Guide and Reference

Engineering and Scientific
Subroutine Library for AIX
Guide and Reference

SA22-7272-00

5765-C42


Notes!



First Edition (December 1997)

This edition applies to Version 3 of the IBM* Engineering and Scientific Subroutine Library (ESSL) for Advanced Interactive Executive (AIX)* licensed program, program number 5765-C42.

In this document, ESSL refers to the above version of ESSL for AIX. Changes are periodically made to the information herein.

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Table of Contents

  • Looking for a Subroutine?

  • Special Notices
  • Trademarks
  • Programming Interfaces
  • About This Book
  • How to Use This Book
  • How to Find a Subroutine Description
  • Where to Find Related Publications
  • How to Look Up a Bibliography Reference
  • Special Terms
  • Short and Long Precision
  • Subroutines and Subprograms
  • How to Interpret the Subroutine Names with a Prefix Underscore
  • Abbreviated Names
  • Fonts
  • Special Notations and Conventions
  • Scalar Data
  • Vectors
  • Matrices
  • Sequences
  • Arrays
  • Special Characters, Symbols, Expressions, and Abbreviations
  • How to Interpret the Subroutine Descriptions
  • Description
  • Syntax
  • On Entry
  • On Return
  • Notes
  • Function
  • Special Usage
  • Error Conditions
  • Examples
  • What's New for ESSL for AIX
  • What's New for ESSL Version 3
  • Future Migration
  • In Brief--What's Provided in ESSL for AIX

  • Guide Information

  • Introduction and Requirements
  • Overview of ESSL
  • Performance and Functional Capability
  • Usability
  • The Variety of Mathematical Functions
  • ESSL--Processing Capabilities
  • Accuracy of the Computations
  • High Performance of ESSL
  • The Fortran Language Interface to the Subroutines
  • Software and Hardware Products That Can Be Used with ESSL
  • For ESSL--Hardware
  • ESSL--Operating Systems
  • ESSL--Software Products
  • Installation and Customization Products
  • Software Products for Displaying ESSL Online Information
  • ESSL Internet Resources
  • Obtaining Documentation
  • Accessing ESSL's Product Home Pages
  • Getting on the ESSL Mailing List
  • List of ESSL Subroutines
  • Linear Algebra Subprograms
  • Matrix Operations
  • Linear Algebraic Equations
  • Eigensystem Analysis
  • Fourier Transforms, Convolutions and Correlations, and Related Computations
  • Sorting and Searching
  • Interpolation
  • Numerical Quadrature
  • Random Number Generation
  • Utilities
  • Planning Your Program
  • Selecting an ESSL Subroutine
  • Which ESSL Library Do You Want to Use?
  • What Type of Data Are You Processing in Your Program?
  • How Is Your Data Structured? And What Storage Technique Are You Using?
  • What about Performance and Accuracy?
  • Avoiding Conflicts with Internal ESSL Routine Names That are Exported
  • Setting Up Your Data
  • How Do You Set Up Your Scalar Data?
  • How Do You Set Up Your Arrays?
  • How Should Your Array Data Be Aligned?
  • What Storage Mode Should You Use for Your Data?
  • How Do You Convert from One Storage Mode to Another?
  • Setting Up Your ESSL Calling Sequences
  • What Is an Input-Output Argument?
  • What Are the General Rules to Follow when Specifying Data for the Arguments?
  • What Happens When a Value of 0 Is Specified for N?
  • How Do You Specify the Beginning of the Data Structure in the ESSL Calling Sequence?
  • Using Auxiliary Storage in ESSL
  • Dynamic Allocation of Auxiliary Storage
  • Setting Up Auxiliary Storage When Dynamic Allocation Is Not Used
  • Who Do You Want to Calculate the Size? You or ESSL?
  • How Do You Calculate the Size Using the Formulas?
  • How Do You Get ESSL to Calculate the Size Using ESSL Error Handling?
  • Providing a Correct Transform Length to ESSL
  • What ESSL Subroutines Require Transform Lengths?
  • Who Do You Want to Calculate the Length? You or ESSL?
  • How Do You Calculate the Length Using the Table or Formula?
  • How Do You Get ESSL to Calculate the Length Using ESSL Error Handling?
  • Getting the Best Accuracy
  • What Precisions Do ESSL Subroutines Operate On?
  • How Does the Nature of the ESSL Computation Affect Accuracy?
  • What Does ESSL Do to Improve Accuracy?
  • What Data Type Standards Are Used by ESSL, and What Exceptions Should You Know About?
  • What Does ESSL Do to Improve Accuracy?
  • How is Underflow Handled?
  • Where Can You Find More Information on Accuracy?
  • Getting the Best Performance
  • What General Coding Techniques Can You Use to Improve Performance?
  • Where Can You Find More Information on Performance?
  • Dealing with Errors when Using ESSL
  • What Can You Do about Program Exceptions?
  • What Can You Do about ESSL Input-Argument Errors?
  • What Can You Do about ESSL Computational Errors?
  • What Can You Do about ESSL Resource Errors?
  • What Can You Do about ESSL Attention Messages?
  • How Do You Control Error Handling by Setting Values in the ESSL Error Option Table?
  • How does Error Handling Work in a Threaded Environment?
  • Where Can You Find More Information on Errors?
  • Setting Up Your Data Structures
  • Concepts
  • Vectors
  • Transpose of a Vector
  • Conjugate Transpose of a Vector
  • In Storage
  • How Stride Is Used for Vectors
  • Sparse Vector
  • Matrices
  • Transpose of a Matrix
  • Conjugate Transpose of a Matrix
  • In Storage
  • How Leading Dimension Is Used for Matrices
  • Symmetric Matrix
  • Positive Definite or Negative Definite Symmetric Matrix
  • Complex Hermitian Matrix
  • Positive Definite or Negative Definite Complex Hermitian Matrix
  • Positive Definite or Negative Definite Symmetric Toeplitz Matrix
  • Positive Definite or Negative Definite Complex Hermitian Toeplitz Matrix
  • Triangular Matrix
  • General Band Matrix
  • Symmetric Band Matrix
  • Positive Definite Symmetric Band Matrix
  • Complex Hermitian Band Matrix
  • Triangular Band Matrix
  • General Tridiagonal Matrix
  • Symmetric Tridiagonal Matrix
  • Positive Definite Symmetric Tridiagonal Matrix
  • Sparse Matrix
  • Sequences
  • Real and Complex Elements in Storage
  • One-Dimensional Sequences
  • Two-Dimensional Sequences
  • Three-Dimensional Sequences
  • How Stride Is Used for Three-Dimensional Sequences
  • Coding Your Program
  • Fortran Programs
  • Calling ESSL Subroutines and Functions in Fortran
  • Setting Up a User-Supplied Subroutine for ESSL in Fortran
  • Setting Up Scalar Data in Fortran
  • Setting Up Arrays in Fortran
  • Creating Multiple Threads and Calling ESSL from Your Fortran Program
  • Handling Errors in Your Fortran Program
  • Example of Handling Errors in a Multithreaded Application Program
  • C Programs
  • Calling ESSL Subroutines and Functions in C
  • Passing Arguments in C
  • Setting Up a User-Supplied Subroutine for ESSL in C
  • Setting Up Scalar Data in C
  • Setting Up Complex and Logical Data Types in C
  • Setting Up Arrays in C
  • Creating Multiple Threads and Calling ESSL from Your C Program
  • Handling Errors in Your C Program
  • C++ Programs
  • Calling ESSL Subroutines and Functions in C++
  • Passing Arguments in C++
  • Setting Up a User-Supplied Subroutine for ESSL in C++
  • Setting Up Scalar Data in C++
  • Setting Up Short-Precision Complex Data Types and Logical Data Types in C++
  • Setting Up Arrays in C++
  • Creating Multiple Threads and Calling ESSL from Your C++ Program
  • Handling Errors in Your C++ Program
  • PL/I Programs
  • Processing Your Program
  • Compiling
  • General Procedures
  • Using Your Own Complex Data Definitions in C Programs
  • Using Your Own Short Complex Data Definitions in C++ Programs
  • Compiling and Linking
  • Fortran Programs
  • C Programs
  • C++ Programs
  • Migrating Your Programs
  • Migrating ESSL Version 2 Programs to Version 3
  • ESSL Subroutines
  • ESSL Messages
  • Planning for Future Migration
  • Migrating between RS/6000 Processors
  • Auxiliary Storage
  • Bitwise-Identical Results
  • Migrating from Other Libraries to ESSL
  • Migrating from ESSL/370
  • Migrating from Another IBM Subroutine Library
  • Migrating from LAPACK
  • Migrating from a Non-IBM Subroutine Library
  • Handling Problems
  • Where to Find More Information About Errors
  • Getting Help from IBM Support
  • National Language Support
  • Dealing with Errors
  • Program Exceptions
  • ESSL Input-Argument Error Messages
  • ESSL Computational Error Messages
  • ESSL Resource Error Messages
  • ESSL Informational and Attention Messages
  • Miscellaneous Error Messages
  • Messages
  • Message Conventions
  • Input-Argument Error Messages
  • Computational Error Messages
  • Resource Error Messages
  • Informational and Attention Error Messages
  • Miscellaneous Error Messages

