DGRQTS(3)

🌸 NAME 🌸

Okay bestie, welcome to the DGRQTS(3) page from the LAPACK Library Functions Manual. The NAME section is literally this path:

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

---

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

---

💖 Function/Subroutine Documentation 💖

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

🎯 Purpose 🎯

Okay so, DGRQTS tests DGGRQF, 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. That's the whole purpose, bestie. 💅

🌈 Parameters 🌈

• M — M is INTEGER. This is the number of rows of the matrix A. M >= 0.
• P — P is INTEGER. This is the number of rows of the matrix B. P >= 0.
• N — N is INTEGER. This is the number of columns of the matrices A and B. N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The M-by-N matrix A.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the GRQ factorization of A and B, as returned by DGGRQF, see SGGRQF for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N). The N-by-N orthogonal matrix Q.
• R — R is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by DGGQRC.
• B — B is DOUBLE PRECISION array, dimension (LDB,N). On entry, the P-by-N matrix A. (Yes, it says A here — I'm keeping it exactly as written, bestie 🙈.)
• BF — BF is DOUBLE PRECISION array, dimension (LDB,N). Details of the GQR factorization of A and B, as returned by DGGRQF, see SGGRQF for further details.
• Z — Z is DOUBLE PRECISION array, dimension (LDB,P). The P-by-P orthogonal matrix Z.
• T — T is DOUBLE PRECISION array, dimension (LDB,max(P,N)).
• BWK — BWK is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(P,N)). The scalar factors of the elementary reflectors, as returned by DGGRQF.
• WORK — WORK is DOUBLE PRECISION 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 dgrqts.f.

---

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

That's the whole page, bestie! The footer tea is: source/version LAPACK, Version 3.12.0, and the path /home/abui...IG/dgrqts.f(3). 🎀✨💖