQRTS(3)

💖 SGQRTS(3) — Library Functions Manual 💖

okay bestie, gather round 🫶 this is the SGQRTS(3) page, and the source file is exactly this:

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

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✨ NAME ✨

This one is SGQRTS(3) from the Library Functions Manual, and its source file is:

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

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🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

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

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🌸 Function/Subroutine Documentation 🌸

Here’s the full signature, iconically long and exact:

   subroutine SGQRTS (integer n, integer m, integer p, 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)
       SGQRTS

🌟 Purpose 🌟

SGQRTS tests SGGQRF, which computes the GQR factorization of an N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z. 💅

🎀 Parameters 🎀

• N — N is INTEGER; the number of rows of the matrices A and B. N >= 0.
• M — M is INTEGER; the number of columns of the matrix A. M >= 0.
• P — P is INTEGER; the number of columns of the matrix B. P >= 0.
• A — A is REAL array, dimension (LDA,M); the N-by-M matrix A.
• AF — AF is REAL array, dimension (LDA,N); details of the GQR factorization of A and B, as returned by SGGQRF, see SGGQRF for further details.
• Q — Q is REAL array, dimension (LDA,N); the M-by-M orthogonal matrix Q.
• R — R is REAL array, dimension (LDA,MAX(M,N)). That’s the whole note, bestie 🫶
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, R and Q. LDA >= max(M,N).
• TAUA — TAUA is REAL array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by SGGQRF.
• B — B is REAL array, dimension (LDB,P); on entry, the N-by-P matrix A. Yes, the manpage literally says A here — I’m keeping it exact, no cap 💀
• BF — BF is REAL array, dimension (LDB,N); details of the GQR factorization of A and B, as returned by SGGQRF, see SGGQRF for further details.
• Z — Z is REAL array, dimension (LDB,P); the P-by-P orthogonal matrix Z.
• T — T is REAL array, dimension (LDB,max(P,N)). No extra description given, just vibes ✨
• BWK — BWK is REAL array, dimension (LDB,N). Same, that’s all it says.
• LDB — LDB is INTEGER; the leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N).
• TAUB — TAUB is REAL array, dimension (min(P,N)); the scalar factors of the elementary reflectors, as returned by SGGRQF.
• WORK — WORK is REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER; the dimension of the array WORK, LWORK >= max(N,M,P)**2.
• RWORK — RWORK is REAL array, dimension (max(N,M,P)).
• RESULT — RESULT is REAL array, dimension (4); the test ratios:

RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - Q'*Q ) / ( M*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 174 of file sgqrts.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Final cutie sign-off ✨: LAPACK Version 3.12.0, source /home/abui...IG/sgqrts.f(3) — mwah 💋🎀💖