# zsyl01.f - Man Page

TESTING/EIG/zsyl01.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

ZSYL01

Purpose:

``` ZSYL01 tests ZTRSYL and ZTRSYL3, 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 ZGET35 by testing with larger,
random matrices, of which some require rescaling of X to avoid overflow.```
Parameters

THRESH

```          THRESH is DOUBLE PRECISION
A test will count as 'failed' if 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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zsyl01(3) is an alias of zsyl01.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK