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<html>
<head>
<title>
SPARSEKIT - Sparse Matrix Utility Package
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPARSEKIT <br> Sparse Matrix Utility Package
</h1>
<hr>
<p>
<b>SPARSEKIT</b>
is a FORTRAN90 library which
carries out a number of
operations on sparse matrices, particularly conversion between
various sparse formats.
</p>
<p>
<b>SPARSEKIT</b> can manipulate sparse matrices in a variety of formats,
and can convert from one to another. For example, a matrix can be
converted from the generalized diagonal format used by ELLPACK and
ITPACK to the format used by the Harwell-Boeing Sparse Matrix
Collection or into LINPACK banded format.
</p>
<p>
Utilities available include converting data structures, printing simple
statistics on a matrix, plotting a matrix profile, performing basic
linear algebra operations (similar to the BLAS for dense matrix),
and so on.
</p>
<p>
Matrix formats that are recognized include:
<ul>
<li>
<b>BND</b>, the LINPACK format for general banded matrices.
</li>
<li>
<b>BSR</b>, block row sparse format.
</li>
<li>
<b>COO</b>, coordinate format.
</li>
<li>
<b>CSC</b>, compressed sparse column format.
</li>
<li>
<b>CSR</b>, compressed sparse row format.
</li>
<li>
<b>DIA</b>, the diagonal sparse matrix format (NOT a diagonal matrix!).
</li>
<li>
<b>DIAG</b>, a diagonal matrix, stored as a vector.
</li>
<li>
<b>DNS</b>, dense storage, also called full storage.
</li>
<li>
<b>ELL</b>, ELLPACK/ITPACK, the format used by ELLPACK and ITPACK.
</li>
<li>
<b>HB</b>, Harwell-Boeing format. (Actually, CSR format plus auxilliary data)
</li>
<li>
<b>JAD</b>, the jagged diagonal format.
</li>
<li>
<b>LNK</b>, linked storage format.
</li>
<li>
<b>MSC</b>, modified sparse column format.
</li>
<li>
<b>MSR</b>, modified sparse row format.
</li>
<li>
<b>SSK</b>, Symmetric skyline format.
</li>
<li>
<b>SSR</b>, Symmetric sparse row format.
</li>
</ul>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SPARSEKIT</b> is available in
<a href = "../../f77_src/sparsekit/sparsekit.html">a FORTRAN77 version</a> and
<a href = "../../f_src/sparsekit/sparsekit.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../c_src/csparse/csparse.html">
CSPARSE</a>,
a C library which
carries out the direct solution of sparse linear systems.
</p>
<p>
<a href = "../../f_src/dlap/dlap.html">
DLAP</a>,
a FORTRAN90 library which
solves sparse linear systems.
</p>
<p>
<a href = "../../f_src/hb_io/hb_io.html">
HB_IO</a>,
a FORTRAN90 library which
reads and writes sparse linear
systems stored in the Harwell-Boeing Sparse Matrix format.
</p>
<p>
<a href = "../../f77_src/hb_to_st/hb_to_st.html">
HB_TO_ST</a>,
a FORTRAN77 program which
converts the sparse matrix information stored in a Harwell-Boeing
file into a sparse triplet file.
</p>
<p>
<a href = "../../f_src/mgmres/mgmres.html">
MGMRES</a>,
a FORTRAN90 library which
applies the restarted GMRES algorithm
to solve a sparse linear system.
</p>
<p>
<a href = "../../f_src/mm_io/mm_io.html">
MM_IO</a>,
a FORTRAN90 library which
reads and writes sparse linear
systems stored in the Matrix Market format.
</p>
<p>
<a href = "../../data/sparse_cc/sparse_cc.html">
SPARSE_CC</a>,
a data directory which
contains a description and examples of the CC format,
("compressed column") for storing a sparse matrix,
including a way to write the matrix as a set of three files.
</p>
<p>
<a href = "../../data/sparse_cr/sparse_cr.html">
SPARSE_CR</a>,
a data directory which
contains a description and examples of the CR format,
("compressed row") for storing a sparse matrix,
including a way to write the matrix as a set of three files.
</p>
<p>
<a href = "../../f_src/sparsepak/sparsepak.html">
SPARSEPAK</a>,
a FORTRAN90 library which
reorders and solves sparse linear systems.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Efstratios Gallopoulos, Youcef Saad,<br>
Efficient solution of parabolic equations by Krylov
approximation methods,<br>
RIACS Technical Report, 90-14.
