TESTING/EIG/cgrqts.f(3)

🎀 NAME 🎀

okay so bestie, the manual name is TESTING/EIG/cgrqts.f and the header is literally TESTING/EIG/cgrqts.f(3) — welcome to the test page, we're doing GRQ factorization gossip today 💖✨

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine cgrqts (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result) — CGRQTS

🌸 Function/Subroutine Documentation 🌸

subroutine cgrqts — CGRQTS

subroutine cgrqts (integer m, integer p, integer n, complex, dimension( lda,
* ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
complex, dimension( lda, * ) r, integer lda, complex, dimension( * )
taua, complex, dimension( ldb, * ) b, complex, dimension( ldb, * ) bf,
complex, dimension( ldb, * ) z, complex, dimension( ldb, * ) t, complex,
dimension( ldb, * ) bwk, integer ldb, complex, dimension( * ) taub,
complex, dimension( lwork ) work, integer lwork, real, dimension( * )
rwork, real, dimension( 4 ) result)
CGRQTS

Purpose ✨

CGRQTS tests CGGRQF, which computes the GRQ factorization of an M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.

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 array, dimension (LDA,N). The M-by-N matrix A.
• AF — COMPLEX array, dimension (LDA,N). Details of the GRQ factorization of A and B, as returned by CGGRQF, see CGGRQF for further details.
• Q — COMPLEX array, dimension (LDA,N). The N-by-N unitary matrix Q.
• R — COMPLEX array, dimension (LDA,MAX(M,N)).
• LDA — INTEGER. The leading dimension of the arrays A, AF, R and Q. LDA >= max(M,N).
• TAUA — COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by SGGQRC.
• B — COMPLEX array, dimension (LDB,N). On entry, the P-by-N matrix A.
• BF — COMPLEX array, dimension (LDB,N). Details of the GQR factorization of A and B, as returned by CGGRQF, see CGGRQF for further details.
• Z — REAL array, dimension (LDB,P). The P-by-P unitary matrix Z.
• T — COMPLEX array, dimension (LDB,max(P,N)).
• BWK — COMPLEX array, dimension (LDB,N).
• LDB — INTEGER. The leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N).
• TAUB — COMPLEX array, dimension (min(P,N)). The scalar factors of the elementary reflectors, as returned by SGGRQF.
• WORK — COMPLEX array, dimension (LWORK).
• LWORK — INTEGER. The dimension of the array WORK, LWORK >= max(M,P,N)**2.
• RWORK — REAL array, dimension (M).
• RESULT — REAL array, dimension (4). The test ratios:
  • RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
  • RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
  • RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
  • RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )

Author 👑

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

Definition at line 174 of file cgrqts.f.

🦋 Author 🦋

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