  • Reference Information

  • Linear Algebra Subprograms
  • Overview of the Linear Algebra Subprograms
  • Vector-Scalar Linear Algebra Subprograms
  • Sparse Vector-Scalar Linear Algebra Subprograms
  • Matrix-Vector Linear Algebra Subprograms
  • Sparse Matrix-Vector Linear Algebra Subprograms
  • Use Considerations
  • Performance and Accuracy Considerations
  • Vector-Scalar Subprograms
  • ISAMAX, IDAMAX, ICAMAX, and IZAMAX--Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude
  • ISAMIN and IDAMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Absolute Value
  • ISMAX and IDMAX--Position of the First or Last Occurrence of the Vector Element Having the Maximum Value
  • ISMIN and IDMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Value
  • SASUM, DASUM, SCASUM, and DZASUM--Sum of the Magnitudes of the Elements in a Vector
  • SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y
  • SCOPY, DCOPY, CCOPY, and ZCOPY--Copy a Vector
  • SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
  • SNAXPY and DNAXPY--Compute SAXPY or DAXPY N Times
  • SNDOT and DNDOT--Compute Special Dot Products N Times
  • SNRM2, DNRM2, SCNRM2, and DZNRM2--Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow
  • SNORM2, DNORM2, CNORM2, and ZNORM2--Euclidean Length of a Vector with No Scaling of Input
  • SROTG, DROTG, CROTG, and ZROTG--Construct a Givens Plane Rotation
  • SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
  • SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
  • SSWAP, DSWAP, CSWAP, and ZSWAP--Interchange the Elements of Two Vectors
  • SVEA, DVEA, CVEA, and ZVEA--Add a Vector X to a Vector Y and Store in a Vector Z
  • SVES, DVES, CVES, and ZVES--Subtract a Vector Y from a Vector X and Store in a Vector Z
  • SVEM, DVEM, CVEM, and ZVEM--Multiply a Vector X by a Vector Y and Store in a Vector Z
  • SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
  • SZAXPY, DZAXPY, CZAXPY, and ZZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z
  • Sparse Vector-Scalar Subprograms
  • SSCTR, DSCTR, CSCTR, ZSCTR--Scatter the Elements of a Sparse Vector X in Compressed-Vector Storage Mode into Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode
  • SGTHR, DGTHR, CGTHR, and ZGTHR--Gather Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode into a Sparse Vector X in Compressed-Vector Storage Mode
  • SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ--Gather Specified Elements of a Sparse Vector Y in Full-Vector Mode into a Sparse Vector X in Compressed-Vector Mode, and Zero the Same Specified Elements of Y
  • SAXPYI, DAXPYI, CAXPYI, and ZAXPYI--Multiply a Sparse Vector X in Compressed-Vector Storage Mode by a Scalar, Add to a Sparse Vector Y in Full-Vector Storage Mode, and Store in the Vector Y
  • SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
  • Matrix-Vector Subprograms
  • SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
  • SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
  • SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
  • SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
  • SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
  • SGBMV, DGBMV, CGBMV, and ZGBMV--Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose
  • SSBMV, DSBMV, CHBMV, and ZHBMV--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix
  • STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
  • STBMV, DTBMV, CTBMV, and ZTBMV--Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose
  • Sparse Matrix-Vector Subprograms
  • DSMMX--Matrix-Vector Product for a Sparse Matrix in Compressed-Matrix Storage Mode
  • DSMTM--Transpose a Sparse Matrix in Compressed-Matrix Storage Mode
  • DSDMX--Matrix-Vector Product for a Sparse Matrix or Its Transpose in Compressed-Diagonal Storage Mode
  • Matrix Operations
  • Overview of the Matrix Operation Subroutines
  • Use Considerations
  • Specifying Normal, Transposed, or Conjugate Transposed Input Matrices
  • Transposing or Conjugate Transposing:
  • Performance and Accuracy Considerations
  • In General
  • For Large Matrices
  • For Combined Operations
  • Matrix Operation Subroutines
  • SGEADD, DGEADD, CGEADD, and ZGEADD--Matrix Addition for General Matrices or Their Transposes
  • SGESUB, DGESUB, CGESUB, and ZGESUB--Matrix Subtraction for General Matrices or Their Transposes
  • SGEMUL, DGEMUL, CGEMUL, and ZGEMUL--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes
  • SGEMMS, DGEMMS, CGEMMS, and ZGEMMS--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm
  • SGEMM, DGEMM, CGEMM, and ZGEMM--Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes
  • SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
  • STRMM, DTRMM, CTRMM, and ZTRMM--Triangular Matrix-Matrix Product
  • SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
  • SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
  • SGETMI, DGETMI, CGETMI, and ZGETMI--General Matrix Transpose (In-Place)
  • SGETMO, DGETMO, CGETMO, and ZGETMO--General Matrix Transpose (Out-of-Place)
  • Linear Algebraic Equations
  • Overview of the Linear Algebraic Equation Subroutines
  • Dense Linear Algebraic Equation Subroutines
  • Banded Linear Algebraic Equation Subroutines
  • Sparse Linear Algebraic Equation Subroutines
  • Linear Least Squares Subroutines
  • Dense and Banded Linear Algebraic Equation Considerations
  • Use Considerations
  • Performance and Accuracy Considerations
  • Sparse Matrix Direct Solver Considerations
  • Use Considerations
  • Performance and Accuracy Considerations
  • Sparse Matrix Skyline Solver Considerations
  • Use Considerations
  • Performance and Accuracy Considerations
  • Sparse Matrix Iterative Solver Considerations
  • Use Considerations
  • Performance and Accuracy Considerations
  • Linear Least Squares Considerations
  • Use Considerations
  • Performance and Accuracy Considerations
  • Dense Linear Algebraic Equation Subroutines
  • SGEF, DGEF, CGEF, and ZGEF--General Matrix Factorization
  • SGES, DGES, CGES, and ZGES--General Matrix, Its Transpose, or Its Conjugate Transpose Solve
  • SGESM, DGESM, CGESM, and ZGESM--General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve
  • SGETRF, DGETRF, CGETRF and ZGETRF--General Matrix Factorization
  • SGETRS, DGETRS, CGETRS, and ZGETRS--General Matrix Multiple Right-Hand Side Solve
  • SGEFCD and DGEFCD--General Matrix Factorization, Condition Number Reciprocal, and Determinant
  • SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
  • SPPS and DPPS--Positive Definite Real Symmetric Matrix Solve
  • SPOSM, DPOSM, CPOSM, and ZPOSM--Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve
  • SPPFCD, DPPFCD, SPOFCD, and DPOFCD--Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant
  • SGEICD and DGEICD--General Matrix Inverse, Condition Number Reciprocal, and Determinant
  • SPPICD, DPPICD, SPOICD, and DPOICD--Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant
  • STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
  • STRSM, DTRSM, CTRSM, and ZTRSM--Solution of Triangular Systems of Equations with Multiple Right-Hand Sides
  • STRI, DTRI, STPI, and DTPI--Triangular Matrix Inverse
  • Banded Linear Algebraic Equation Subroutines
  • SGBF and DGBF--General Band Matrix Factorization
  • SGBS and DGBS--General Band Matrix Solve
  • SPBF, DPBF, SPBCHF, and DPBCHF--Positive Definite Symmetric Band Matrix Factorization
  • SPBS, DPBS, SPBCHS, and DPBCHS--Positive Definite Symmetric Band Matrix Solve
  • SGTF and DGTF--General Tridiagonal Matrix Factorization
  • SGTS and DGTS--General Tridiagonal Matrix Solve
  • SGTNP, DGTNP, CGTNP, and ZGTNP--General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting
  • SGTNPF, DGTNPF, CGTNPF, and ZGTNPF--General Tridiagonal Matrix Factorization with No Pivoting
  • SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting
  • SPTF and DPTF--Positive Definite Symmetric Tridiagonal Matrix Factorization
  • SPTS and DPTS--Positive Definite Symmetric Tridiagonal Matrix Solve
  • STBSV, DTBSV, CTBSV, and ZTBSV--Triangular Band Equation Solve