</li>
<li>
Noborou Kikuchi,<br>
Finite element methods in mechanics,<br>
Cambridge University Press, 1986.
</li>
<li>
David Kincaid, Thomas Oppe, John Respess, David Young,<br>
ITPACKV 2C User's Guide,<br>
Technical Report CNA-191.<br>
Center for Numerical Analysis,<br>
University of Texas at Austin, 1984.
</li>
<li>
Donald Knuth,<br>
The Art of Computer Programming,<br>
Volume 3: Sorting and Searching,<br>
Addison-Wesley, 1973.
</li>
<li>
Ole Osterby, Zahari Zlatev,<br>
Direct Methods for Sparse Matrices,<br>
Springer-Verlag 1983.
</li>
<li>
Youcef Saad,<br>
Sparsekit: a basic tool kit for sparse matrix computations,<br>
Technical Report, Computer Science Department,<br>
University of Minnesota, June 1994.
</li>
<li>
Youcef Saad,<br>
Analysis of some Krylov subspace approximations to the
matrix exponential operator,<br>
RIACS Technical Report, 90-14.
</li>
<li>
Yousef Saad,<br>
Iterative Methods for Sparse Linear Systems,<br>
Second Edition,<br>
SIAM, 2003,<br>
ISBN: 0898715342.
</li>
<li>
Zahari Zlatev, Kjeld Schaumburg, Jerzy Wasniewski,<br>
A testing Scheme for Subroutines Solving Large Linear Problems,<br>
Computers and Chemistry,<br>
Volume 5, Number 2-3, pages 91-100, 1981.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sparsekit.f90">sparsekit.f90</a>, the source code.
</li>
<li>
<a href = "sparsekit.sh">sparsekit.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
Sample problem 1:
<ul>
<li>
<a href = "sparsekit_prb01.f90">sparsekit_prb01.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb01.sh">sparsekit_prb01.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb01_output.txt">sparsekit_prb01_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 2:
<ul>
<li>
<a href = "sparsekit_prb02.f90">sparsekit_prb02.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb02.sh">sparsekit_prb02.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb02_output.txt">sparsekit_prb02_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 3:
<ul>
<li>
<a href = "sparsekit_prb03.f90">sparsekit_prb03.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb03.sh">sparsekit_prb03.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb03_output.txt">sparsekit_prb03_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 4 takes a banded matrix of order 16, stored
as a dense matrix, converts it to CSR format and sorted CSR
format.
<ul>
<li>
<a href = "sparsekit_prb04.f90">sparsekit_prb04.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb04.sh">sparsekit_prb04.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb04_output.txt">sparsekit_prb04_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 5:
<ul>
<li>
<a href = "sparsekit_prb05.f90">sparsekit_prb05.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb05.sh">sparsekit_prb05.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb05_output.txt">sparsekit_prb05_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 6:
<ul>
<li>
<a href = "sparsekit_prb06.f90">sparsekit_prb06.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb06.sh">sparsekit_prb06.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb06_output.txt">sparsekit_prb06_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 7:
<ul>
<li>
<a href = "sparsekit_prb07.f90">sparsekit_prb07.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb07.sh">sparsekit_prb07.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb07_output.txt">sparsekit_prb07_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 8 generates three sample matrices from the
Zlatev set, and writes them to Harwell-Boeing format files:
<ul>
<li>
<a href = "sparsekit_prb08.f90">sparsekit_prb08.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb08.sh">sparsekit_prb08.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb08_output.txt">sparsekit_prb08_output.txt</a>,
the output from a run of the sample program.
</li>
<li>
<a href = "zlatev1_hb.txt">zlatev1_hb.txt</a>,
Zlatev sample matrix 1.
</li>
<li>
<a href = "zlatev2_hb.txt">zlatev2_hb.txt</a>,
Zlatev sample matrix 2.
</li>
<li>
<a href = "zlatev3_hb.txt">zlatev3_hb.txt</a>,
Zlatev sample matrix 3.
