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<HTML>
<HEAD><TITLE>MB01PD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB01PD">MB01PD</A></H2>
<H3>
Matrix scaling (higher level routine)
</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 scale a matrix or undo scaling. Scaling is performed, if
necessary, so that the matrix norm will be in a safe range of
representable numbers.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB01PD( SCUN, TYPE, M, N, KL, KU, ANRM, NBL, NROWS, A,
$ LDA, INFO )
C .. Scalar Arguments ..
CHARACTER SCUN, TYPE
INTEGER INFO, KL, KU, LDA, M, MN, N, NBL
DOUBLE PRECISION ANRM
C .. Array Arguments ..
INTEGER NROWS ( * )
DOUBLE PRECISION A( LDA, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
SCUN CHARACTER*1
SCUN indicates the operation to be performed.
= 'S': scale the matrix.
= 'U': undo scaling of the matrix.
TYPE CHARACTER*1
TYPE indicates the storage type of the input matrix.
= 'G': A is a full matrix.
= 'L': A is a (block) lower triangular matrix.
= 'U': A is an (block) upper triangular matrix.
= 'H': A is an (block) upper Hessenberg matrix.
= 'B': A is a symmetric band matrix with lower bandwidth
KL and upper bandwidth KU and with the only the
lower half stored.
= 'Q': A is a symmetric band matrix with lower bandwidth
KL and upper bandwidth KU and with the only the
upper half stored.
= 'Z': A is a band matrix with lower bandwidth KL and
upper bandwidth KU.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
KL (input) INTEGER
The lower bandwidth of A. Referenced only if TYPE = 'B',
'Q' or 'Z'.
KU (input) INTEGER
The upper bandwidth of A. Referenced only if TYPE = 'B',
'Q' or 'Z'.
ANRM (input) DOUBLE PRECISION
The norm of the initial matrix A. ANRM >= 0.
When ANRM = 0 then an immediate return is effected.
ANRM should be preserved between the call of the routine
with SCUN = 'S' and the corresponding one with SCUN = 'U'.
NBL (input) INTEGER
The number of diagonal blocks of the matrix A, if it has a
block structure. To specify that matrix A has no block
structure, set NBL = 0. NBL >= 0.
NROWS (input) INTEGER array, dimension max(1,NBL)
NROWS(i) contains the number of rows and columns of the
i-th diagonal block of matrix A. The sum of the values
NROWS(i), for i = 1: NBL, should be equal to min(M,N).
The elements of the array NROWS are not referenced if
NBL = 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading M by N part of this array must
contain the matrix to be scaled/unscaled.
On exit, the leading M by N part of A will contain
the modified matrix.
The storage mode of A is specified by TYPE.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
Denote by ANRM the norm of the matrix, and by SMLNUM and BIGNUM,
two positive numbers near the smallest and largest safely
representable numbers, respectively. The matrix is scaled, if
needed, such that the norm of the result is in the range
[SMLNUM, BIGNUM]. The scaling factor is represented as a ratio
of two numbers, one of them being ANRM, and the other one either
SMLNUM or BIGNUM, depending on ANRM being less than SMLNUM or
larger than BIGNUM, respectively. For undoing the scaling, the
norm is again compared with SMLNUM or BIGNUM, and the reciprocal
of the previous scaling factor is used.
</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>
<HR>
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