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<B> Next:</B> <A NAME="tex2html2019" HREF="node8.html">Essentials</A>
<B>Up:</B> <A NAME="tex2html2017" HREF="scalapack_slug.html">ScaLAPACK Users' Guide</A>
<B> Previous:</B> <A NAME="tex2html2011" HREF="node6.html">List of Notation</A>
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<H1><A NAME="SECTION04000000000000000000">Guide</A></H1>
<P>
<BR><BR><BR> <HR>
<UL><A NAME="CHILD_LINKS"> </A>
<LI> <A NAME="tex2html2022" HREF="node8.html#SECTION04100000000000000000">Essentials</A>
<UL>
<LI> <A NAME="tex2html2023" HREF="node9.html#SECTION04110000000000000000">ScaLAPACK</A>
<LI> <A NAME="tex2html2024" HREF="node10.html#SECTION04120000000000000000">Structure and Functionality</A>
<LI> <A NAME="tex2html2025" HREF="node11.html#SECTION04130000000000000000">Software Components</A>
<UL>
<LI> <A NAME="tex2html2026" HREF="node12.html#SECTION04131000000000000000">LAPACK</A>
<LI> <A NAME="tex2html2027" HREF="node13.html#SECTION04132000000000000000">BLAS</A>
<LI> <A NAME="tex2html2028" HREF="node14.html#SECTION04133000000000000000">PBLAS</A>
<LI> <A NAME="tex2html2029" HREF="node15.html#SECTION04134000000000000000">BLACS</A>
</UL>
<LI> <A NAME="tex2html2030" HREF="node16.html#SECTION04140000000000000000">Efficiency and Portability</A>
<LI> <A NAME="tex2html2031" HREF="node17.html#SECTION04150000000000000000">Availability</A>
<LI> <A NAME="tex2html2032" HREF="node18.html#SECTION04160000000000000000">Commercial Use</A>
<LI> <A NAME="tex2html2033" HREF="node19.html#SECTION04170000000000000000">Installation</A>
<LI> <A NAME="tex2html2034" HREF="node20.html#SECTION04180000000000000000">Documentation</A>
<LI> <A NAME="tex2html2035" HREF="node21.html#SECTION04190000000000000000">Support</A>
<LI> <A NAME="tex2html2036" HREF="node22.html#SECTION041100000000000000000">Errata</A>
<LI> <A NAME="tex2html2037" HREF="node23.html#SECTION041110000000000000000">Related Projects</A>
<LI> <A NAME="tex2html2038" HREF="node24.html#SECTION041120000000000000000">Contents of the CD-ROM</A>
</UL>
<LI> <A NAME="tex2html2039" HREF="node25.html#SECTION04200000000000000000">Getting Started with ScaLAPACK</A>
<UL>
<LI> <A NAME="tex2html2040" HREF="node26.html#SECTION04210000000000000000">How to Run an Example Program Using MPI</A>
<LI> <A NAME="tex2html2041" HREF="node27.html#SECTION04220000000000000000">Source Code for Example Program #1</A>
<LI> <A NAME="tex2html2042" HREF="node28.html#SECTION04230000000000000000">Details of Example Program #1</A>
<UL>
<LI> <A NAME="tex2html2043" HREF="node29.html#SECTION04231000000000000000">Simplifying Assumptions Used in Example Program</A>
<LI> <A NAME="tex2html2044" HREF="node30.html#SECTION04232000000000000000">Notation Used in Example Program</A>
<LI> <A NAME="tex2html2045" HREF="node31.html#SECTION04233000000000000000">Output of Example Program #1 Using MPI</A>
<LI> <A NAME="tex2html2046" HREF="node32.html#SECTION04234000000000000000">Output of Example Program #1 Using PVM</A>
</UL>
<LI> <A NAME="tex2html2047" HREF="node33.html#SECTION04240000000000000000">Four Basic Steps Required to Call a ScaLAPACK Routine</A>
<UL>
<LI> <A NAME="tex2html2048" HREF="node34.html#SECTION04241000000000000000">Initialize the Process Grid</A>
<LI> <A NAME="tex2html2049" HREF="node35.html#SECTION04242000000000000000">Distribute the Matrix on the Process Grid</A>