</li>
</ul>
</p>
<p>
Sample problem 9:
<ul>
<li>
<a href = "sparsekit_prb09.f90">sparsekit_prb09.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb09.sh">sparsekit_prb09.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb09_output.txt">sparsekit_prb09_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 10:
<ul>
<li>
<a href = "sparsekit_prb10.f90">sparsekit_prb10.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb10.sh">sparsekit_prb10.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb10_output.txt">sparsekit_prb10_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 11:
<ul>
<li>
<a href = "sparsekit_prb11.f90">sparsekit_prb11.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb11.sh">sparsekit_prb11.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb11_output.txt">sparsekit_prb11_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 12:
<ul>
<li>
<a href = "sparsekit_prb12.f90">sparsekit_prb12.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb12.sh">sparsekit_prb12.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb12_output.txt">sparsekit_prb12_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 13:
<ul>
<li>
<a href = "sparsekit_prb13.f90">sparsekit_prb13.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb13.sh">sparsekit_prb13.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb13_output.txt">sparsekit_prb13_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
Sample problem 14 generates a sample CSR matrix and
converts it to an NCF (nonsymmetric coordinate format)
used by NSPCG.
<ul>
<li>
<a href = "sparsekit_prb14.f90">sparsekit_prb14.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sparsekit_prb14.sh">sparsekit_prb14.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparsekit_prb14_output.txt">sparsekit_prb14_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>AMASK</b> extracts a sparse matrix from a masked input matrix.
</li>
<li>
<b>AMUB</b> performs the matrix by matrix product C = A * B.
</li>
<li>
<b>AMUBDG</b> gets the number of nonzero elements in each row of A*B.
</li>
<li>
<b>AMUDIA</b> performs the matrix by matrix product B = A * Diag (in place)
</li>
<li>
<b>AMUX</b> multiplies a CSR matrix A times a vector.
</li>
<li>
<b>AMUXD</b> multiplies a DIA matrix times a vector.
</li>
<li>
<b>AMUXE</b> multiplies an ELL matrix times a vector.
</li>
<li>
<b>AMUXJ</b> multiplies a JAD matrix times a vector.
</li>
<li>
<b>APLB</b> performs the CSR matrix sum C = A + B.
</li>
<li>
<b>APLB1</b> performs the matrix sum C = A+B for matrices in sorted CSR format.
</li>
<li>
<b>APLBDG</b> gets the number of nonzero elements in each row of A+B and the total
</li>
<li>
<b>APLDIA</b> adds a diagonal matrix to a general sparse matrix: B = A + Diag
</li>
<li>
<b>APLSB</b> performs the matrix linear combination C = A+s*B
</li>
<li>
<b>APLSB1</b> performs the operation C = A+s B for matrices in sorted CSR format.
</li>
<li>
<b>APLSBT</b> performs the matrix sum C = A + B'.
</li>
<li>
<b>APLSCA</b> adds a scalar to the diagonal entries of a sparse matrix A :=A + s I
</li>
<li>
<b>APMBT</b> performs the matrix sum C = A + B' or C = A - B'.
</li>
<li>
<b>ASSMB1</b> ???
</li>
<li>
<b>ASSMBO</b> ???
</li>
<li>
<b>ATMUX</b> computes A' * x for a CSR matrix A.
</li>
<li>
<b>BLKCHK</b> checks whether the input matrix is a block
</li>
<li>
<b>BLKFND</b> attemptps to determine whether or not the input
</li>
<li>
<b>BNDCSR</b> converts Banded Linpack format to Compressed Sparse Row format.
</li>
<li>
<b>BOUND</b> counts the number of boundary points and
</li>
<li>
<b>BSORT2</b> simple bubble sort for getting the ncut largest
</li>
<li>
<b>BSRCSR</b> converts Block Sparse Row to Compressed Sparse Row.
</li>
<li>
<b>BSTEN</b> calculates the correct block-stencil values for
</li>
<li>
<b>CHECKREF</b> returns the expected the new number of nodes and
</li>
<li>
<b>CHKELMT</b> checks the labeling within each element and reorders
</li>
<li>
<b>CNRMS</b> gets the norms of each column of A. (choice of three norms)
</li>
<li>
<b>COICSR</b> converts COO to CSR in place.
</li>
<li>
<b>COOCSR</b> converts COO to CSR.
</li>
<li>
<b>COOELL</b> converts coordinate format to ellpack format.
