TESTING/EIG/dgsvts3.f(3)

🎀 TESTING/EIG/dgsvts3.f(3) 🎀

okay so bestie, this page comes from the Library Functions Manual, and it’s all about TESTING/EIG/dgsvts3.f. It’s the test-routine page for the GSVD vibe check, and we are keeping every parameter, constraint, formula, and author credit exactly intact. No cap. 💅

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✨ NAME ✨

TESTING/EIG/dgsvts3.f

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🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

• subroutine dgsvts3 (...) — the full signature is right here, and then it says DGSVTS3. Iconic, honestly.

subroutine dgsvts3 (integer m, integer p, integer n, double precision,
     dimension( lda, * ) a, double precision, dimension( lda, * ) af, integer
     lda, double precision, dimension( ldb, * ) b, double precision,
     dimension( ldb, * ) bf, integer ldb, double precision, dimension( ldu, *
     ) u, integer ldu, double precision, dimension( ldv, * ) v, integer ldv,
     double precision, dimension( ldq, * ) q, integer ldq, double precision,
     dimension( * ) alpha, double precision, dimension( * ) beta, double
     precision, dimension( ldr, * ) r, integer ldr, integer, dimension( * )
     iwork, double precision, dimension( lwork ) work, integer lwork, double
     precision, dimension( * ) rwork, double precision, dimension( 6 )
     result)
     DGSVTS3

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💅 Function/Subroutine Documentation 💅

okay so here’s the signature again, because this page is thorough like that, plus the DGSVTS3 label. We love consistency. 🫶

subroutine dgsvts3 (integer m, integer p, integer n, double precision,
     dimension( lda, * ) a, double precision, dimension( lda, * ) af, integer
     lda, double precision, dimension( ldb, * ) b, double precision,
     dimension( ldb, * ) bf, integer ldb, double precision, dimension( ldu, *
     ) u, integer ldu, double precision, dimension( ldv, * ) v, integer ldv,
     double precision, dimension( ldq, * ) q, integer ldq, double precision,
     dimension( * ) alpha, double precision, dimension( * ) beta, double
     precision, dimension( ldr, * ) r, integer ldr, integer, dimension( * )
     iwork, double precision, dimension( lwork ) work, integer lwork, double
     precision, dimension( * ) rwork, double precision, dimension( 6 )
     result)
     DGSVTS3

🎀 Purpose 🎀

DGSVTS3 tests DGGSVD3, 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 DOUBLE PRECISION array, dimension (LDA,M). The M-by-N matrix A.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the GSVD of A and B, as returned by DGGSVD3; see DGGSVD3 for further details.
• LDA — LDA is INTEGER. The leading dimension of the arrays A and AF. LDA >= max( 1,M ).
• B — B is DOUBLE PRECISION array, dimension (LDB,P). On entry, the P-by-N matrix B.
• BF — BF is DOUBLE PRECISION array, dimension (LDB,N). Details of the GSVD of A and B, as returned by DGGSVD3; see DGGSVD3 for further details.
• LDB — LDB is INTEGER. The leading dimension of the arrays B and BF. LDB >= max(1,P).
• U — U is DOUBLE PRECISION array, dimension (LDU,M). The M by M orthogonal matrix U.
• LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= max(1,M).
• V — V is DOUBLE PRECISION array, dimension (LDV,M). The P by P orthogonal matrix V.
• LDV — LDV is INTEGER. The leading dimension of the array V. LDV >= max(1,P).
• Q — Q is DOUBLE PRECISION array, dimension (LDQ,N). The N by N orthogonal 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 DGGSVD3 for details.
• R — R is DOUBLE PRECISION 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 DOUBLE PRECISION 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 207 of file dgsvts3.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie! Source/version: LAPACK Version 3.12.0, and the footer also has TESTING/EIG/dgsvts3.f(3). Date on the footer? Not listed, so we’re not making one up. Bye 💜✨