TESTING/EIG/zsyl01.f(3)

📦
version 3.12.1 · 3 versions
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💖 NAME 💖

okay bestie, this is the Library Functions Manual page for TESTING/EIG/zsyl01.f(3) — the zsyl01 routine, and it is lowkey all about testing the Sylvester-equation girlies ZTRSYL and ZTRSYL3. ✨

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

subroutine zsyl01 (thresh, nfail, rmax, ninfo, knt)
    ZSYL01

🦋 Function/Subroutine Documentation 🦋

💫 subroutine zsyl01 💫

subroutine zsyl01 (double precision thresh, integer, dimension( 3 ) nfail,
    double precision, dimension( 2 ) rmax, integer, dimension( 2 ) ninfo,
    integer knt)

🌟 ZSYL01 🌟

🎀 Purpose 🎀

bestie, <pink>ZSYL01</pink> tests <purple>ZTRSYL</purple> and <purple>ZTRSYL3</purple>, the routines for solving the Sylvester matrix equation:

op(A)*X + ISGN*X*op(B) = scale*C,

where op(A) and op(B) are both upper triangular form, op() represents an optional conjugate transpose, and ISGN can be -1 or +1. Scale is an output less than or equal to 1, chosen to avoid overflow in X. 🫶

The test code verifies that the following residual does not exceed the provided threshold:

norm(op(A)*X + ISGN*X*op(B) - scale*C) /
    (EPS*max(norm(A),norm(B))*norm(X))

This routine complements <cyan>ZGET35</cyan> by testing with larger, random matrices, of which some require rescaling of X to avoid overflow. no cap, that part is important. 💅

🍓 Parameters 🍓

  • THRESH — THRESH is DOUBLE PRECISION. A test counts as a fail when the residual, computed as described above, exceeds THRESH.
  • NFAIL — NFAIL is INTEGER array, dimension (3).
    • NFAIL(1) = No. of times residual ZTRSYL exceeds threshold THRESH
    • NFAIL(2) = No. of times residual ZTRSYL3 exceeds threshold THRESH
    • NFAIL(3) = No. of times ZTRSYL3 and ZTRSYL deviate
  • RMAX — RMAX is DOUBLE PRECISION array, dimension (2).
    • RMAX(1) = Value of the largest test ratio of ZTRSYL
    • RMAX(2) = Value of the largest test ratio of ZTRSYL3
  • NINFO — NINFO is INTEGER array, dimension (2).
    • NINFO(1) = No. of times ZTRSYL returns an expected INFO
    • NINFO(2) = No. of times ZTRSYL3 returns an expected INFO
  • KNT — KNT is INTEGER. Total number of examples tested. 🧚

Definition at line 88 of file zsyl01.f.

🌸 Author 🌸

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xoxo, LAPACK Version 3.12.0 manual page TESTING/EIG/zsyl01.f(3) 🫶💖

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