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<H2><A NAME="SECTION04436000000000000000">Matrix and Vector Storage Conventions</A></H2>
<P>
Whether a dense coefficient
matrix<A NAME="2660"> </A>
operand is nonsymmetric, symmetric
or Hermitian, the entire
two-dimensional global
array is distributed onto
the process grid.
<P>
For symmetric<A NAME="2661"> </A>
and Hermitian<A NAME="2662"> </A>
matrix operands, only the upper (<TT>UPLO='U'</TT>)
triangle or the lower (<TT>UPLO='L'</TT>)
triangle of the global array is accessed.
For triangular<A NAME="2665"> </A>
matrix operands, the argument <TT>UPLO</TT> defines
whether the matrix is upper (<TT>UPLO='U'</TT>)
or lower (<TT>UPLO='L'</TT>) triangular. Only
the elements of the relevant triangle of
the global array are accessed. Some ScaLAPACK
routines have an option to handle unit triangular
matrix operands (that is, triangular matrices
with diagonal elements = 1). This option is
specified by an argument DIAG<A NAME="2669"> </A>.
If DIAG = 'U' (Unit triangular), the local array
elements corresponding to the diagonal
elements of the matrix are not referenced
by the ScaLAPACK routines.
<P>
If an input matrix operand is Hermitian<A NAME="2670"> </A>,
the imaginary parts of the diagonal elements
are zero, and thus the imaginary parts of the
corresponding local arrays need not be set,
but are assumed to be zero. If an output matrix
operand is Hermitian, the imaginary parts of
the diagonal elements are set to zero (e.g.,
PCPOTRF and PCHETRD).
<P>
Similarly, if the matrix is upper Hessenberg,
the local array elements corresponding to
global array elements below the first subdiagonal
are not referenced.
<P>
Vectors can be distributed across
<A NAME="2671"> </A>
<A NAME="2672"> </A>
<A NAME="2673"> </A>
process rows or across process columns.
A vector of length <I>N</I> distributed
across process rows is distributed
the same way that a <I>N</I>-by-1 matrix
is. A vector of length <I>N</I> distributed
across process columns is distributed
the same way that a 1-by-<I>N</I> matrix
is.
<P>
Within some ScaLAPACK routines, some
vectors are replicated in one dimension
and distributed in the other dimension.
These vectors always aligned with one
dimension of another distributed matrix.
For example, in PDSYTRD, the vectors D,
E, and TAU are replicated across process
rows, distributed across process columns,
and aligned with the distributed matrix
operand <I>A</I>. The data distribution of
these replicated vectors is inferred
from the distribution of the matrix
they are associated with. There is no
specific array descriptors for these
particular vectors at the present time.
<A NAME="2674"> </A>
<A NAME="2675"> </A>
<A NAME="2676"> </A>
<P>
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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