TESTING/LIN/zqrt17.f(3)

💅 NAME 💅

Okay bestie, this page is all about TESTING/LIN/zqrt17.f, and the full manual name is TESTING/LIN/zqrt17.f(3). The main character here is the zqrt17 routine — no cap, it's giving LAPACK testing-file energy. 💖

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✨ SYNOPSIS ✨

Functions/Subroutines

double precision function zqrt17 (trans, iresid, m, n, nrhs, a, lda, x,
    ldx, b, ldb, c, work, lwork)
    ZQRT17

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🛠️ Function/Subroutine Documentation 🛠️

double precision function zqrt17 (character trans, integer iresid, integer
    m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer
    lda, complex*16, dimension( ldx, * ) x, integer ldx, complex*16,
    dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldb, * ) c,
    complex*16, dimension( lwork ) work, integer lwork)
    ZQRT17

🎯 Purpose 🎯

So, ZQRT17 computes the ratio:

norm(R**H * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),

where R = B - op(A)*X, op(A) is A or A**H, depending on TRANS, EPS is the machine epsilon, and:

alpha = norm(B) if IRESID = 1 (zero-residual problem)
alpha = norm(R) if IRESID = 2 (otherwise).

The norm used is the 1-norm. Periodt. 💅

🧾 Parameters 🧾

• TRANS — TRANS is CHARACTER*1. Specifies whether or not the transpose of A is used. = 'N': No transpose, op(A) = A. = 'C': Conjugate transpose, op(A) = A**H.
• IRESID — IRESID is INTEGER. IRESID = 1 indicates zero-residual problem. IRESID = 2 indicates non-zero residual.
• M — M is INTEGER. The number of rows of the matrix A. If TRANS = 'N', the number of rows of the matrix B. If TRANS = 'C', the number of rows of the matrix X.
• N — N is INTEGER. The number of columns of the matrix A. If TRANS = 'N', the number of rows of the matrix X. If TRANS = 'C', the number of rows of the matrix B.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X and B.
• A — A is COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= M.
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). If TRANS = 'N', the n-by-nrhs matrix X. If TRANS = 'C', the m-by-nrhs matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. If TRANS = 'N', LDX >= N. If TRANS = 'C', LDX >= M.
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). If TRANS = 'N', the m-by-nrhs matrix B. If TRANS = 'C', the n-by-nrhs matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. If TRANS = 'N', LDB >= M. If TRANS = 'C', LDB >= N.
• C — C is COMPLEX*16 array, dimension (LDB,NRHS).
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= NRHS*(M+N).

🫶 Author 🫶

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

Definition at line 151 of file zqrt17.f.

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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Byeee bestie! 🎀 This iconic page is from LAPACK Version 3.12.0, manual name TESTING/LIN/zqrt17.f(3) — slay, stay sparkly, and go compute that ratio. ✨💅