<LI> <A NAME="tex2html2050" HREF="node36.html#SECTION04243000000000000000">Call the ScaLAPACK Routine</A>
<LI> <A NAME="tex2html2051" HREF="node37.html#SECTION04244000000000000000">Release the Process Grid</A>
</UL>
</UL>
<LI> <A NAME="tex2html2052" HREF="node38.html#SECTION04300000000000000000">Contents of ScaLAPACK</A>
<UL>
<LI> <A NAME="tex2html2053" HREF="node39.html#SECTION04310000000000000000">Structure of ScaLAPACK</A>
<UL>
<LI> <A NAME="tex2html2054" HREF="node40.html#SECTION04311000000000000000">Levels of Routines</A>
<LI> <A NAME="tex2html2055" HREF="node41.html#SECTION04312000000000000000">Data Types and Precision</A>
<LI> <A NAME="tex2html2056" HREF="node42.html#SECTION04313000000000000000">Naming Scheme</A>
</UL>
<LI> <A NAME="tex2html2057" HREF="node43.html#SECTION04320000000000000000">Driver Routines</A>
<UL>
<LI> <A NAME="tex2html2058" HREF="node44.html#SECTION04321000000000000000">Linear Equations</A>
<LI> <A NAME="tex2html2059" HREF="node45.html#SECTION04322000000000000000">Linear Least Squares Problems</A>
<LI> <A NAME="tex2html2060" HREF="node46.html#SECTION04323000000000000000">Standard Eigenvalue and Singular Value Problems</A>
<UL>
<LI> <A NAME="tex2html2061" HREF="node47.html#SECTION04323100000000000000">Symmetric Eigenproblems </A>
<LI> <A NAME="tex2html2062" HREF="node48.html#SECTION04323200000000000000">Singular Value Decomposition</A>
</UL>
<LI> <A NAME="tex2html2063" HREF="node49.html#SECTION04324000000000000000">Generalized Symmetric Definite Eigenproblems (GSEP)</A>
</UL>
<LI> <A NAME="tex2html2064" HREF="node50.html#SECTION04330000000000000000">Computational Routines</A>
<UL>
<LI> <A NAME="tex2html2065" HREF="node51.html#SECTION04331000000000000000">Linear Equations</A>
<LI> <A NAME="tex2html2066" HREF="node52.html#SECTION04332000000000000000">Orthogonal Factorizations and Linear Least Squares Problems</A>
<UL>
<LI> <A NAME="tex2html2067" HREF="node53.html#SECTION04332100000000000000"><I>QR</I> Factorization</A>
<LI> <A NAME="tex2html2068" HREF="node54.html#SECTION04332200000000000000"><I>LQ</I> Factorization</A>
<LI> <A NAME="tex2html2069" HREF="node55.html#SECTION04332300000000000000"><I>QR</I> Factorization with Column Pivoting</A>
<LI> <A NAME="tex2html2070" HREF="node56.html#SECTION04332400000000000000">Complete Orthogonal Factorization</A>
<LI> <A NAME="tex2html2071" HREF="node57.html#SECTION04332500000000000000">Other Factorizations</A>
</UL>
<LI> <A NAME="tex2html2072" HREF="node58.html#SECTION04333000000000000000">Generalized Orthogonal Factorizations</A>
<UL>
<LI> <A NAME="tex2html2073" HREF="node59.html#SECTION04333100000000000000">Generalized <I>QR</I> Factorization</A>
<LI> <A NAME="tex2html2074" HREF="node60.html#SECTION04333200000000000000">Generalized <I>RQ</I> factorization</A>
</UL>
<LI> <A NAME="tex2html2075" HREF="node61.html#SECTION04334000000000000000">Symmetric Eigenproblems</A>
<LI> <A NAME="tex2html2076" HREF="node62.html#SECTION04335000000000000000">Nonsymmetric Eigenproblems</A>
<UL>
<LI> <A NAME="tex2html2077" HREF="node63.html#SECTION04335100000000000000">Eigenvalues, Eigenvectors, and Schur Factorization</A>
</UL>
<LI> <A NAME="tex2html2078" HREF="node64.html#SECTION04336000000000000000">Singular Value Decomposition</A>
<LI> <A NAME="tex2html2079" HREF="node65.html#SECTION04337000000000000000">Generalized Symmetric Definite Eigenproblems</A>