  • Sparse Linear Algebraic Equation Subroutines
  • DGSF--General Sparse Matrix Factorization Using Storage by Indices, Rows, or Columns
  • DGSS--General Sparse Matrix or Its Transpose Solve Using Storage by Indices, Rows, or Columns
  • DGKFS--General Sparse Matrix or Its Transpose Factorization, Determinant, and Solve Using Skyline Storage Mode
  • DSKFS--Symmetric Sparse Matrix Factorization, Determinant, and Solve Using Skyline Storage Mode
  • DSRIS--Iterative Linear System Solver for a General or Symmetric Sparse Matrix Stored by Rows
  • DSMCG--Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Matrix Storage Mode
  • DSDCG--Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Diagonal Storage Mode
  • DSMGCG--General Sparse Matrix Iterative Solve Using Compressed-Matrix Storage Mode
  • DSDGCG--General Sparse Matrix Iterative Solve Using Compressed-Diagonal Storage Mode
  • Linear Least Squares Subroutines
  • SGESVF and DGESVF--Singular Value Decomposition for a General Matrix
  • SGESVS and DGESVS--Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition
  • SGELLS and DGELLS--Linear Least Squares Solution for a General Matrix Using a QR Decomposition with Column Pivoting
  • Eigensystem Analysis
  • Overview of the Eigensystem Analysis Subroutines
  • Performance and Accuracy Considerations
  • Eigensystem Analysis Subroutines
  • SGEEV, DGEEV, CGEEV, and ZGEEV--Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix
  • SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
  • SSPSV, DSPSV, CHPSV, and ZHPSV--Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
  • SGEGV and DGEGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Eigensystem, Az=wBz, where A and B Are Real General Matrices
  • SSYGV and DSYGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Symmetric Eigensystem, Az=wBz, where A Is Real Symmetric and B Is Real Symmetric Positive Definite
  • Fourier Transforms, Convolutions and Correlations, and Related Computations
  • Overview of the Signal Processing Subroutines
  • Fourier Transforms Subroutines
  • Convolution and Correlation Subroutines
  • Related-Computation Subroutines
  • Fourier Transforms, Convolutions, and Correlations Considerations
  • Use Considerations
  • Initializing Auxiliary Working Storage
  • Determining the Amount of Auxiliary Working Storage That You Need
  • Performance and Accuracy Considerations
  • When Running on the Workstation Processors
  • Defining Arrays
  • Fourier Transform Considerations
  • How the Fourier Transform Subroutines Achieve High Performance
  • Convolution and Correlation Considerations
  • Related Computation Considerations
  • Accuracy Considerations
  • Fourier Transform Subroutines
  • SCFT and DCFT--Complex Fourier Transform
  • SRCFT and DRCFT--Real-to-Complex Fourier Transform
  • SCRFT and DCRFT--Complex-to-Real Fourier Transform
  • SCOSF and DCOSF--Cosine Transform
  • SSINF and DSINF--Sine Transform
  • SCFT2 and DCFT2--Complex Fourier Transform in Two Dimensions
  • SRCFT2 and DRCFT2--Real-to-Complex Fourier Transform in Two Dimensions
  • SCRFT2 and DCRFT2--Complex-to-Real Fourier Transform in Two Dimensions
  • SCFT3 and DCFT3--Complex Fourier Transform in Three Dimensions
  • SRCFT3 and DRCFT3--Real-to-Complex Fourier Transform in Three Dimensions
  • SCRFT3 and DCRFT3--Complex-to-Real Fourier Transform in Three Dimensions
  • Convolution and Correlation Subroutines
  • SCON and SCOR--Convolution or Correlation of One Sequence with One or More Sequences
  • SCOND and SCORD--Convolution or Correlation of One Sequence with Another Sequence Using a Direct Method
  • SCONF and SCORF--Convolution or Correlation of One Sequence with One or More Sequences Using the Mixed-Radix Fourier Method
  • SDCON, DDCON, SDCOR, and DDCOR--Convolution or Correlation with Decimated Output Using a Direct Method
  • SACOR--Autocorrelation of One or More Sequences
  • SACORF--Autocorrelation of One or More Sequences Using the Mixed-Radix Fourier Method
  • Related-Computation Subroutines
  • SPOLY and DPOLY--Polynomial Evaluation
  • SIZC and DIZC--I-th Zero Crossing
  • STREC and DTREC--Time-Varying Recursive Filter
  • SQINT and DQINT--Quadratic Interpolation
  • SWLEV, DWLEV, CWLEV, and ZWLEV--Wiener-Levinson Filter Coefficients
  • Sorting and Searching
  • Overview of the Sorting and Searching Subroutines
  • Use Considerations
  • Performance and Accuracy Considerations
  • Sorting and Searching Subroutines
  • ISORT, SSORT, and DSORT--Sort the Elements of a Sequence
  • ISORTX, SSORTX, and DSORTX--Sort the Elements of a Sequence and Note the Original Element Positions
  • ISORTS, SSORTS, and DSORTS--Sort the Elements of a Sequence Using a Stable Sort and Note the Original Element Positions
  • IBSRCH, SBSRCH, and DBSRCH--Binary Search for Elements of a Sequence X in a Sorted Sequence Y
  • ISSRCH, SSSRCH, and DSSRCH--Sequential Search for Elements of a Sequence X in the Sequence Y
  • Interpolation
  • Overview of the Interpolation Subroutines
  • Use Considerations
  • Performance and Accuracy Considerations
  • Interpolation Subroutines
  • SPINT and DPINT--Polynomial Interpolation
  • STPINT and DTPINT--Local Polynomial Interpolation
  • SCSINT and DCSINT--Cubic Spline Interpolation
  • SCSIN2 and DCSIN2--Two-Dimensional Cubic Spline Interpolation
  • Numerical Quadrature
  • Overview of the Numerical Quadrature Subroutines
  • Use Considerations
  • Choosing the Method
  • Performance and Accuracy Considerations
  • Programming Considerations for the SUBF Subroutine
  • Designing SUBF
  • Coding and Setting Up SUBF in Your Program
  • Numerical Quadrature Subroutines
  • SPTNQ and DPTNQ--Numerical Quadrature Performed on a Set of Points
  • SGLNQ and DGLNQ--Numerical Quadrature Performed on a Function Using Gauss-Legendre Quadrature
  • SGLNQ2 and DGLNQ2--Numerical Quadrature Performed on a Function Over a Rectangle Using Two-Dimensional Gauss-Legendre Quadrature
  • SGLGQ and DGLGQ--Numerical Quadrature Performed on a Function Using Gauss-Laguerre Quadrature
  • SGRAQ and DGRAQ--Numerical Quadrature Performed on a Function Using Gauss-Rational Quadrature
  • SGHMQ and DGHMQ--Numerical Quadrature Performed on a Function Using Gauss-Hermite Quadrature
  • Random Number Generation
  • Overview of the Random Number Generation Subroutines
  • Use Considerations
  • Random Number Generation Subroutines
  • SURAND and DURAND--Generate a Vector of Uniformly Distributed Random Numbers
  • SNRAND and DNRAND--Generate a Vector of Normally Distributed Random Numbers
  • SURXOR and DURXOR--Generate a Vector of Long Period Uniformly Distributed Random Numbers
  • Utilities
  • Overview of the Utility Subroutines
  • Use Considerations
  • Determining the Level of ESSL Installed
  • Finding the Optimal Stride(s) for Your Fourier Transforms
  • Converting Sparse Matrix Storage
  • Utility Subroutines
  • EINFO--ESSL Error Information-Handler Subroutine
  • ERRSAV--ESSL ERRSAV Subroutine for ESSL
  • ERRSET--ESSL ERRSET Subroutine for ESSL
  • ERRSTR--ESSL ERRSTR Subroutine for ESSL
  • IESSL--Determine the Level of ESSL Installed
  • STRIDE--Determine the Stride Value for Optimal Performance in Specified Fourier Transform Subroutines
  • DSRSM--Convert a Sparse Matrix from Storage-by-Rows to Compressed-Matrix Storage Mode
  • DGKTRN--For a General Sparse Matrix, Convert Between Diagonal-Out and Profile-In Skyline Storage Mode
  • DSKTRN--For a Symmetric Sparse Matrix, Convert Between Diagonal-Out and Profile-In Skyline Storage Mode

  • Appendixes

  • Appendix A. Basic Linear Algebra Subprograms (BLAS)
  • Level 1 BLAS
  • Level 2 BLAS
  • Level 3 BLAS
  • Appendix B. LAPACK
  • LAPACK
  • Appendix C. Glossary

  • Appendix D. Bibliography
  • References
  • ESSL Publications
  • Evaluation and Planning
  • Installation
  • Application Programming
  • Related Publications
  • AIX Version 4 for the RS/6000
  • XL Fortran
  • XL C and C++
  • PL/I
  • Workstation Processors
  • IBM 3838 Array Processor
  • Index

  • Looking for a Subroutine?


