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<HTML>
<HEAD><TITLE>MB01VD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB01VD">MB01VD</A></H2>
<H3>
Kronecker product of two matrices
</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 perform the following matrix operation
C = alpha*kron( op(A), op(B) ) + beta*C,
where alpha and beta are real scalars, op(M) is either matrix M or
its transpose, M', and kron( X, Y ) denotes the Kronecker product
of the matrices X and Y.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB01VD( TRANA, TRANB, MA, NA, MB, NB, ALPHA, BETA,
$ A, LDA, B, LDB, C, LDC, MC, NC, INFO )
C .. Scalar Arguments ..
CHARACTER TRANA, TRANB
INTEGER INFO, LDA, LDB, LDC, MA, MB, MC, NA, NB, NC
DOUBLE PRECISION ALPHA, BETA
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
TRANA CHARACTER*1
Specifies the form of op(A) to be used as follows:
= 'N': op(A) = A;
= 'T': op(A) = A';
= 'C': op(A) = A'.
TRANB CHARACTER*1
Specifies the form of op(B) to be used as follows:
= 'N': op(B) = B;
= 'T': op(B) = B';
= 'C': op(B) = B'.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
MA (input) INTEGER
The number of rows of the matrix op(A). MA >= 0.
NA (input) INTEGER
The number of columns of the matrix op(A). NA >= 0.
MB (input) INTEGER
The number of rows of the matrix op(B). MB >= 0.
NB (input) INTEGER
The number of columns of the matrix op(B). NB >= 0.
ALPHA (input) DOUBLE PRECISION
The scalar alpha. When alpha is zero then A and B need not
be set before entry.
BETA (input) DOUBLE PRECISION
The scalar beta. When beta is zero then C need not be
set before entry.
A (input) DOUBLE PRECISION array, dimension (LDA,ka),
where ka is NA when TRANA = 'N', and is MA otherwise.
If TRANA = 'N', the leading MA-by-NA part of this array
must contain the matrix A; otherwise, the leading NA-by-MA
part of this array must contain the matrix A.
LDA INTEGER
The leading dimension of the array A.
LDA >= max(1,MA), if TRANA = 'N';
LDA >= max(1,NA), if TRANA = 'T' or 'C'.
B (input) DOUBLE PRECISION array, dimension (LDB,kb)
where kb is NB when TRANB = 'N', and is MB otherwise.
If TRANB = 'N', the leading MB-by-NB part of this array
must contain the matrix B; otherwise, the leading NB-by-MB
part of this array must contain the matrix B.
LDB INTEGER
The leading dimension of the array B.
LDB >= max(1,MB), if TRANB = 'N';
LDB >= max(1,NB), if TRANB = 'T' or 'C'.
C (input/output) DOUBLE PRECISION array, dimension (LDC,NC)
On entry, if beta is nonzero, the leading MC-by-NC part of
this array must contain the given matric C, where
MC = MA*MB and NC = NA*NB.
On exit, the leading MC-by-NC part of this array contains
the computed matrix expression
C = alpha*kron( op(A), op(B) ) + beta*C.
LDC INTEGER
The leading dimension of the array C.
LDC >= max(1,MC).
MC (output) INTEGER
The number of rows of the matrix C. MC = MA*MB.
NC (output) INTEGER
The number of columns of the matrix C. NC = NA*NB.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO 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>
The Kronecker product of the matrices op(A) and op(B) is computed
column by column.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
The multiplications by zero elements in A are avoided, if the
matrix A is considered to be sparse, i.e., if
(number of zeros in A)/(MA*NA) >= SPARST = 0.8. The code makes
NB+1 passes through the matrix A, and MA*NA passes through the
matrix B. If LDA and/or LDB are very large, and op(A) = A' and/or
op(B) = B', it could be more efficient to transpose A and/or B
before calling this routine, and use the 'N' values for TRANA
and/or TRANB.
</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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