.TH "TESTING/EIG/zsyl01.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/zsyl01.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzsyl01\fP (thresh, nfail, rmax, ninfo, knt)"
.br
.RI "\fBZSYL01\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zsyl01 (double precision thresh, integer, dimension( 3 ) nfail, double precision, dimension( 2 ) rmax, integer, dimension( 2 ) ninfo, integer knt)"

.PP
\fBZSYL01\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITHRESH\fP 
.PP
.nf
          THRESH is DOUBLE PRECISION
          A test will count as 'failed' if the residual, computed as
          described above, exceeds THRESH\&.
.fi
.PP
.br
\fINFAIL\fP 
.PP
.nf
          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
.fi
.PP
.br
\fIRMAX\fP 
.PP
.nf
          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
.fi
.PP
.br
\fININFO\fP 
.PP
.nf
          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
.fi
.PP
.br
\fIKNT\fP 
.PP
.nf
          KNT is INTEGER
          Total number of examples tested\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB88\fP of file \fBzsyl01\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.