TESTING/EIG/zgsvts3.f(3)

okay bestie, welcome to TESTING/EIG/zgsvts3.f(3) 💖 — that's the page title, and it's living in the Library Functions Manual. This is the LAPACK reference page for the zgsvts3 subroutine, and we're gonna go through every detail like it's a group-chat receipt check. no cap. ✨

🎀 NAME 🎀

TESTING/EIG/zgsvts3.f — that's the name, periodt. Not me being a whole file path, but yes. 💅

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

subroutine zgsvts3 (m, p, n, a, af, lda, b, bf, ldb, u, ldu, v, ldv, q,
           ldq, alpha, beta, r, ldr, iwork, work, lwork, rwork, result)

The label under it is ZGSVTS3, iconic. 💖

🌈 Function/Subroutine Documentation 🌈

subroutine zgsvts3 (integer m, integer p, integer n, complex*16, dimension(
       lda, * ) a, complex*16, dimension( lda, * ) af, integer lda, complex*16,
       dimension( ldb, * ) b, complex*16, dimension( ldb, * ) bf, integer ldb,
       complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension(
       ldv, * ) v, integer ldv, complex*16, dimension( ldq, * ) q, integer ldq,
       double precision, dimension( * ) alpha, double precision, dimension( * )
       beta, complex*16, dimension( ldr, * ) r, integer ldr, integer,
       dimension( * ) iwork, complex*16, dimension( lwork ) work, integer
       lwork, double precision, dimension( * ) rwork, double precision,
       dimension( 6 ) result)

ZGSVTS3 — main character energy, honestly. 👑

💖 Purpose 💖

!>
!> ZGSVTS3 tests ZGGSVD3, which computes the GSVD of an M-by-N matrix A
!> and a P-by-N matrix B:
!>              U'*A*Q = D1*R and V'*B*Q = D2*R.
!>

🍓 Parameters 🍓

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. 🫶
• P — P is INTEGER. The number of rows of the matrix B. P >= 0.
• N — N is INTEGER. The number of columns of the matrices A and B. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,M). The M-by-N matrix A.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the GSVD of A and B, as returned by ZGGSVD3, see ZGGSVD3 for further details.
• LDA — LDA is INTEGER. The leading dimension of the arrays A and AF. LDA >= max( 1,M ).
• B — B is COMPLEX*16 array, dimension (LDB,P). On entry, the P-by-N matrix B.
• BF — BF is COMPLEX*16 array, dimension (LDB,N). Details of the GSVD of A and B, as returned by ZGGSVD3, see ZGGSVD3 for further details.
• LDB — LDB is INTEGER. The leading dimension of the arrays B and BF. LDB >= max(1,P).
• U — U is COMPLEX*16 array, dimension(LDU,M). The M by M unitary matrix U.
• LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= max(1,M).
• V — V is COMPLEX*16 array, dimension(LDV,M). The P by P unitary matrix V.
• LDV — LDV is INTEGER. The leading dimension of the array V. LDV >= max(1,P).
• Q — Q is COMPLEX*16 array, dimension(LDQ,N). The N by N unitary matrix Q.
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• ALPHA — ALPHA is DOUBLE PRECISION array, dimension (N).
• BETA — BETA is DOUBLE PRECISION array, dimension (N). The generalized singular value pairs of A and B, the ``diagonal'' matrices D1 and D2 are constructed from ALPHA and BETA, see subroutine ZGGSVD3 for details.
• R — R is COMPLEX*16 array, dimension(LDQ,N). The upper triangular matrix R.
• LDR — LDR is INTEGER. The leading dimension of the array R. LDR >= max(1,N).
• IWORK — IWORK is INTEGER array, dimension (N).
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK, LWORK >= max(M,P,N)*max(M,P,N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (max(M,P,N)).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (6). The test ratios:

RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - U'*U ) / ( M*ULP )
RESULT(4) = norm( I - V'*V ) / ( P*ULP )
RESULT(5) = norm( I - Q'*Q ) / ( N*ULP )
RESULT(6) = 0        if ALPHA is in decreasing order;
          = ULPINV   otherwise.

💜 Author 💜

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 206 of file zgsvts3.f. — exact, bestie. 🦋

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. — the bot did its thing, no cap. 🤖✨

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okay that's the whole thing bestie 💖 source/version check: LAPACK Version 3.12.0, and the page is TESTING/EIG/zgsvts3.f(3). bye diva 👑✨