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<BR> <P>
<H2><A NAME="SECTION04447000000000000000">Argument Descriptions for Band and Tridiagonal Routines</A></H2>
<P>
<A NAME="secargdescband"> </A>
<A NAME="3233"> </A>
<A NAME="3234"> </A>
<A NAME="3235"> </A>
<A NAME="3236"> </A>
<A NAME="3237"> </A>
<P>
All ScaLAPACK narrow band and
tridiagonal routines assume
that the global matrices are
distributed in a one-dimensional
block data distribution. Thus,
each process has at most one
block of data. With selective
choices for the block size
NB_ and the order N_ of
the global matrix, it is
possible that some processes
in the process grid may not
receive any data, or the last
process receiving data will
receive a smaller block of
data than the other processes.
<P>
For further information on
one-dimensional block-column
or block-row data distribution,
please refer to section <A HREF="node82.html#sec1dbd">4.4.1</A>.
<P>
The description of a block-column
distributed band matrix consists
of <TT>(N, A, JA, DESCA)</TT>
<UL>
<LI> the order <TT>N</TT> of the band matrix operand,
<LI> a pointer to the local array containing the
entire global array (<TT>A</TT>, for example),
<LI> the column index, <TT>JA</TT>, of the global array, and
<LI> the array descriptor, <TT>DESCA</TT>, of the global array.
</UL>
<P>
The description of a block-row
distributed right-hand-side matrix
consists of <TT>(NRHS, B, IB, DESCB)</TT>
<UL>
<LI> the number of right-hand-side vectors <TT>NRHS</TT> in the matrix,
<LI> a pointer to the local array containing the
entire global array (<TT>B</TT>, for example),
<LI> the row index, <TT>IB</TT>, of the global array, and
<LI> the array descriptor, <TT>DESCB</TT>, for the global array.
</UL>
<P>
The description of a block-distributed
diagonally dominant-like tridiagonal
matrix consists of <TT>(N, DL, D, DU, JA, DESCA)</TT>
<UL>
<LI> the order <TT>N</TT> of the tridiagonal matrix operand,
<LI> pointer to the local arrays, (<TT>DL, D, DU</TT>, for example),
<LI> the column index, <TT>JA</TT>, of the global array, and
<LI> the array descriptor, <TT>DESCA</TT>, for the global array.
</UL>
<P>
The description of a block-distributed
symmetric positive definite tridiagonal
matrix consists of <TT>(N, D, E, JA, DESCA)</TT>
<UL>
<LI> the order <TT>N</TT> of the tridiagonal matrix operand,
<LI> pointer to the local arrays, (<TT>D, E</TT>, for example),
<LI> the column index, <TT>JA</TT>, of the global array,
<LI> the array descriptor, <TT>DESCA</TT>, for the global array.
</UL>
<P>
The name of the row or column index
for the global array has the form
I<array_name><A NAME="3267"> </A> or
J<array_name><A NAME="3268"> </A>,
respectively. The array descriptor
has a name of the form DESC<array_name><A NAME="3269"> </A>.
<A NAME="3270"> </A><A NAME="3271"> </A>
The length of the array descriptor is
specified by DLEN_ and varies according
to the descriptor type DTYPE_.
<P>
Included in the leading comments of each
subroutine (immediately preceding the Argument
section), is a brief note describing the
<B>array descriptor</B><A NAME="3273"> </A><A NAME="3274"> </A><A NAME="3275"> </A> and some commonly used expressions in
calculating workspace.
<P>
The style of the argument<A NAME="3276"> </A>
descriptions for symmetric positive
definite narrow band routines (PxPByyy)
and diagonally dominant-like narrow band
routines (PxDByyy) is illustrated by the
following example:
<P>
<UL>
<DT>N
<DD> (global input) INTEGER <BR>
The number of rows and columns of the matrix A(JA:JA+N-1,JA:JA+N-1)
on which to be operated. N <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>NRHS
<DD> (global input) INTEGER <BR>
The number of right hand sides, i.e., the number of columns
of the matrix B(IB:IB+N-1,*). NRHS <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>A
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LLD_A, LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1)) <BR>
On entry, the local part of the N-by-N global symmetric band matrix
A(JA:JA+N-1,JA:JA+N-1).
<DT>JA
<DD> (global input) INTEGER <BR>
The column index of the global matrix A.