    CAXPY...
    SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y
    CAXPYI...
    SAXPYI, DAXPYI, CAXPYI, and ZAXPYI--Multiply a Sparse Vector X in Compressed-Vector Storage Mode by a Scalar, Add to a Sparse Vector Y in Full-Vector Storage Mode, and Store in the Vector Y
    CCOPY...
    SCOPY, DCOPY, CCOPY, and ZCOPY--Copy a Vector
    CDOTC...
    SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
    CDOTCI...
    SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
    CDOTU...
    SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
    CDOTUI...
    SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
    CGBMV...
    SGBMV, DGBMV, CGBMV, and ZGBMV--Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose
    CGEADD...
    SGEADD, DGEADD, CGEADD, and ZGEADD--Matrix Addition for General Matrices or Their Transposes
    CGEEV...
    SGEEV, DGEEV, CGEEV, and ZGEEV--Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix
    CGEF...
    SGEF, DGEF, CGEF, and ZGEF--General Matrix Factorization
    CGEMM...
    SGEMM, DGEMM, CGEMM, and ZGEMM--Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes
    CGEMMS...
    SGEMMS, DGEMMS, CGEMMS, and ZGEMMS--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm
    CGEMUL...
    SGEMUL, DGEMUL, CGEMUL, and ZGEMUL--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes
    CGEMV...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    CGERC...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    CGERU...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    CGES...
    SGES, DGES, CGES, and ZGES--General Matrix, Its Transpose, or Its Conjugate Transpose Solve
    CGESM...
    SGESM, DGESM, CGESM, and ZGESM--General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve
    CGESUB...
    SGESUB, DGESUB, CGESUB, and ZGESUB--Matrix Subtraction for General Matrices or Their Transposes
    CGETMI...
    SGETMI, DGETMI, CGETMI, and ZGETMI--General Matrix Transpose (In-Place)
    CGETMO...
    SGETMO, DGETMO, CGETMO, and ZGETMO--General Matrix Transpose (Out-of-Place)
    CGETRF...
    SGETRF, DGETRF, CGETRF and ZGETRF--General Matrix Factorization
    CGETRS...
    SGETRS, DGETRS, CGETRS, and ZGETRS--General Matrix Multiple Right-Hand Side Solve
    CGTHR...
    SGTHR, DGTHR, CGTHR, and ZGTHR--Gather Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode into a Sparse Vector X in Compressed-Vector Storage Mode
    CGTHRZ...
    SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ--Gather Specified Elements of a Sparse Vector Y in Full-Vector Mode into a Sparse Vector X in Compressed-Vector Mode, and Zero the Same Specified Elements of Y
    CGTNP...
    SGTNP, DGTNP, CGTNP, and ZGTNP--General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting
    CGTNPF...
    SGTNPF, DGTNPF, CGTNPF, and ZGTNPF--General Tridiagonal Matrix Factorization with No Pivoting
    CGTNPS...
    SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting
    CHBMV...
    SSBMV, DSBMV, CHBMV, and ZHBMV--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix
    CHEMM...
    SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
    CHEMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    CHER...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    CHER2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    CHER2K...
    SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    CHERK...
    SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    CHLEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    CHPEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    CHPMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    CHPR...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    CHPR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    CHPSV...
    SSPSV, DSPSV, CHPSV, and ZHPSV--Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    CNORM2...
    SNORM2, DNORM2, CNORM2, and ZNORM2--Euclidean Length of a Vector with No Scaling of Input
    CPOF...
    SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
    CPOSM...
    SPOSM, DPOSM, CPOSM, and ZPOSM--Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve
    CROT...
    SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
    CROTG...
    SROTG, DROTG, CROTG, and ZROTG--Construct a Givens Plane Rotation
    CSCAL...
    SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
    

    CSCTR...
    SSCTR, DSCTR, CSCTR, ZSCTR--Scatter the Elements of a Sparse Vector X in Compressed-Vector Storage Mode into Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode
    CSROT...
    SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
    CSSCAL...
    SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
    CSWAP...
    SSWAP, DSWAP, CSWAP, and ZSWAP--Interchange the Elements of Two Vectors
    CSYAX...
    SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
    CSYMM...
    SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
    CSYR2K...
    SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    CSYRK...
    SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    CTBMV...
    STBMV, DTBMV, CTBMV, and ZTBMV--Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose
    CTBSV...
    STBSV, DTBSV, CTBSV, and ZTBSV--Triangular Band Equation Solve
    CTPMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    CTPSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    CTRMM...
    STRMM, DTRMM, CTRMM, and ZTRMM--Triangular Matrix-Matrix Product
    CTRMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    CTRSM...
    STRSM, DTRSM, CTRSM, and ZTRSM--Solution of Triangular Systems of Equations with Multiple Right-Hand Sides
    CTRSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    CVEA...
    SVEA, DVEA, CVEA, and ZVEA--Add a Vector X to a Vector Y and Store in a Vector Z
    CVEM...
    SVEM, DVEM, CVEM, and ZVEM--Multiply a Vector X by a Vector Y and Store in a Vector Z
    CVES...
    SVES, DVES, CVES, and ZVES--Subtract a Vector Y from a Vector X and Store in a Vector Z
    CWLEV...
    SWLEV, DWLEV, CWLEV, and ZWLEV--Wiener-Levinson Filter Coefficients
    CYAX...
    SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
    CZAXPY...
    SZAXPY, DZAXPY, CZAXPY, and ZZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z
    DASUM...
    SASUM, DASUM, SCASUM, and DZASUM--Sum of the Magnitudes of the Elements in a Vector
    DAXPY...
    SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y
    DAXPYI...
    SAXPYI, DAXPYI, CAXPYI, and ZAXPYI--Multiply a Sparse Vector X in Compressed-Vector Storage Mode by a Scalar, Add to a Sparse Vector Y in Full-Vector Storage Mode, and Store in the Vector Y
    DBSRCH...
    IBSRCH, SBSRCH, and DBSRCH--Binary Search for Elements of a Sequence X in a Sorted Sequence Y
    DCFT...
    SCFT and DCFT--Complex Fourier Transform
    DCOSF...
    SCOSF and DCOSF--Cosine Transform
    DCFT2...
    SCFT2 and DCFT2--Complex Fourier Transform in Two Dimensions
    DCFT3...
    SCFT3 and DCFT3--Complex Fourier Transform in Three Dimensions
    DCOPY...
    SCOPY, DCOPY, CCOPY, and ZCOPY--Copy a Vector
    DCRFT...
    SCRFT and DCRFT--Complex-to-Real Fourier Transform
    DCRFT2...
    SCRFT2 and DCRFT2--Complex-to-Real Fourier Transform in Two Dimensions
    DCRFT3...
    SCRFT3 and DCRFT3--Complex-to-Real Fourier Transform in Three Dimensions
    DCSIN2...
    SCSIN2 and DCSIN2--Two-Dimensional Cubic Spline Interpolation
    DCSINT...
    SCSINT and DCSINT--Cubic Spline Interpolation
    DDCON...
    SDCON, DDCON, SDCOR, and DDCOR--Convolution or Correlation with Decimated Output Using a Direct Method
    DDCOR...
    SDCON, DDCON, SDCOR, and DDCOR--Convolution or Correlation with Decimated Output Using a Direct Method
    DDOT...
    SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
    DDOTI...
    SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
    DGBF...
    SGBF and DGBF--General Band Matrix Factorization
    DGBMV...
    SGBMV, DGBMV, CGBMV, and ZGBMV--Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose
    DGBS...
    SGBS and DGBS--General Band Matrix Solve
    DGEADD...
    SGEADD, DGEADD, CGEADD, and ZGEADD--Matrix Addition for General Matrices or Their Transposes
    DGEEV...
    SGEEV, DGEEV, CGEEV, and ZGEEV--Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix
    DGEF...
    SGEF, DGEF, CGEF, and ZGEF--General Matrix Factorization
    DGEFCD...
    SGEFCD and DGEFCD--General Matrix Factorization, Condition Number Reciprocal, and Determinant
    DGEGV...
    SGEGV and DGEGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Eigensystem, Az=wBz, where A and B Are Real General Matrices
    

