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<HTML>
<HEAD><TITLE>MB01QD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB01QD">MB01QD</A></H2>
<H3>
Matrix scaling (lower 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 multiply the M by N real matrix A by the real scalar CTO/CFROM.
This is done without over/underflow as long as the final result
CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
A may be full, (block) upper triangular, (block) lower triangular,
(block) upper Hessenberg, or banded.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB01QD( TYPE, M, N, KL, KU, CFROM, CTO, NBL, NROWS, A,
$ LDA, INFO )
C .. Scalar Arguments ..
CHARACTER TYPE
INTEGER INFO, KL, KU, LDA, M, N, NBL
DOUBLE PRECISION CFROM, CTO
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>
TYPE CHARACTER*1
TYPE indices the storage type of the input matrix.
= 'G': A is a full matrix.
= 'L': A is a (block) lower triangular matrix.
= 'U': A is a (block) upper triangular matrix.
= 'H': A is a (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'.
CFROM (input) DOUBLE PRECISION
CTO (input) DOUBLE PRECISION
The matrix A is multiplied by CTO/CFROM. A(I,J) is
computed without over/underflow if the final result
CTO*A(I,J)/CFROM can be represented without over/
underflow. CFROM must be nonzero.
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 array NROWS is not referenced if NBL = 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
The matrix to be multiplied by CTO/CFROM. See TYPE for
the storage type.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
Not used in this implementation.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
Matrix A is multiplied by the real scalar CTO/CFROM, taking into
account the specified storage mode of the matrix.
MB01QD is a version of the LAPACK routine DLASCL, modified for
dealing with block triangular, or block Hessenberg matrices.
For efficiency, no tests of the input scalar parameters are
performed.
</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>
<p>
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