TESTING/EIG/zgrqts.f(3)

🌸 NAME 🌸

TESTING/EIG/zgrqts.f — okay bestie, this is the page for that file, and the manual it belongs to is the Library Functions Manual. It's all about the zgrqts subroutine — a.k.a. the ZGRQTS function/subroutine situation. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

   subroutine zgrqts (integer m, integer p, integer n, 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)
       ZGRQTS

🎯 Purpose

ZGRQTS tests ZGGRQF, 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.

🔍 Parameters

• M — M is INTEGER; the number of rows of the matrix A. Constraint: M >= 0.
• P — P is INTEGER; the number of rows of the matrix B. Constraint: P >= 0.
• N — N is INTEGER; the number of columns of the matrices A and B. Constraint: N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N); the M-by-N matrix A.
• AF — AF is COMPLEX*16 array, dimension (LDA,N); details of the GRQ factorization of A and B, as returned by ZGGRQF, see CGGRQF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N); the N-by-N 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. Constraint: LDA >= max(M,N).
• TAUA — TAUA is COMPLEX*16 array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by DGGQRC.
• B — B is COMPLEX*16 array, dimension (LDB,N); on entry, the P-by-N matrix A.
• BF — BF is COMPLEX*16 array, dimension (LDB,N); details of the GQR factorization of A and B, as returned by ZGGRQF, see CGGRQF for further details.
• Z — Z is DOUBLE PRECISION 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. Constraint: 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(M,P,N)**2.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (4); the test ratios:

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 174 of file zgrqts.f.

---

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💋 — signing off with the footer details: LAPACK, Version 3.12.0, TESTING/EIG/zgrqts.f(3). That's the whole vibe, bestie. 🫶