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<HTML>
<HEAD><TITLE>MA02ID - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MA02ID">MA02ID</A></H2>
<H3>
Matrix 1-, Frobenius, or infinity norms of a skew-Hamiltonian matrix
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To compute the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value
of a real skew-Hamiltonian matrix
[ A G ] T T
X = [ T ], G = -G, Q = -Q,
[ Q A ]
or of a real Hamiltonian matrix
[ A G ] T T
X = [ T ], G = G, Q = Q,
[ Q -A ]
where A, G and Q are real n-by-n matrices.
Note that for this kind of matrices the infinity norm is equal
to the one norm.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
DOUBLE PRECISION FUNCTION MA02ID( TYP, NORM, N, A, LDA, QG,
$ LDQG, DWORK )
C .. Scalar Arguments ..
CHARACTER NORM, TYP
INTEGER LDA, LDQG, N
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), DWORK(*), QG(LDQG,*)
</PRE>
<B><FONT SIZE="+1">Function Value</FONT></B>
<PRE>
MA02ID DOUBLE PRECISION
The computed norm.
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
TYP CHARACTER*1
Specifies the type of the input matrix X:
= 'S': X is skew-Hamiltonian;
= 'H': X is Hamiltonian.
NORM CHARACTER*1
Specifies the value to be returned in MA02ID:
= '1' or 'O': one norm of X;
= 'F' or 'E': Frobenius norm of X;
= 'I': infinity norm of X;
= 'M': max(abs(X(i,j)).
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the matrix A.
LDA INTEGER
The leading dimension of the array A. LDA >= MAX(1,N).
QG (input) DOUBLE PRECISION array, dimension (LDQG,N+1)
On entry, the leading N-by-N+1 part of this array must
contain in columns 1:N the lower triangular part of the
matrix Q and in columns 2:N+1 the upper triangular part
of the matrix G. If TYP = 'S', the parts containing the
diagonal and the first supdiagonal of this array are not
referenced.
LDQG INTEGER
The leading dimension of the array QG. LDQG >= MAX(1,N).
</PRE>
<B>Workspace</B>
<PRE>
DWORK DOUBLE PRECISION array, dimension (LDWORK)
where LDWORK >= 2*N when NORM = '1', NORM = 'I' or
NORM = 'O'; otherwise, DWORK is not referenced.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
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