</UL>
<LI> <A NAME="tex2html2080" HREF="node66.html#SECTION04340000000000000000">Orthogonal or Unitary Matrices</A>
<LI> <A NAME="tex2html2081" HREF="node67.html#SECTION04350000000000000000">Algorithmic Differences between LAPACK and ScaLAPACK</A>
</UL>
<LI> <A NAME="tex2html2082" HREF="node68.html#SECTION04400000000000000000">Data Distributions and Software Conventions</A>
<UL>
<LI> <A NAME="tex2html2083" HREF="node69.html#SECTION04410000000000000000">Basics</A>
<UL>
<LI> <A NAME="tex2html2084" HREF="node70.html#SECTION04411000000000000000">Process Grid</A>
<LI> <A NAME="tex2html2085" HREF="node71.html#SECTION04412000000000000000">Contexts</A>
<LI> <A NAME="tex2html2086" HREF="node72.html#SECTION04413000000000000000">Scoped Operations</A>
</UL>
<LI> <A NAME="tex2html2087" HREF="node73.html#SECTION04420000000000000000">Array Descriptors</A>
<LI> <A NAME="tex2html2088" HREF="node74.html#SECTION04430000000000000000">In-core Dense Matrices</A>
<UL>
<LI> <A NAME="tex2html2089" HREF="node75.html#SECTION04431000000000000000">The Two-dimensional Block-Cyclic Distribution</A>
<LI> <A NAME="tex2html2090" HREF="node76.html#SECTION04432000000000000000">Local Storage Scheme and Block-Cyclic Mapping</A>
<LI> <A NAME="tex2html2091" HREF="node77.html#SECTION04433000000000000000">Array Descriptor for In-core Dense Matrices</A>
<LI> <A NAME="tex2html2092" HREF="node78.html#SECTION04434000000000000000">Example</A>
<LI> <A NAME="tex2html2093" HREF="node79.html#SECTION04435000000000000000">Submatrix Argument Descriptions</A>
<LI> <A NAME="tex2html2094" HREF="node80.html#SECTION04436000000000000000">Matrix and Vector Storage Conventions</A>
</UL>
<LI> <A NAME="tex2html2095" HREF="node81.html#SECTION04440000000000000000">In-Core Narrow Band and Tridiagonal Matrices</A>
<UL>
<LI> <A NAME="tex2html2096" HREF="node82.html#SECTION04441000000000000000">The Block Column and Row Distributions</A>
<LI> <A NAME="tex2html2097" HREF="node83.html#SECTION04442000000000000000">The Block Mapping</A>
<LI> <A NAME="tex2html2098" HREF="node84.html#SECTION04443000000000000000">Local Storage Scheme for Narrow Band Matrices</A>
<LI> <A NAME="tex2html2099" HREF="node85.html#SECTION04444000000000000000">Local Storage Schemes for Tridiagonal Matrices</A>
<LI> <A NAME="tex2html2100" HREF="node86.html#SECTION04445000000000000000">Array Descriptor for Narrow Band and Tridiagonal Matrices</A>
<LI> <A NAME="tex2html2101" HREF="node87.html#SECTION04446000000000000000">Array Descriptor for the Matrix of Right-Hand-Side Vectors</A>
<LI> <A NAME="tex2html2102" HREF="node88.html#SECTION04447000000000000000">Argument Descriptions for Band and Tridiagonal Routines</A>
<LI> <A NAME="tex2html2103" HREF="node89.html#SECTION04448000000000000000">Matrix Storage Conventions for Band and Tridiagonal Matrices</A>
</UL>
<LI> <A NAME="tex2html2104" HREF="node90.html#SECTION04450000000000000000">Out-of-Core Matrices</A>
<UL>
<LI> <A NAME="tex2html2105" HREF="node91.html#SECTION04451000000000000000">Array Descriptor for Out-core Dense Matrices</A>
</UL>
<LI> <A NAME="tex2html2106" HREF="node92.html#SECTION04460000000000000000">Design and Documentation of Argument Lists</A>
<UL>
<LI> <A NAME="tex2html2107" HREF="node93.html#SECTION04461000000000000000">Structure of the Documentation</A>
