# 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