</li>
<li>
<b>COPMAT</b> copies the matrix a, ja, ia, into the matrix ao, jao, iao.
</li>
<li>
<b>CPERM</b> permutes the columns of a matrix.
</li>
<li>
<b>CSCAL</b> scales the columns of A such that their norms are one on return
</li>
<li>
<b>CSORT</b> sorts the elements of a matrix (stored in Compressed
</li>
<li>
<b>CSRBND</b> converts Compressed Sparse Row to Banded (Linpack ) format.
</li>
<li>
<b>CSRBSR</b> converts Compressed Sparse Row to Block Sparse Row
</li>
<li>
<b>CSRCOO</b> converts Compressed Sparse Row to Coordinate
</li>
<li>
<b>CSRCSC</b> converts Compressed Sparse Row to Compressed Sparse Column
</li>
<li>
<b>CSRDIA</b> converts Compressed sparse row to diagonal format
</li>
<li>
<b>CSRDNS</b> converts Compressed Sparse Row to Dense
</li>
<li>
<b>CSRELL</b> converts Compressed Sparse Row to Ellpack - Itpack format
</li>
<li>
<b>CSRJAD</b> converts Compressed Sparse Row to JAgged Diagonal storage.
</li>
<li>
<b>CSRLNK</b> converts Compressed Sparse Row to Linked storage format.
</li>
<li>
<b>CSRMSR</b> converts Compressed Sparse Row to Modified - Sparse Row
</li>
<li>
<b>CSRSSK</b> converts Compressed Sparse Row to Symmetric Skyline Format
</li>
<li>
<b>CSRSSR</b> converts Compressed Sparse Row to Symmetric Sparse Row
</li>
<li>
<b>DCN</b> generates sparse square matrices of type D(N,C).
</li>
<li>
<b>DCSORT</b> computes a permutation which, when applied to the
</li>
<li>
<b>DIACSR</b> converts diagonal format to compressed sparse row
</li>
<li>
<b>DIAMUA</b> performs the matrix by matrix product B = Diag * A (in place)
</li>
<li>
<b>DIAPOS</b> returns the positions of the diagonal elements of a
</li>
<li>
<b>DINFO1</b> computes and prints matrix statistics.
</li>
<li>
<b>DIRIC</b> takes into account the boundary conditions
</li>
<li>
<b>DLAUNY</b> is a simple, nonoptimal Delaunay triangulation code.
</li>
<li>
<b>DNSCSR</b> converts Dense to Compressed Row Sparse
</li>
<li>
<b>DPERM</b> permutes the rows and columns of a matrix stored in CSR
</li>
<li>
<b>DSCALDG</b> scales rows by diag where diag is either given (job=0)
</li>
<li>
<b>DUMP</b> writes the matrix in a file, one row at a time in a nice readable
</li>
<li>
<b>DVPERM</b> performs an in-place permutation of a real vector x
</li>
<li>
<b>ECN</b> generates sparse (square) matrices of the type E(N,C).
</li>
<li>
<b>ELLCSR</b> converts Ellpack-Itpack to Compressed Sparse Row.
</li>
<li>
<b>ESTIF3</b> constructs the element stiffness matrix using 3-node triangular elements
</li>
<li>
<b>EXPHES</b> computes the Arnoldi basis and the corresponding
</li>
<li>
<b>EXPPRO</b> computes an approximation to the vector
</li>
<li>
<b>EXPPROD</b> computes an approximation to the vector
</li>
<li>
<b>EXTBDG</b> extracts the main diagonal blocks of a
</li>
<li>
<b>FILTER</b> removes any elements whose absolute value
</li>
<li>
<b>GEN57BL</b> computes the sparse matrix in compressed
</li>
<li>
<b>GEN57PT</b> computes the sparse matrix in compressed
</li>
<li>
<b>GENFEA</b> generates finite element matrices for heat
</li>
<li>
<b>GENFEU</b> generates finite element matrices for heat
</li>
<li>
<b>GETBWD</b> gets the bandwidth of lower part and upper part of A.
</li>
<li>
<b>GETDIA</b> extracts a given diagonal from a matrix stored in CSR
</li>
<li>
<b>GETELM</b> returns the element a(i,j) of a matrix A,
</li>
<li>
<b>GETL</b> extracts the lower triangular part of a matrix
</li>
<li>
<b>GETSTEN</b> calculates the correct stencil values for
</li>
<li>
<b>GETU</b> extracts the upper triangular part of a matrix
</li>
<li>
<b>GRADI3</b> constructs the first derivative of the shape functions.
