TESTING/EIG/csyl01.f(3)

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💅 TESTING/EIG/csyl01.f(3) 💅

okay so this page is from the Library Functions Manual, and the manual name is literally folded right here so you don't have to reread that header line, bestie. It's all about TESTING/EIG/csyl01.f — and yes, the title ate. 🎀

✨ NAME ✨

TESTING/EIG/csyl01.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine csyl01 (thresh, nfail, rmax, ninfo, knt)
    CSYL01

🦋 Function/Subroutine Documentation 🦋

subroutine csyl01 (real thresh, integer, dimension( 3 ) nfail, real,
       dimension( 2 ) rmax, integer, dimension( 2 ) ninfo, integer knt)

CSYL01

🎀 Purpose: 🎀

CSYL01 tests CTRSYL and CTRSYL3, 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 CGET35 by testing with larger, random matrices, of which some require rescaling of X to avoid overflow.

🍓 Parameters 🍓

  • THRESH — THRESH is REAL. A test will count as (the source has a lil blank here, bless) if the residual, computed as described above, exceeds THRESH.
  • NFAIL — NFAIL is INTEGER array, dimension (3). NFAIL(1) = No. of times residual CTRSYL exceeds threshold THRESH; NFAIL(2) = No. of times residual CTRSYL3 exceeds threshold THRESH; NFAIL(3) = No. of times CTRSYL3 and CTRSYL deviate.
  • RMAX — RMAX is DOUBLE PRECISION array, dimension (2). RMAX(1) = Value of the largest test ratio of CTRSYL; RMAX(2) = Value of the largest test ratio of CTRSYL3.
  • NINFO — NINFO is INTEGER array, dimension (2). NINFO(1) = No. of times CTRSYL where INFO is nonzero; NINFO(2) = No. of times CTRSYL3 where INFO is nonzero.
  • KNT — KNT is INTEGER. Total number of examples tested.
📌 Definition at line 88 of file csyl01.f.

👑 Author 👑

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