TESTING/EIG/zgqrts.f(3)

💅 TESTING/EIG/zgqrts.f

okay so this page comes from the Library Functions Manual, and the title is literally TESTING/EIG/zgqrts.f — bestie, we are deep in LAPACK testing land and it’s giving subroutine-documentation realness ✨

🌸 NAME

TESTING/EIG/zgqrts.f

📜 SYNOPSIS

🧚 Functions/Subroutines

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

📚 Function/Subroutine Documentation

🧬 subroutine zgqrts

subroutine zgqrts (integer n, integer m, integer p, complex*16, dimension(
    lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension(
    lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16,
    dimension( * ) taua, complex*16, dimension( ldb, * ) b, complex*16,
    dimension( ldb, * ) bf, complex*16, dimension( ldb, * ) z, complex*16,
    dimension( ldb, * ) t, complex*16, dimension( ldb, * ) bwk, integer ldb,
    complex*16, dimension( * ) taub, complex*16, dimension( lwork ) work,
    integer lwork, double precision, dimension( * ) rwork, double precision,
    dimension( 4 ) result)
    ZGQRTS

🎯 Purpose

okay so ZGQRTS tests ZGGQRF, 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 💖

🧾 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 COMPLEX*16 array, dimension (LDA,M). The N-by-M matrix A.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the GQR factorization of A and B, as returned by ZGGQRF, see CGGQRF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N). The M-by-M unitary matrix Q.
• R — R is COMPLEX*16 array, dimension (LDA,MAX(M,N)).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, R and Q. LDA >= max(M,N).
• TAUA — TAUA is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by ZGGQRF.
• B — B is COMPLEX*16 array, dimension (LDB,P). On entry, the N-by-P matrix A.
• BF — BF is COMPLEX*16 array, dimension (LDB,N). Details of the GQR factorization of A and B, as returned by ZGGQRF, see CGGQRF for further details.
• Z — Z is COMPLEX*16 array, dimension (LDB,P). The P-by-P unitary matrix Z.
• T — T is COMPLEX*16 array, dimension (LDB,max(P,N)).
• BWK — BWK is COMPLEX*16 array, dimension (LDB,N).
• LDB — LDB is INTEGER. The leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N).
• TAUB — TAUB is COMPLEX*16 array, dimension (min(P,N)). The scalar factors of the elementary reflectors, as returned by DGGRQF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK, LWORK >= max(N,M,P)**2.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (max(N,M,P)).
• RESULT — RESULT is DOUBLE PRECISION 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 )

vibe check: all those bounds are part of the lore — N >= 0, M >= 0, P >= 0, LDA >= max(M,N), LDB >= max(P,N), and LWORK >= max(N,M,P)**2. do not skip them 💀

🫶 Author

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

Definition at line 174 of file zgqrts.f.

🛠️ Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page 💖 the auto-generated sign-off is: generated automatically by Doxygen for LAPACK from the source code; footer vibes are LAPACK Version 3.12.0 and TESTING/EIG/zgqrts.f(3) — slay, stay bounded, and read the test ratios 🫶✨