    DGEICD...
    SGEICD and DGEICD--General Matrix Inverse, Condition Number Reciprocal, and Determinant
    DGELLS...
    SGELLS and DGELLS--Linear Least Squares Solution for a General Matrix Using a QR Decomposition with Column Pivoting
    DGEMM...
    SGEMM, DGEMM, CGEMM, and ZGEMM--Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes
    DGEMMS...
    SGEMMS, DGEMMS, CGEMMS, and ZGEMMS--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm
    DGEMTX...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    DGEMUL...
    SGEMUL, DGEMUL, CGEMUL, and ZGEMUL--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes
    DGEMV...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    DGEMX...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    DGER...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    DGER1...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    DGES...
    SGES, DGES, CGES, and ZGES--General Matrix, Its Transpose, or Its Conjugate Transpose Solve
    DGESM...
    SGESM, DGESM, CGESM, and ZGESM--General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve
    DGESUB...
    SGESUB, DGESUB, CGESUB, and ZGESUB--Matrix Subtraction for General Matrices or Their Transposes
    DGESVF...
    SGESVF and DGESVF--Singular Value Decomposition for a General Matrix
    DGESVS...
    SGESVS and DGESVS--Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition
    DGETMI...
    SGETMI, DGETMI, CGETMI, and ZGETMI--General Matrix Transpose (In-Place)
    DGETMO...
    SGETMO, DGETMO, CGETMO, and ZGETMO--General Matrix Transpose (Out-of-Place)
    DGETRF...
    SGETRF, DGETRF, CGETRF and ZGETRF--General Matrix Factorization
    DGETRS...
    SGETRS, DGETRS, CGETRS, and ZGETRS--General Matrix Multiple Right-Hand Side Solve
    DGHMQ...
    SGHMQ and DGHMQ--Numerical Quadrature Performed on a Function Using Gauss-Hermite Quadrature
    DGKFS...
    DGKFS--General Sparse Matrix or Its Transpose Factorization, Determinant, and Solve Using Skyline Storage Mode
    DGKTRN...
    DGKTRN--For a General Sparse Matrix, Convert Between Diagonal-Out and Profile-In Skyline Storage Mode
    DGLGQ...
    SGLGQ and DGLGQ--Numerical Quadrature Performed on a Function Using Gauss-Laguerre Quadrature
    DGLNQ...
    SGLNQ and DGLNQ--Numerical Quadrature Performed on a Function Using Gauss-Legendre Quadrature
    DGLNQ2...
    SGLNQ2 and DGLNQ2--Numerical Quadrature Performed on a Function Over a Rectangle Using Two-Dimensional Gauss-Legendre Quadrature
    DGRAQ...
    SGRAQ and DGRAQ--Numerical Quadrature Performed on a Function Using Gauss-Rational Quadrature
    DGSF...
    DGSF--General Sparse Matrix Factorization Using Storage by Indices, Rows, or Columns
    DGSS...
    DGSS--General Sparse Matrix or Its Transpose Solve Using Storage by Indices, Rows, or Columns
    DGTF...
    SGTF and DGTF--General Tridiagonal Matrix Factorization
    DGTHR...
    SGTHR, DGTHR, CGTHR, and ZGTHR--Gather Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode into a Sparse Vector X in Compressed-Vector Storage Mode
    DGTHRZ...
    SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ--Gather Specified Elements of a Sparse Vector Y in Full-Vector Mode into a Sparse Vector X in Compressed-Vector Mode, and Zero the Same Specified Elements of Y
    DGTNP...
    SGTNP, DGTNP, CGTNP, and ZGTNP--General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting
    DGTNPF...
    SGTNPF, DGTNPF, CGTNPF, and ZGTNPF--General Tridiagonal Matrix Factorization with No Pivoting
    DGTNPS...
    SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting
    DGTS...
    SGTS and DGTS--General Tridiagonal Matrix Solve
    DIZC...
    SIZC and DIZC--I-th Zero Crossing
    DNAXPY...
    SNAXPY and DNAXPY--Compute SAXPY or DAXPY N Times
    DNDOT...
    SNDOT and DNDOT--Compute Special Dot Products N Times
    DNORM2...
    SNORM2, DNORM2, CNORM2, and ZNORM2--Euclidean Length of a Vector with No Scaling of Input
    DNRAND...
    SNRAND and DNRAND--Generate a Vector of Normally Distributed Random Numbers
    DNRM2...
    SNRM2, DNRM2, SCNRM2, and DZNRM2--Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow
    DPBCHF...
    SPBF, DPBF, SPBCHF, and DPBCHF--Positive Definite Symmetric Band Matrix Factorization
    DPBCHS...
    SPBS, DPBS, SPBCHS, and DPBCHS--Positive Definite Symmetric Band Matrix Solve
    DPBF...
    SPBF, DPBF, SPBCHF, and DPBCHF--Positive Definite Symmetric Band Matrix Factorization
    DPBS...
    SPBS, DPBS, SPBCHS, and DPBCHS--Positive Definite Symmetric Band Matrix Solve
    DPINT...
    SPINT and DPINT--Polynomial Interpolation
    DPOF...
    SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
    DPOFCD...
    SPPFCD, DPPFCD, SPOFCD, and DPOFCD--Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant
    

    DPOICD...
    SPPICD, DPPICD, SPOICD, and DPOICD--Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant
    DPOLY...
    SPOLY and DPOLY--Polynomial Evaluation
    DPOSM...
    SPOSM, DPOSM, CPOSM, and ZPOSM--Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve
    DPPF...
    SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
    DPPFCD...
    SPPFCD, DPPFCD, SPOFCD, and DPOFCD--Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant
    DPPICD...
    SPPICD, DPPICD, SPOICD, and DPOICD--Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant
    DPPS...
    SPPS and DPPS--Positive Definite Real Symmetric Matrix Solve
    DPTF...
    SPTF and DPTF--Positive Definite Symmetric Tridiagonal Matrix Factorization
    DPTNQ...
    SPTNQ and DPTNQ--Numerical Quadrature Performed on a Set of Points
    DPTS...
    SPTS and DPTS--Positive Definite Symmetric Tridiagonal Matrix Solve
    DQINT...
    SQINT and DQINT--Quadratic Interpolation
    DRCFT...
    SRCFT and DRCFT--Real-to-Complex Fourier Transform
    DRCFT2...
    SRCFT2 and DRCFT2--Real-to-Complex Fourier Transform in Two Dimensions
    DRCFT3...
    SRCFT3 and DRCFT3--Real-to-Complex Fourier Transform in Three Dimensions
    DROT...
    SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
    DROTG...
    SROTG, DROTG, CROTG, and ZROTG--Construct a Givens Plane Rotation
    DSBMV...
    SSBMV, DSBMV, CHBMV, and ZHBMV--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix
    DSCAL...
    SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
    DSCTR...
    SSCTR, DSCTR, CSCTR, ZSCTR--Scatter the Elements of a Sparse Vector X in Compressed-Vector Storage Mode into Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode
    DSDCG...
    DSDCG--Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Diagonal Storage Mode
    DSDGCG...
    DSDGCG--General Sparse Matrix Iterative Solve Using Compressed-Diagonal Storage Mode
    DSDMX...
    DSDMX--Matrix-Vector Product for a Sparse Matrix or Its Transpose in Compressed-Diagonal Storage Mode
    DSINF...
    SSINF and DSINF--Sine Transform
    DSKFS...
    DSKFS--Symmetric Sparse Matrix Factorization, Determinant, and Solve Using Skyline Storage Mode
    DSKTRN...
    DSKTRN--For a Symmetric Sparse Matrix, Convert Between Diagonal-Out and Profile-In Skyline Storage Mode
    DSLEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    DSLMX...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    DSLR1...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    DSLR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    DSMCG...
    DSMCG--Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Matrix Storage Mode
    DSMGCG...
    DSMGCG--General Sparse Matrix Iterative Solve Using Compressed-Matrix Storage Mode
    DSMMX...
    DSMMX--Matrix-Vector Product for a Sparse Matrix in Compressed-Matrix Storage Mode
    DSMTM...
    DSMTM--Transpose a Sparse Matrix in Compressed-Matrix Storage Mode
    DSORT...
    ISORT, SSORT, and DSORT--Sort the Elements of a Sequence
    DSORTS...
    ISORTS, SSORTS, and DSORTS--Sort the Elements of a Sequence Using a Stable Sort and Note the Original Element Positions
    DSORTX...
    ISORTX, SSORTX, and DSORTX--Sort the Elements of a Sequence and Note the Original Element Positions
    DSPEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    DSPMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    DSPR...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    DSPR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    DSPSV...
    SSPSV, DSPSV, CHPSV, and ZHPSV--Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    DSRIS...
    DSRIS--Iterative Linear System Solver for a General or Symmetric Sparse Matrix Stored by Rows
    DSRSM...
    DSRSM--Convert a Sparse Matrix from Storage-by-Rows to Compressed-Matrix Storage Mode
    DSSRCH...
    ISSRCH, SSSRCH, and DSSRCH--Sequential Search for Elements of a Sequence X in the Sequence Y
    DSWAP...
    SSWAP, DSWAP, CSWAP, and ZSWAP--Interchange the Elements of Two Vectors
    DSYGV...
    SSYGV and DSYGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Symmetric Eigensystem, Az=wBz, where A Is Real Symmetric and B Is Real Symmetric Positive Definite
    DSYMM...
    SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
    DSYMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    

