TESTING/EIG/sgsvts3.f(3)

💖 NAME 💖

TESTING/EIG/sgsvts3.f — bestie, this is the LAPACK Library Functions Manual page for that file. The routine it documents is SGSVTS3, and yes, it's giving very specific matrix-testing energy. ✨

✨ SYNOPSIS ✨

Functions/Subroutines

• sgsvts3 — the subroutine. Official name: SGSVTS3.

subroutine sgsvts3 (integer m, integer p, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, integer ldb, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) alpha, real, dimension( * ) beta, real, dimension( ldr, * ) r, integer ldr, integer, dimension( * ) iwork, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 6 ) result)

🦋 Function/Subroutine Documentation 🦋

subroutine sgsvts3 (integer m, integer p, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, integer ldb, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) alpha, real, dimension( * ) beta, real, dimension( ldr, * ) r, integer ldr, integer, dimension( * ) iwork, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 6 ) result)

This one is SGSVTS3. Iconic name, extremely specific job. 💅

🌸 Purpose 🌸

SGSVTS3 tests SGGSVD3, 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.

That's the whole point, iykyk. 🫶

💅 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 REAL array, dimension (LDA,M); the M-by-N matrix A.
• AF — AF is REAL array, dimension (LDA,N); details of the GSVD of A and B, as returned by SGGSVD3, see SGGSVD3 for further details.
• LDA — LDA is INTEGER; the leading dimension of the arrays A and AF. LDA >= max( 1,M ).
• B — B is REAL array, dimension (LDB,P); on entry, the P-by-N matrix B.
• BF — BF is REAL array, dimension (LDB,N); details of the GSVD of A and B, as returned by SGGSVD3, see SGGSVD3 for further details.
• LDB — LDB is INTEGER; the leading dimension of the arrays B and BF. LDB >= max(1,P).
• U — U is REAL 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 REAL 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 REAL 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 REAL array, dimension (N).
• BETA — BETA is REAL 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 SGGSVD3 for details.
• R — R is REAL 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 REAL 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 REAL array, dimension (max(M,P,N)).
• RESULT — RESULT is REAL 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 sgsvts3.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That's the whole manual, bestie! Source/version: LAPACK Version 3.12.0; page: TESTING/EIG/sgsvts3.f(3). Periodt. 💅