TESTING/EIG/cgsvts3.f(3)

🌸 NAME 🌸

TESTING/EIG/cgsvts3.f — from the Library Functions Manual, bestie. This is the page for CGSVTS3, and it's giving “test routine with a whole lot of arrays.” 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine cgsvts3 (m, p, n, a, af, lda, b, bf, ldb, u, ldu, v, ldv, q, ldq, alpha, beta, r, ldr, iwork, work, lwork, rwork, result)

CGSVTS3

💅 Function/Subroutine Documentation 💅

Full signature, exactly as written:

subroutine cgsvts3 (integer m, integer p, integer n, complex, dimension( lda, * ) a, complex, dimension( lda, * ) af, integer lda, complex, dimension( ldb, * ) b, complex, dimension( ldb, * ) bf, integer ldb, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldq, * ) q, integer ldq, real, dimension( * ) alpha, real, dimension( * ) beta, complex, dimension( ldr, * ) r, integer ldr, integer, dimension( * ) iwork, complex, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 6 ) result)

CGSVTS3

🎀 Purpose: 🎀

Okay so CGSVTS3 tests CGGSVD3, 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 purpose, and it ate. ✨

🍓 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 array, dimension (LDA,M). The M-by-N matrix A.
• AF — AF is COMPLEX array, dimension (LDA,N). Details of the GSVD of A and B, as returned by CGGSVD3, see CGGSVD3 for further details.
• LDA — LDA is INTEGER. The leading dimension of the arrays A and AF. LDA >= max( 1,M ).
• B — B is COMPLEX array, dimension (LDB,P). On entry, the P-by-N matrix B.
• BF — BF is COMPLEX array, dimension (LDB,N). Details of the GSVD of A and B, as returned by CGGSVD3, see CGGSVD3 for further details.
• LDB — LDB is INTEGER. The leading dimension of the arrays B and BF. LDB >= max(1,P).
• U — U is COMPLEX 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 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 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 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 CGGSVD3 for details.
• R — R is COMPLEX 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 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 206 of file cgsvts3.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

That's the page, bestie! 🌈 Footer vibes: LAPACK, Version 3.12.0, and the page title TESTING/EIG/cgsvts3.f(3). The original footer didn't print a date, so no fake date here — periodt. 💖🎀