<LI> <A NAME="tex2html2108" HREF="node94.html#SECTION04462000000000000000">Order of Arguments</A>
<LI> <A NAME="tex2html2109" HREF="node95.html#SECTION04463000000000000000">Option Arguments</A>
<LI> <A NAME="tex2html2110" HREF="node96.html#SECTION04464000000000000000">Problem Dimensions</A>
<LI> <A NAME="tex2html2111" HREF="node97.html#SECTION04465000000000000000">Workspace Issues</A>
<UL>
<LI> <A NAME="tex2html2112" HREF="node98.html#SECTION04465100000000000000">WORK Arrays</A>
<LI> <A NAME="tex2html2113" HREF="node99.html#SECTION04465200000000000000">LWORK Query</A>
<LI> <A NAME="tex2html2114" HREF="node100.html#SECTION04465300000000000000">LWORK <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> WORK(1)</A>
</UL>
<LI> <A NAME="tex2html2115" HREF="node101.html#SECTION04466000000000000000">Error Handling and the Diagnostic Argument INFO</A>
<LI> <A NAME="tex2html2116" HREF="node102.html#SECTION04467000000000000000">Alignment Restrictions</A>
</UL>
<LI> <A NAME="tex2html2117" HREF="node103.html#SECTION04470000000000000000">Extensions</A>
</UL>
<LI> <A NAME="tex2html2118" HREF="node104.html#SECTION04500000000000000000">Performance of ScaLAPACK</A>
<UL>
<LI> <A NAME="tex2html2119" HREF="node105.html#SECTION04510000000000000000">Achieving High Performance with ScaLAPACK</A>
<UL>
<LI> <A NAME="tex2html2120" HREF="node106.html#SECTION04511000000000000000">Achieving High Performance on a Distributed Memory
Computer</A>
<LI> <A NAME="tex2html2121" HREF="node107.html#SECTION04512000000000000000">Achieving High Performance on a Network of Workstations</A>
</UL>
<LI> <A NAME="tex2html2122" HREF="node108.html#SECTION04520000000000000000">Performance, Portability and Scalability</A>
<UL>
<LI> <A NAME="tex2html2123" HREF="node109.html#SECTION04521000000000000000">The BLAS as the Key to (Trans)portable Efficiency</A>
<LI> <A NAME="tex2html2124" HREF="node110.html#SECTION04522000000000000000">Two-Dimensional Block Cyclic Data Distribution as a Key
to Load Balancing and Software Reuse</A>
<LI> <A NAME="tex2html2125" HREF="node111.html#SECTION04523000000000000000">BLACS as an Efficient, Portable and Adequate
Message-Passing Interface</A>
<UL>
<LI> <A NAME="tex2html2126" HREF="node112.html#SECTION04523100000000000000">Parallel Efficiency</A>
</UL>
<LI> <A NAME="tex2html2127" HREF="node113.html#SECTION04524000000000000000">ScaLAPACK Performance</A>
<LI> <A NAME="tex2html2128" HREF="node114.html#SECTION04525000000000000000">Performance of Selected BLACS and Level 3 BLAS Routines</A>
<UL>
<LI> <A NAME="tex2html2129" HREF="node115.html#SECTION04525100000000000000">Performance of Selected PBLAS routines</A>
<LI> <A NAME="tex2html2130" HREF="node116.html#SECTION04525200000000000000">Solution of Common Numerical Linear Algebra Problems</A>
</UL>
<LI> <A NAME="tex2html2131" HREF="node117.html#SECTION04526000000000000000">Solving Linear Systems of Equations</A>
<UL>
<LI> <A NAME="tex2html2132" HREF="node118.html#SECTION04526100000000000000">Solving Linear Least Squares Problems</A>
<LI> <A NAME="tex2html2133" HREF="node119.html#SECTION04526200000000000000">Eigenvalue Problems</A>
</UL>
</UL>
<LI> <A NAME="tex2html2134" HREF="node120.html#SECTION04530000000000000000">Performance Evaluation</A>
<UL>
<LI> <A NAME="tex2html2135" HREF="node121.html#SECTION04531000000000000000">Obtaining High Performance with ScaLAPACK Codes</A>