</li>
<li>
<b>HES</b> computes exp ( H dt) * y (1)
</li>
<li>
<b>HSOURC</b> generates the load vector f in assembled form from the
</li>
<li>
<b>ILU0</b> is an ILU(0) preconditioner.
</li>
<li>
<b>ILUT</b> is an ILUT preconditioner.
</li>
<li>
<b>INFDIA</b> obtains information on the diagonals of A.
</li>
<li>
<b>IVPERM</b> performs an in-place permutation of an integer vector
</li>
<li>
<b>JADSCR</b> converts Jagged Diagonal Storage to Compressed Sparse Row
</li>
<li>
<b>LDSOL</b> solves L x = y L = triangular. MSR format
</li>
<li>
<b>LDSOLC</b> solves L x = y ; L = nonunit Low. Triang. MSC format
</li>
<li>
<b>LDSOLL</b> solves L x = y L = triangular. Uses LEVEL SCHEDULING/MSR format
</li>
<li>
<b>LEVELS</b> gets the level structure of a lower triangular matrix
</li>
<li>
<b>LNKCSR</b> converts linked list storage format to Compressed Sparse Row format.
</li>
<li>
<b>LSOL</b> solves L x = y ; L = lower unit triang. / CSR format
</li>
<li>
<b>LSOLC</b> solves L x = y ; where L = unit lower trang. CSC format
</li>
<li>
<b>LUSOL0</b> performs a forward followed by a backward solve
</li>
<li>
<b>MARKGEN</b> is a matrix generator for a markov model of a random walk on a triang. grid
</li>
<li>
<b>MATRF2</b> generates sparse (rectangular or square) matrices.
</li>
<li>
<b>MGSR</b> is a modified gram - schmidt with partial reortho.
</li>
<li>
<b>MILU0</b> is a simple milu(0) preconditioner. *** *
</li>
<li>
<b>MSRCSR</b> converts Modified - Sparse Row to Compressed Sparse Row
</li>
<li>
<b>PGMRES</b> is an ILUT - Preconditioned GMRES solver.
</li>
<li>
<b>PLTMT</b> creates a 'pic' file for plotting the pattern of
</li>
<li>
<b>PLTMTPS</b> creates a 'PS' file for plotting the pattern of
</li>
<li>
<b>PRTMT</b> writes a matrix in Harwell-Boeing format into a file.
</li>
<li>
<b>READMT</b> reads a boeing/harwell matrix. handles right hand
</li>
<li>
<b>REFALL</b> refines a finite element grid using triangular elements.
</li>
<li>
<b>RETMX</b> returns in dd(*) the max absolute value of elements in row *.
</li>
<li>
<b>RNRMS</b> gets the norms of each row of A. (choice of three norms)
</li>
<li>
<b>RPERM</b> permutes the rows of a matrix in CSR format.
</li>
<li>
<b>RSCAL</b> scales the rows of A such that their norms are one on return
</li>
<li>
<b>SSKSSR</b> converts Symmetric Skyline Format to Symmetric Sparse Row format.
</li>
<li>
<b>SSRCSR</b> converts Symmetric Sparse Row to (regular) Compressed Sparse Row
</li>
<li>
<b>SUBMAT</b> extracts the submatrix A(i1:i2,j1:j2) and puts the result in
</li>
<li>
<b>TRANSP</b> carries out in-place transposition routine.
</li>
<li>
<b>UDSOL</b> solves U x = y ; U = upper triangular in MSR format
</li>
<li>
<b>UDSOLC</b> Solves U x = y ; U = nonunit Up. Triang. MSC format
</li>
<li>
<b>UNASSBL</b> ???
</li>
<li>
<b>USOL</b> solves U x = y U = unit upper triangular.
</li>
<li>
<b>USOLC</b> solves U x = y ; where U = unit upper trang. CSC format
</li>
<li>
<b>SAXPY</b> CONSTANT TIMES A VECTOR PLUS A VECTOR.
</li>
<li>
<b>SDOT</b> FORMS THE DOT PRODUCT OF TWO VECTORS.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 30 August 2005.
</i>
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