TESTING/EIG/sgqrts.f(3)

💅 TESTING/EIG/sgqrts.f(3) 💅

okay so bestie, this page is from the Library Functions Manual — yes, that's the manual name — and it's all about TESTING/EIG/sgqrts.f. The vibe? Fortran test-helper subroutine, extremely specific, we love her. 💖

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✨ NAME ✨

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 🧚

   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. periodt, that's the whole purpose. 💫

💖 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 in the original, 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, it literally says A there — we're keeping the original wording exactly, 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 in the source.
• BWK — BWK is REAL array, dimension (LDB,N). No extra description in the source.
• 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). No extra description in the source.
• 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)). No extra description in the source.
• 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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okay that's the whole page, bestie — this one is from LAPACK, Version 3.12.0, and it's the TESTING/EIG/sgqrts.f(3) page. bye 💋✨