<LI> <A NAME="tex2html2136" HREF="node122.html#SECTION04532000000000000000">Checking the BLAS and BLACS Libraries</A>
<LI> <A NAME="tex2html2137" HREF="node123.html#SECTION04533000000000000000">Estimate Execution Time</A>
<LI> <A NAME="tex2html2138" HREF="node124.html#SECTION04534000000000000000">Determine Whether Reasonable Performance Is Achieved</A>
<LI> <A NAME="tex2html2139" HREF="node125.html#SECTION04535000000000000000">Identify Performance Bottlenecks</A>
<LI> <A NAME="tex2html2140" HREF="node126.html#SECTION04536000000000000000">Performance Bottlenecks in the Expert Symmetric
Eigenproblem Drivers</A>
</UL>
<LI> <A NAME="tex2html2141" HREF="node127.html#SECTION04540000000000000000">Performance Improvement</A>
<UL>
<LI> <A NAME="tex2html2142" HREF="node128.html#SECTION04541000000000000000">Choosing a Faster BLACS Library</A>
<LI> <A NAME="tex2html2143" HREF="node129.html#SECTION04542000000000000000">Choosing a Faster BLAS Library</A>
<LI> <A NAME="tex2html2144" HREF="node130.html#SECTION04543000000000000000">Tuning the Distribution Parameters for Better Performance</A>
</UL>
<LI> <A NAME="tex2html2145" HREF="node131.html#SECTION04550000000000000000">Performance of Banded and Out-of-Core Drivers</A>
</UL>
<LI> <A NAME="tex2html2146" HREF="node132.html#SECTION04600000000000000000">Accuracy and Stability</A>
<UL>
<LI> <A NAME="tex2html2147" HREF="node133.html#SECTION04610000000000000000">Sources of Error in Numerical Calculations</A>
<LI> <A NAME="tex2html2148" HREF="node134.html#SECTION04620000000000000000">New Sources of Error in Parallel Numerical Computations</A>
<LI> <A NAME="tex2html2149" HREF="node135.html#SECTION04630000000000000000">How to Measure Errors</A>
<LI> <A NAME="tex2html2150" HREF="node136.html#SECTION04640000000000000000">Further Details: How Error Bounds Are Derived</A>
<UL>
<LI> <A NAME="tex2html2151" HREF="node137.html#SECTION04641000000000000000">Standard Error Analysis</A>
<LI> <A NAME="tex2html2152" HREF="node138.html#SECTION04642000000000000000">Improved Error Bounds</A>
</UL>
<LI> <A NAME="tex2html2153" HREF="node139.html#SECTION04650000000000000000">Error Bounds for Linear Equation Solving</A>
<LI> <A NAME="tex2html2154" HREF="node140.html#SECTION04660000000000000000">Error Bounds for Linear Least Squares Problems</A>
<LI> <A NAME="tex2html2155" HREF="node141.html#SECTION04670000000000000000">Error Bounds for the Symmetric Eigenproblem </A>
<LI> <A NAME="tex2html2156" HREF="node142.html#SECTION04680000000000000000">Error Bounds for the Singular Value Decomposition</A>
<UL>
<LI> <A NAME="tex2html2157" HREF="node143.html#SECTION04681000000000000000">Further Details: Error Bounds for the Singular Value Decomposition</A>
</UL>
<LI> <A NAME="tex2html2158" HREF="node144.html#SECTION04690000000000000000">Error Bounds for the Generalized Symmetric Definite
Eigenproblem</A>
</UL>
<LI> <A NAME="tex2html2159" HREF="node145.html#SECTION04700000000000000000">Troubleshooting</A>
<UL>
<LI> <A NAME="tex2html2160" HREF="node147.html#SECTION04720000000000000000">Installation Debugging Hints</A>
<LI> <A NAME="tex2html2161" HREF="node148.html#SECTION04730000000000000000">Application Debugging Hints</A>
<LI> <A NAME="tex2html2162" HREF="node149.html#SECTION04740000000000000000">Common Errors in Calling ScaLAPACK Routines</A>