<DT>DESCA
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix A.
<DT>B
<DD> (local input/local output) REAL array, dimension (LLD_B, NRHS)<BR>
On entry, the local part of the N-by-NRHS right-hand-side matrix.
<DT>IB
<DD> (global input) INTEGER <BR>
The row index of the global matrix B.
<DT>DESCB
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix B.
</UL>
<P>
The style of the argument<A NAME="3298"> </A>
descriptions for diagonally dominant-like tridiagonal routines
(PxDTyyy) is illustrated by the following example:
<P>
<UL>
<DT>N
<DD> (global input) INTEGER <BR>
The number of rows and columns of the matrix A(JA:JA+N-1,JA:JA+N-1)
on which to be operated. N <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>NRHS
<DD> (global input) INTEGER <BR>
The number of right hand sides, i.e., the number of columns
of the matrix B(IB:IB+N-1,*). NRHS <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>DL
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1)) <BR>
On entry, the local part of the subdiagonal entries of the global
tridiagonal matrix A(JA:JA+N-1,JA:JA+N-1).
<DT>D
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1)) <BR>
On entry, the local part of the diagonal entries of the global
tridiagonal matrix A(JA:JA+N-1,JA:JA+N-1).
<DT>DU
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1)) <BR>
On entry, the local part of the superdiagonal entries of the global
tridiagonal matrix A(JA:JA+N-1,JA:JA+N-1).
<DT>JA
<DD> (global input) INTEGER <BR>
The column index of the global matrix A.
<DT>DESCA
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix A.
<DT>B
<DD> (local input/local output) REAL array, dimension (LLD_B, NRHS)<BR>
On entry, the local part of the N-by-NRHS right-hand-side matrix.
<DT>IB
<DD> (global input) INTEGER <BR>
The row index of the global matrix B.
<DT>DESCB
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix B.
</UL>
<P>
The style of the argument<A NAME="3322"> </A>
descriptions for symmetric positive definite tridiagonal routines
(PxPTyyy) is illustrated by the following example:
<P>
<UL>
<DT>N
<DD> (global input) INTEGER <BR>
The number of rows and columns of the matrix A(JA:JA+N-1,JA:JA+N-1)
on which to be operated. N <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>NRHS
<DD> (global input) INTEGER <BR>
The number of right hand sides, i.e., the number of columns
of the matrix B(IB:IB+N-1,*). NRHS <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>D
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1)) <BR>
On entry, the local part of the diagonal entries of the global
tridiagonal matrix A(JA:JA+N-1,JA:JA+N-1).
<DT>E
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1)) <BR>
On entry, the local part of the off-diagonal entries of the global
tridiagonal matrix A(JA:JA+N-1,JA:JA+N-1).
<DT>JA
<DD> (global input) INTEGER <BR>
The column index of the global matrix A.
<DT>DESCA
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix A.
<DT>B
<DD> (local input/local output) REAL array, dimension (LLD_B, NRHS)<BR>
On entry, the local part of the N-by-NRHS right-hand-side matrix.
<DT>IB
<DD> (global input) INTEGER <BR>
The row index of the global matrix B.
<DT>DESCB
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix B.
</UL>
<P>
The description of each argument contains
the following information:
<P>
<UL>
<LI> A classification of the argument as (local input), (global and
local input), (local input/local output), (global input),
(local output), (global output), (global input/global output),
(local or global input)<A NAME="tex2html838" HREF="footnode.html#3346"><IMG ALIGN=BOTTOM ALT="gif" SRC="http://www.netlib.org/utk/icons/foot_motif.gif"></A> (local workspace),
or (local workspace/local output).
<LI> The type of the argument;
<LI> For an array, its dimension(s).
<P>
These dimensions are often expressed
in terms of LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12112" SRC="img15.gif">() and LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">()
calculations. For further details,
please refer to section <A HREF="node83.html#secblockmap">4.4.2</A>.
<LI> A specification of the value(s) that must be supplied for the
argument (if it is an input argument), or of the value(s) returned
by the routine (if it is an output argument), or both (if it is an
input/output argument). In the last case, the two parts of the
description are introduced by the phrases ``On entry'' and ``On exit''.
<LI> For a scalar input argument, any constraints that the supplied
values must satisfy (such as ``N <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0'' in the example above).
<P>
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
</ADDRESS>
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