/home/abui.../zgsvts3.f(3)

hey bestie 💖 welcome to the zgsvts3.f(3) page from the Library Functions Manual — it's giving serious LAPACK test-routine energy and I'm obsessed 🫶

🌸 NAME 🌸

This is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zgsvts3.f.

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✨ 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)
           ZGSVTS3

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💖 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

🎯 Purpose 🎯

Okay so ZGSVTS3 is the test bestie for 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.

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🌟 Parameters 🌟

• M — INTEGER. The number of rows of the matrix A. M >= 0.
• P — INTEGER. The number of rows of the matrix B. P >= 0.
• N — INTEGER. The number of columns of the matrices A and B. N >= 0.
• A — COMPLEX*16 array, dimension (LDA,M). The M-by-N matrix A.
• AF — COMPLEX*16 array, dimension (LDA,N). Details of the GSVD of A and B, as returned by ZGGSVD3, see ZGGSVD3 for further details.
• LDA — INTEGER. The leading dimension of the arrays A and AF. LDA >= max( 1,M ).
• B — COMPLEX*16 array, dimension (LDB,P). On entry, the P-by-N matrix B.
• BF — COMPLEX*16 array, dimension (LDB,N). Details of the GSVD of A and B, as returned by ZGGSVD3, see ZGGSVD3 for further details.
• LDB — INTEGER. The leading dimension of the arrays B and BF. LDB >= max(1,P).
• U — COMPLEX*16 array, dimension(LDU,M). The M by M unitary matrix U.
• LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,M).
• V — COMPLEX*16 array, dimension(LDV,M). The P by P unitary matrix V.
• LDV — INTEGER. The leading dimension of the array V. LDV >= max(1,P).
• Q — COMPLEX*16 array, dimension(LDQ,N). The N by N unitary matrix Q.
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• ALPHA — DOUBLE PRECISION array, dimension (N).
• BETA — 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 — COMPLEX*16 array, dimension(LDQ,N). The upper triangular matrix R.
• LDR — INTEGER. The leading dimension of the array R. LDR >= max(1,N).
• IWORK — INTEGER array, dimension (N).
• WORK — COMPLEX*16 array, dimension (LWORK).
• LWORK — INTEGER. The dimension of the array WORK, LWORK >= max(M,P,N)*max(M,P,N).
• RWORK — DOUBLE PRECISION array, dimension (max(M,P,N)).
• RESULT — 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.

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 206 of file zgsvts3.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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