    DSYR...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    DSYR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    DSYR2K...
    SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    DSYRK...
    SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    DTBMV...
    STBMV, DTBMV, CTBMV, and ZTBMV--Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose
    DTBSV...
    STBSV, DTBSV, CTBSV, and ZTBSV--Triangular Band Equation Solve
    DTPI...
    STRI, DTRI, STPI, and DTPI--Triangular Matrix Inverse
    DTPINT...
    STPINT and DTPINT--Local Polynomial Interpolation
    DTPMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    DTPSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    DTREC...
    STREC and DTREC--Time-Varying Recursive Filter
    DTRI...
    STRI, DTRI, STPI, and DTPI--Triangular Matrix Inverse
    DTRMM...
    STRMM, DTRMM, CTRMM, and ZTRMM--Triangular Matrix-Matrix Product
    DTRMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    DTRSM...
    STRSM, DTRSM, CTRSM, and ZTRSM--Solution of Triangular Systems of Equations with Multiple Right-Hand Sides
    DTRSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    DURAND...
    SURAND and DURAND--Generate a Vector of Uniformly Distributed Random Numbers
    DURXOR...
    SURXOR and DURXOR--Generate a Vector of Long Period Uniformly Distributed Random Numbers
    DVEA...
    SVEA, DVEA, CVEA, and ZVEA--Add a Vector X to a Vector Y and Store in a Vector Z
    DVEM...
    SVEM, DVEM, CVEM, and ZVEM--Multiply a Vector X by a Vector Y and Store in a Vector Z
    DVES...
    SVES, DVES, CVES, and ZVES--Subtract a Vector Y from a Vector X and Store in a Vector Z
    DWLEV...
    SWLEV, DWLEV, CWLEV, and ZWLEV--Wiener-Levinson Filter Coefficients
    DYAX...
    SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
    DZASUM...
    SASUM, DASUM, SCASUM, and DZASUM--Sum of the Magnitudes of the Elements in a Vector
    DZAXPY...
    SZAXPY, DZAXPY, CZAXPY, and ZZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z
    DZNRM2...
    SNRM2, DNRM2, SCNRM2, and DZNRM2--Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow
    EINFO...
    EINFO--ESSL Error Information-Handler Subroutine
    ERRSAV...
    ERRSAV--ESSL ERRSAV Subroutine for ESSL
    ERRSET...
    ERRSET--ESSL ERRSET Subroutine for ESSL
    ERRSTR...
    ERRSTR--ESSL ERRSTR Subroutine for ESSL
    IBSRCH...
    IBSRCH, SBSRCH, and DBSRCH--Binary Search for Elements of a Sequence X in a Sorted Sequence Y
    ICAMAX...
    ISAMAX, IDAMAX, ICAMAX, and IZAMAX--Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude
    IDAMAX...
    ISAMAX, IDAMAX, ICAMAX, and IZAMAX--Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude
    IDAMIN...
    ISAMIN and IDAMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Absolute Value
    IDMAX...
    ISMAX and IDMAX--Position of the First or Last Occurrence of the Vector Element Having the Maximum Value
    IDMIN...
    ISMIN and IDMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Value
    IESSL...
    IESSL--Determine the Level of ESSL Installed
    ISAMAX...
    ISAMAX, IDAMAX, ICAMAX, and IZAMAX--Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude
    ISAMIN...
    ISAMIN and IDAMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Absolute Value
    ISMAX...
    ISMAX and IDMAX--Position of the First or Last Occurrence of the Vector Element Having the Maximum Value
    ISMIN...
    ISMIN and IDMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Value
    ISORT...
    ISORT, SSORT, and DSORT--Sort the Elements of a Sequence
    ISORTS...
    ISORTS, SSORTS, and DSORTS--Sort the Elements of a Sequence Using a Stable Sort and Note the Original Element Positions
    ISORTX...
    ISORTX, SSORTX, and DSORTX--Sort the Elements of a Sequence and Note the Original Element Positions
    ISSRCH...
    ISSRCH, SSSRCH, and DSSRCH--Sequential Search for Elements of a Sequence X in the Sequence Y
    IZAMAX...
    ISAMAX, IDAMAX, ICAMAX, and IZAMAX--Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude
    SACOR...
    SACOR--Autocorrelation of One or More Sequences
    

    SACORF...
    SACORF--Autocorrelation of One or More Sequences Using the Mixed-Radix Fourier Method
    SASUM...
    SASUM, DASUM, SCASUM, and DZASUM--Sum of the Magnitudes of the Elements in a Vector
    SAXPY...
    SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y
    SAXPYI...
    SAXPYI, DAXPYI, CAXPYI, and ZAXPYI--Multiply a Sparse Vector X in Compressed-Vector Storage Mode by a Scalar, Add to a Sparse Vector Y in Full-Vector Storage Mode, and Store in the Vector Y
    SBSRCH...
    IBSRCH, SBSRCH, and DBSRCH--Binary Search for Elements of a Sequence X in a Sorted Sequence Y
    SCASUM...
    SASUM, DASUM, SCASUM, and DZASUM--Sum of the Magnitudes of the Elements in a Vector
    SCFT...
    SCFT and DCFT--Complex Fourier Transform
    SCFT2...
    SCFT2 and DCFT2--Complex Fourier Transform in Two Dimensions
    SCFT3...
    SCFT3 and DCFT3--Complex Fourier Transform in Three Dimensions
    SCNRM2...
    SNRM2, DNRM2, SCNRM2, and DZNRM2--Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow
    SCON...
    SCON and SCOR--Convolution or Correlation of One Sequence with One or More Sequences
    SCOND...
    SCOND and SCORD--Convolution or Correlation of One Sequence with Another Sequence Using a Direct Method
    SCONF...
    SCONF and SCORF--Convolution or Correlation of One Sequence with One or More Sequences Using the Mixed-Radix Fourier Method
    SCOPY...
    SCOPY, DCOPY, CCOPY, and ZCOPY--Copy a Vector
    SCOR...
    SCON and SCOR--Convolution or Correlation of One Sequence with One or More Sequences
    SCORD...
    SCOND and SCORD--Convolution or Correlation of One Sequence with Another Sequence Using a Direct Method
    SCORF...
    SCONF and SCORF--Convolution or Correlation of One Sequence with One or More Sequences Using the Mixed-Radix Fourier Method
    SCOSF...
    SCOSF and DCOSF--Cosine Transform
    SCRFT...
    SCRFT and DCRFT--Complex-to-Real Fourier Transform
    SCRFT2...
    SCRFT2 and DCRFT2--Complex-to-Real Fourier Transform in Two Dimensions
    SCRFT3...
    SCRFT3 and DCRFT3--Complex-to-Real Fourier Transform in Three Dimensions
    SCSIN2...
    SCSIN2 and DCSIN2--Two-Dimensional Cubic Spline Interpolation
    SCSINT...
    SCSINT and DCSINT--Cubic Spline Interpolation
    SDCON...
    SDCON, DDCON, SDCOR, and DDCOR--Convolution or Correlation with Decimated Output Using a Direct Method
    SDCOR...
    SDCON, DDCON, SDCOR, and DDCOR--Convolution or Correlation with Decimated Output Using a Direct Method
    SDOT...
    SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
    SDOTI...
    SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
    SGBF...
    SGBF and DGBF--General Band Matrix Factorization
    SGBMV...
    SGBMV, DGBMV, CGBMV, and ZGBMV--Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose
    SGBS...
    SGBS and DGBS--General Band Matrix Solve
    SGEADD...
    SGEADD, DGEADD, CGEADD, and ZGEADD--Matrix Addition for General Matrices or Their Transposes
    SGEEV...
    SGEEV, DGEEV, CGEEV, and ZGEEV--Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix
    SGEF...
    SGEF, DGEF, CGEF, and ZGEF--General Matrix Factorization
    SGEFCD...
    SGEFCD and DGEFCD--General Matrix Factorization, Condition Number Reciprocal, and Determinant
    SGEGV...
    SGEGV and DGEGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Eigensystem, Az=wBz, where A and B Are Real General Matrices
    SGEICD...
    SGEICD and DGEICD--General Matrix Inverse, Condition Number Reciprocal, and Determinant
    SGELLS...
    SGELLS and DGELLS--Linear Least Squares Solution for a General Matrix Using a QR Decomposition with Column Pivoting
    SGEMM...
    SGEMM, DGEMM, CGEMM, and ZGEMM--Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes
    SGEMMS...
    SGEMMS, DGEMMS, CGEMMS, and ZGEMMS--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm
    SGEMTX...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    SGEMUL...
    SGEMUL, DGEMUL, CGEMUL, and ZGEMUL--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes
    SGEMV...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    SGEMX...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    SGER...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    SGER1...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    SGES...
    SGES, DGES, CGES, and ZGES--General Matrix, Its Transpose, or Its Conjugate Transpose Solve
    SGESM...
    SGESM, DGESM, CGESM, and ZGESM--General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve
    