<LI> <A NAME="tex2html2163" HREF="node150.html#SECTION04750000000000000000">Failures Detected by ScaLAPACK Routines</A>
<UL>
<LI> <A NAME="tex2html2164" HREF="node151.html#SECTION04751000000000000000">Invalid Arguments and PXERBLA</A>
<LI> <A NAME="tex2html2165" HREF="node152.html#SECTION04752000000000000000">Computational Failures and INFO > 0</A>
</UL>
<LI> <A NAME="tex2html2166" HREF="node153.html#SECTION04760000000000000000">Wrong Results</A>
<LI> <A NAME="tex2html2167" HREF="node154.html#SECTION04770000000000000000">Error Handling in the PBLAS</A>
<LI> <A NAME="tex2html2168" HREF="node155.html#SECTION04780000000000000000">Error Handling in the BLACS</A>
<UL>
<LI> <A NAME="tex2html2169" HREF="node156.html#SECTION04781000000000000000">BLACS Warning and Error Messages</A>
</UL>
<LI> <A NAME="tex2html2170" HREF="node157.html#SECTION04790000000000000000">System Error Messages</A>
<LI> <A NAME="tex2html2171" HREF="node158.html#SECTION047100000000000000000">Poor Performance</A>
</UL>
<LI> <A NAME="tex2html2172" HREF="node159.html#SECTION04800000000000000000">Index of ScaLAPACK Routines</A>
<UL>
<LI> <A NAME="tex2html2173" HREF="node160.html#SECTION04810000000000000000">Index of Driver and Computational Routines</A>
<LI> <A NAME="tex2html2174" HREF="node162.html#SECTION04830000000000000000">Index of Auxiliary Routines</A>
<LI> <A NAME="tex2html2175" HREF="node164.html#SECTION04850000000000000000">Matrix Redistribution/Copy Routines</A>
<UL>
<LI> <A NAME="tex2html2176" HREF="node165.html#SECTION04851000000000000000">Fortran Interface</A>
<LI> <A NAME="tex2html2177" HREF="node172.html#SECTION04854000000000000000">C Interface</A>
<LI> <A NAME="tex2html2178" HREF="node173.html#SECTION04855000000000000000">Code Fragment Calling C Interface Cpdgemr2d</A>
</UL>
</UL>
<LI> <A NAME="tex2html2179" HREF="node174.html#SECTION04900000000000000000">Call Conversion: LAPACK to ScaLAPACK and BLAS to PBLAS</A>
<UL>
<LI> <A NAME="tex2html2180" HREF="node175.html#SECTION04910000000000000000">Translating BLAS-based programs to the PBLAS</A>
<LI> <A NAME="tex2html2181" HREF="node176.html#SECTION04920000000000000000">Translating LAPACK-based programs to ScaLAPACK</A>
<UL>
<LI> <A NAME="tex2html2182" HREF="node177.html#SECTION04921000000000000000">Sequential LU Factorization</A>
<LI> <A NAME="tex2html2183" HREF="node178.html#SECTION04922000000000000000">Parallel LU Factorization</A>
</UL>
</UL>
<LI> <A NAME="tex2html2184" HREF="node179.html#SECTION041000000000000000000">Example Programs</A>
<UL>
<LI> <A NAME="tex2html2185" HREF="node180.html#SECTION041010000000000000000">Example Program #2</A>
<LI> <A NAME="tex2html2186" HREF="node181.html#SECTION041020000000000000000">HPF Interface to ScaLAPACK</A>
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<LI> <A NAME="tex2html2187" HREF="node182.html#SECTION041100000000000000000">Quick Reference Guides</A>
<UL>
<LI> <A NAME="tex2html2188" HREF="node183.html#SECTION041110000000000000000">ScaLAPACK Quick Reference Guide</A>
<LI> <A NAME="tex2html2189" HREF="node184.html#SECTION041120000000000000000">Quick Reference
Guide to the PBLAS</A>
<LI> <A NAME="tex2html2190" HREF="node185.html#SECTION041130000000000000000">Quick Reference Guide to the BLACS</A>
</UL>
</UL>
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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