ZQLT02(3)

okay so bestie, welcome to the Library Functions Manual page for ZQLT02(3) 💅✨

🎀 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqlt02.f

🌈 SYNOPSIS

🦋 Functions/Subroutines

• subroutine ZQLT02 — the whole subroutine vibe, with these args:

       subroutine ZQLT02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
           result)
           ZQLT02

💖 Function/Subroutine Documentation

   subroutine ZQLT02 (integer m, integer n, integer k, complex*16, dimension(
       lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension(
       lda, * ) q, complex*16, dimension( lda, * ) l, integer lda, complex*16,
       dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork,
       double precision, dimension( * ) rwork, double precision, dimension( * )
       result)
       ZQLT02

✨ Purpose

okay so here’s the tea: ZQLT02 tests ZUNGQL, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors. 🫶

Given the QL factorization of an m-by-n matrix A, ZQLT02 generates the orthogonal matrix Q defined by the factorization of the last k columns of A; it compares L(m-n+1:m,n-k+1:n) with Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are orthonormal. 💖

🍓 Parameters

• M — M is INTEGER; the number of rows of the matrix Q to be generated. M >= 0.
• N — N is INTEGER; the number of columns of the matrix Q to be generated. M >= N >= 0.
• K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N); the m-by-n matrix A which was factorized by ZQLT01.
• AF — AF is COMPLEX*16 array, dimension (LDA,N); details of the QL factorization of A, as returned by ZGEQLF. See ZGEQLF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N).
• L — L is COMPLEX*16 array, dimension (LDA,N).
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, Q and L. LDA >= M.
• TAU — TAU is COMPLEX*16 array, dimension (N); the scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER; the dimension of the array WORK.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2); the test ratios:
  • RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
  • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

👑 Author

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

Definition at line 134 of file zqlt02.f.

🧚 Author

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