    SGESUB...
    SGESUB, DGESUB, CGESUB, and ZGESUB--Matrix Subtraction for General Matrices or Their Transposes
    SGESVF...
    SGESVF and DGESVF--Singular Value Decomposition for a General Matrix
    SGESVS...
    SGESVS and DGESVS--Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition
    SGETMI...
    SGETMI, DGETMI, CGETMI, and ZGETMI--General Matrix Transpose (In-Place)
    SGETMO...
    SGETMO, DGETMO, CGETMO, and ZGETMO--General Matrix Transpose (Out-of-Place)
    SGETRF...
    SGETRF, DGETRF, CGETRF and ZGETRF--General Matrix Factorization
    SGETRS...
    SGETRS, DGETRS, CGETRS, and ZGETRS--General Matrix Multiple Right-Hand Side Solve
    SGHMQ...
    SGHMQ and DGHMQ--Numerical Quadrature Performed on a Function Using Gauss-Hermite Quadrature
    SGLGQ...
    SGLGQ and DGLGQ--Numerical Quadrature Performed on a Function Using Gauss-Laguerre Quadrature
    SGLNQ...
    SGLNQ and DGLNQ--Numerical Quadrature Performed on a Function Using Gauss-Legendre Quadrature
    SGLNQ2...
    SGLNQ2 and DGLNQ2--Numerical Quadrature Performed on a Function Over a Rectangle Using Two-Dimensional Gauss-Legendre Quadrature
    SGRAQ...
    SGRAQ and DGRAQ--Numerical Quadrature Performed on a Function Using Gauss-Rational Quadrature
    SGTF...
    SGTF and DGTF--General Tridiagonal Matrix Factorization
    SGTHR...
    SGTHR, DGTHR, CGTHR, and ZGTHR--Gather Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode into a Sparse Vector X in Compressed-Vector Storage Mode
    SGTHRZ...
    SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ--Gather Specified Elements of a Sparse Vector Y in Full-Vector Mode into a Sparse Vector X in Compressed-Vector Mode, and Zero the Same Specified Elements of Y
    SGTNP...
    SGTNP, DGTNP, CGTNP, and ZGTNP--General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting
    SGTNPF...
    SGTNPF, DGTNPF, CGTNPF, and ZGTNPF--General Tridiagonal Matrix Factorization with No Pivoting
    SGTNPS...
    SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting
    SGTS...
    SGTS and DGTS--General Tridiagonal Matrix Solve
    SIZC...
    SIZC and DIZC--I-th Zero Crossing
    SNAXPY...
    SNAXPY and DNAXPY--Compute SAXPY or DAXPY N Times
    SNDOT...
    SNDOT and DNDOT--Compute Special Dot Products N Times
    SNORM2...
    SNORM2, DNORM2, CNORM2, and ZNORM2--Euclidean Length of a Vector with No Scaling of Input
    SNRAND...
    SNRAND and DNRAND--Generate a Vector of Normally Distributed Random Numbers
    SNRM2...
    SNRM2, DNRM2, SCNRM2, and DZNRM2--Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow
    SPBCHF...
    SPBF, DPBF, SPBCHF, and DPBCHF--Positive Definite Symmetric Band Matrix Factorization
    SPBCHS...
    SPBS, DPBS, SPBCHS, and DPBCHS--Positive Definite Symmetric Band Matrix Solve
    SPBF...
    SPBF, DPBF, SPBCHF, and DPBCHF--Positive Definite Symmetric Band Matrix Factorization
    SPBS...
    SPBS, DPBS, SPBCHS, and DPBCHS--Positive Definite Symmetric Band Matrix Solve
    SPINT...
    SPINT and DPINT--Polynomial Interpolation
    SPOF...
    SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
    SPOFCD...
    SPPFCD, DPPFCD, SPOFCD, and DPOFCD--Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant
    SPOICD...
    SPPICD, DPPICD, SPOICD, and DPOICD--Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant
    SPOLY...
    SPOLY and DPOLY--Polynomial Evaluation
    SPOSM...
    SPOSM, DPOSM, CPOSM, and ZPOSM--Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve
    SPPF...
    SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
    SPPFCD...
    SPPFCD, DPPFCD, SPOFCD, and DPOFCD--Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant
    SPPICD...
    SPPICD, DPPICD, SPOICD, and DPOICD--Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant
    SPPS...
    SPPS and DPPS--Positive Definite Real Symmetric Matrix Solve
    SPTF...
    SPTF and DPTF--Positive Definite Symmetric Tridiagonal Matrix Factorization
    SPTNQ...
    SPTNQ and DPTNQ--Numerical Quadrature Performed on a Set of Points
    SPTS...
    SPTS and DPTS--Positive Definite Symmetric Tridiagonal Matrix Solve
    SQINT...
    SQINT and DQINT--Quadratic Interpolation
    SRCFT...
    SRCFT and DRCFT--Real-to-Complex Fourier Transform
    SRCFT2...
    SRCFT2 and DRCFT2--Real-to-Complex Fourier Transform in Two Dimensions
    SRCFT3...
    SRCFT3 and DRCFT3--Real-to-Complex Fourier Transform in Three Dimensions
    SROT...
    SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
    SROTG...
    SROTG, DROTG, CROTG, and ZROTG--Construct a Givens Plane Rotation
    

    SSBMV...
    SSBMV, DSBMV, CHBMV, and ZHBMV--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix
    SSCAL...
    SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
    SSCTR...
    SSCTR, DSCTR, CSCTR, ZSCTR--Scatter the Elements of a Sparse Vector X in Compressed-Vector Storage Mode into Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode
    SSINF...
    SSINF and DSINF--Sine Transform
    SSLEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    SSLMX...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    SSLR1...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    SSLR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    SSORT...
    ISORT, SSORT, and DSORT--Sort the Elements of a Sequence
    SSORTS...
    ISORTS, SSORTS, and DSORTS--Sort the Elements of a Sequence Using a Stable Sort and Note the Original Element Positions
    SSORTX...
    ISORTX, SSORTX, and DSORTX--Sort the Elements of a Sequence and Note the Original Element Positions
    SSPEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    SSPMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    SSPR...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    SSPR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    SSPSV...
    SSPSV, DSPSV, CHPSV, and ZHPSV--Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    SSSRCH...
    ISSRCH, SSSRCH, and DSSRCH--Sequential Search for Elements of a Sequence X in the Sequence Y
    SSWAP...
    SSWAP, DSWAP, CSWAP, and ZSWAP--Interchange the Elements of Two Vectors
    SSYGV...
    SSYGV and DSYGV--Eigenvalues and, Optionally, the Eigenvectors of a Generalized Real Symmetric Eigensystem, Az=wBz, where A Is Real Symmetric and B Is Real Symmetric Positive Definite
    SSYMM...
    SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
    SSYMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    SSYR...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    SSYR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    SSYR2K...
    SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    SSYRK...
    SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    STBMV...
    STBMV, DTBMV, CTBMV, and ZTBMV--Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose
    STBSV...
    STBSV, DTBSV, CTBSV, and ZTBSV--Triangular Band Equation Solve
    STPI...
    STRI, DTRI, STPI, and DTPI--Triangular Matrix Inverse
    STPINT...
    STPINT and DTPINT--Local Polynomial Interpolation
    STPMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    STPSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    STREC...
    STREC and DTREC--Time-Varying Recursive Filter
    STRI...
    STRI, DTRI, STPI, and DTPI--Triangular Matrix Inverse
    STRIDE...
    STRIDE--Determine the Stride Value for Optimal Performance in Specified Fourier Transform Subroutines
    STRMM...
    STRMM, DTRMM, CTRMM, and ZTRMM--Triangular Matrix-Matrix Product
    STRMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    STRSM...
    STRSM, DTRSM, CTRSM, and ZTRSM--Solution of Triangular Systems of Equations with Multiple Right-Hand Sides
    STRSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    SURAND...
    SURAND and DURAND--Generate a Vector of Uniformly Distributed Random Numbers
    SURXOR...
    SURXOR and DURXOR--Generate a Vector of Long Period Uniformly Distributed Random Numbers
    SVEA...
    SVEA, DVEA, CVEA, and ZVEA--Add a Vector X to a Vector Y and Store in a Vector Z
    SVEM...
    SVEM, DVEM, CVEM, and ZVEM--Multiply a Vector X by a Vector Y and Store in a Vector Z
    SVES...
    SVES, DVES, CVES, and ZVES--Subtract a Vector Y from a Vector X and Store in a Vector Z
    SWLEV...
    SWLEV, DWLEV, CWLEV, and ZWLEV--Wiener-Levinson Filter Coefficients
    SYAX...
    SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
    SZAXPY...
    SZAXPY, DZAXPY, CZAXPY, and ZZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z
    ZAXPY...
    SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y
    ZAXPYI...
    SAXPYI, DAXPYI, CAXPYI, and ZAXPYI--Multiply a Sparse Vector X in Compressed-Vector Storage Mode by a Scalar, Add to a Sparse Vector Y in Full-Vector Storage Mode, and Store in the Vector Y
    

    ZCOPY...
    SCOPY, DCOPY, CCOPY, and ZCOPY--Copy a Vector
    ZDOTC...
    SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
    ZDOTCI...
    SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
    ZDOTU...
    SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
    ZDOTUI...
    SDOTI, DDOTI, CDOTUI, ZDOTUI, CDOTCI, and ZDOTCI--Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode
    ZDROT...
    SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
    ZDSCAL...
    SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
    ZDYAX...
    SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
    ZGBMV...
    SGBMV, DGBMV, CGBMV, and ZGBMV--Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose
    ZGEADD...
    SGEADD, DGEADD, CGEADD, and ZGEADD--Matrix Addition for General Matrices or Their Transposes
    ZGEEV...
    SGEEV, DGEEV, CGEEV, and ZGEEV--Eigenvalues and, Optionally, All or Selected Eigenvectors of a General Matrix
    ZGEF...
    SGEF, DGEF, CGEF, and ZGEF--General Matrix Factorization
    ZGEMM...
    SGEMM, DGEMM, CGEMM, and ZGEMM--Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes
    ZGEMMS...
    SGEMMS, DGEMMS, CGEMMS, and ZGEMMS--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm
    ZGEMUL...
    SGEMUL, DGEMUL, CGEMUL, and ZGEMUL--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes
    ZGEMV...
    SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
    ZGERC...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    ZGERU...
    SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
    ZGES...
    SGES, DGES, CGES, and ZGES--General Matrix, Its Transpose, or Its Conjugate Transpose Solve
    ZGESM...
    SGESM, DGESM, CGESM, and ZGESM--General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve
    ZGESUB...
    SGESUB, DGESUB, CGESUB, and ZGESUB--Matrix Subtraction for General Matrices or Their Transposes
    ZGETMI...
    SGETMI, DGETMI, CGETMI, and ZGETMI--General Matrix Transpose (In-Place)
    ZGETMO...
    SGETMO, DGETMO, CGETMO, and ZGETMO--General Matrix Transpose (Out-of-Place)
    ZGETRF...
    SGETRF, DGETRF, CGETRF and ZGETRF--General Matrix Factorization
    ZGETRS...
    SGETRS, DGETRS, CGETRS, and ZGETRS--General Matrix Multiple Right-Hand Side Solve
    ZGTHR...
    SGTHR, DGTHR, CGTHR, and ZGTHR--Gather Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode into a Sparse Vector X in Compressed-Vector Storage Mode
    ZGTHRZ...
    SGTHRZ, DGTHRZ, CGTHRZ, and ZGTHRZ--Gather Specified Elements of a Sparse Vector Y in Full-Vector Mode into a Sparse Vector X in Compressed-Vector Mode, and Zero the Same Specified Elements of Y
    ZGTNP...
    SGTNP, DGTNP, CGTNP, and ZGTNP--General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting
    ZGTNPF...
    SGTNPF, DGTNPF, CGTNPF, and ZGTNPF--General Tridiagonal Matrix Factorization with No Pivoting
    ZGTNPS...
    SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting
    ZHBMV...
    SSBMV, DSBMV, CHBMV, and ZHBMV--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix
    ZHEMM...
    SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
    ZHEMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    ZHER...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    ZHER2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    ZHER2K...
    SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    ZHERK...
    SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    ZHLEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    ZHPEV...
    SSPEV, DSPEV, CHPEV, and ZHPEV--Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    ZHPMV...
    SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
    ZHPR...
    SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
    ZHPR2...
    SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
    ZHPSV...
    SSPSV, DSPSV, CHPSV, and ZHPSV--Extreme Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix or a Complex Hermitian Matrix
    ZNORM2...
    SNORM2, DNORM2, CNORM2, and ZNORM2--Euclidean Length of a Vector with No Scaling of Input
    ZPOF...
    SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
    ZPOSM...
    SPOSM, DPOSM, CPOSM, and ZPOSM--Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve
    ZROT...
    SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
    ZROTG...
    SROTG, DROTG, CROTG, and ZROTG--Construct a Givens Plane Rotation
    

    ZSCAL...
    SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
    ZSCTR...
    SSCTR, DSCTR, CSCTR, ZSCTR--Scatter the Elements of a Sparse Vector X in Compressed-Vector Storage Mode into Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode
    ZSWAP...
    SSWAP, DSWAP, CSWAP, and ZSWAP--Interchange the Elements of Two Vectors
    ZSYMM...
    SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
    ZSYR2K...
    SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    ZSYRK...
    SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
    ZTBMV...
    STBMV, DTBMV, CTBMV, and ZTBMV--Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose
    ZTBSV...
    STBSV, DTBSV, CTBSV, and ZTBSV--Triangular Band Equation Solve
    ZTPMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    ZTPSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    ZTRMM...
    STRMM, DTRMM, CTRMM, and ZTRMM--Triangular Matrix-Matrix Product
    ZTRMV...
    STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
    ZTRSM...
    STRSM, DTRSM, CTRSM, and ZTRSM--Solution of Triangular Systems of Equations with Multiple Right-Hand Sides
    ZTRSV...
    STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side
    ZVEA...
    SVEA, DVEA, CVEA, and ZVEA--Add a Vector X to a Vector Y and Store in a Vector Z
    ZVEM...
    SVEM, DVEM, CVEM, and ZVEM--Multiply a Vector X by a Vector Y and Store in a Vector Z
    ZVES...
    SVES, DVES, CVES, and ZVES--Subtract a Vector Y from a Vector X and Store in a Vector Z
    ZWLEV...
    SWLEV, DWLEV, CWLEV, and ZWLEV--Wiener-Levinson Filter Coefficients
    ZYAX...
    SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
    ZZAXPY...
    SZAXPY, DZAXPY, CZAXPY, and ZZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z
    


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