Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Overview of the Linear Algebra Subprograms

This section describes the subprograms in each of the four linear algebra subprogram areas:

Vector-scalar linear algebra subprograms (Table 32)
Sparse vector-scalar linear algebra subprograms (Table 33)
Matrix-vector linear algebra subprograms (Table 34)
Sparse matrix-vector linear algebra subprograms (Table 35)

Notes:

The term subprograms is used to be consistent with the Basic Linear Algebra Subprograms (BLAS), because many of these subprograms correspond to the BLAS.
Some of the linear algebra subprograms were designed in accordance with the Level 1 and Level 2 BLAS de facto standard. If these subprograms do not comply with the standard as approved, IBM will consider updating them to do so. If IBM updates these subprograms, the updates could require modifications of the calling application program.

Vector-Scalar Linear Algebra Subprograms

The vector-scalar linear algebra subprograms include a subset of the standard set of Level 1 BLAS. For details on the BLAS, see reference [79]. The remainder of the vector-scalar linear algebra subprograms are commonly used computations provided for your applications. Both real and complex versions of the subprograms are provided.

Table 32. List of Vector-Scalar Linear Algebra Subprograms

Sparse Vector-Scalar Linear Algebra Subprograms

The sparse vector-scalar linear algebra subprograms operate on sparse vectors using optimized storage techniques; that is, only the nonzero elements of the vector are stored. These subprograms provide similar functions to the vector-scalar subprograms. These subprograms represent a subset of the sparse extensions to the Level 1 BLAS described in reference [29]. Both real and complex versions of the subprograms are provided.

Table 33. List of Sparse Vector-Scalar Linear Algebra Subprograms

Descriptive Name	Short- Precision Subprogram	Long- Precision Subprogram	Page
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	SSCTR CSCTR	DSCTR 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
Gather Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode into a Sparse Vector X in Compressed-Vector Storage Mode	SGTHR CGTHR	DGTHR 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
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	SGTHRZ CGTHRZ	DGTHRZ 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
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	SAXPYI CAXPYI	DAXPYI 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
Dot Product of a Sparse Vector X in Compressed-Vector Storage Mode and a Sparse Vector Y in Full-Vector Storage Mode	SDOTI^& CDOTCI^& CDOTUI^&	DDOTI^& ZDOTCI^& 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
^& This subprogram is invoked as a function in a Fortran program.

Matrix-Vector Linear Algebra Subprograms

The matrix-vector linear algebra subprograms operate on a higher-level data structure--matrix-vector rather than vector-scalar--using optimized algorithms to improve performance. These subprograms represent a subset of the Level 2 BLAS described in references [34] and [35]. Both real and complex versions of the subprograms are provided.

Table 34. List of Matrix-Vector Linear Algebra Subprograms

Descriptive Name	Short- Precision Subprogram	Long- Precision Subprogram	Page
Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose	SGEMV^ø CGEMV^ø SGEMX^§ SGEMTX^§	DGEMV^ø ZGEMV^ø DGEMX^§ DGEMTX^§	SGEMV, DGEMV, CGEMV, ZGEMV, SGEMX, DGEMX, SGEMTX, and DGEMTX--Matrix-Vector Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
Rank-One Update of a General Matrix	SGER^ø CGERU^ø CGERC^ø	DGER^ø ZGERU^ø ZGERC^ø	SGER, DGER, CGERU, ZGERU, CGERC, and ZGERC--Rank-One Update of a General Matrix
Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix	SSPMV^ø CHPMV^ø SSYMV^ø CHEMV^ø SSLMX^§	DSPMV^ø ZHPMV^ø DSYMV^ø ZHEMV^ø DSLMX^§	SSPMV, DSPMV, CHPMV, ZHPMV, SSYMV, DSYMV, CHEMV, ZHEMV, SSLMX, and DSLMX--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Matrix
Rank-One Update of a Real Symmetric or Complex Hermitian Matrix	SSPR^ø CHPR^ø SSYR^ø CHER^ø SSLR1^§	DSPR^ø ZHPR^ø DSYR^ø ZHER^ø DSLR1^§	SSPR, DSPR, CHPR, ZHPR, SSYR, DSYR, CHER, ZHER, SSLR1, and DSLR1 --Rank-One Update of a Real Symmetric or Complex Hermitian Matrix
Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix	SSPR2^ø CHPR2^ø SSYR2^ø CHER2^ø SSLR2^§	DSPR2^ø ZHPR2^ø DSYR2^ø ZHER2^ø DSLR2^§	SSPR2, DSPR2, CHPR2, ZHPR2, SSYR2, DSYR2, CHER2, ZHER2, SSLR2, and DSLR2--Rank-Two Update of a Real Symmetric or Complex Hermitian Matrix
Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose	SGBMV^ø CGBMV^ø	DGBMV^ø ZGBMV^ø	SGBMV, DGBMV, CGBMV, and ZGBMV--Matrix-Vector Product for a General Band Matrix, Its Transpose, or Its Conjugate Transpose
Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix	SSBMV^ø CHBMV^ø	DSBMV^ø ZHBMV^ø	SSBMV, DSBMV, CHBMV, and ZHBMV--Matrix-Vector Product for a Real Symmetric or Complex Hermitian Band Matrix
Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose	STRMV^ø CTRMV^ø STPMV^ø CTPMV^ø	DTRMV^ø ZTRMV^ø DTPMV^ø ZTPMV^ø	STRMV, DTRMV, CTRMV, ZTRMV, STPMV, DTPMV, CTPMV, and ZTPMV--Matrix-Vector Product for a Triangular Matrix, Its Transpose, or Its Conjugate Transpose
Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose	STBMV^ø CTBMV^ø	DTBMV^ø ZTBMV^ø	STBMV, DTBMV, CTBMV, and ZTBMV--Matrix-Vector Product for a Triangular Band Matrix, Its Transpose, or Its Conjugate Transpose
^ø Level 2 BLAS ^§ These subroutines are provided only for migration from earlier releases of ESSL and are not intended for use in new programs.

Sparse Matrix-Vector Linear Algebra Subprograms

The sparse matrix-vector linear algebra subprograms operate on sparse matrices using optimized storage techniques; that is, only the nonzero elements of the vector are stored. These subprograms provide similar functions to the matrix-vector subprograms.

Table 35. List of Sparse Matrix-Vector Linear Algebra Subprograms

Descriptive Name	Long- Precision Subprogram	Page
Matrix-Vector Product for a Sparse Matrix in Compressed-Matrix Storage Mode	DSMMX	DSMMX--Matrix-Vector Product for a Sparse Matrix in Compressed-Matrix Storage Mode
Transpose a Sparse Matrix in Compressed-Matrix Storage Mode	DSMTM	DSMTM--Transpose a Sparse Matrix in Compressed-Matrix Storage Mode
Matrix-Vector Product for a Sparse Matrix or Its Transpose in Compressed-Diagonal Storage Mode	DSDMX	DSDMX--Matrix-Vector Product for a Sparse Matrix or Its Transpose in Compressed-Diagonal Storage Mode

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Descriptive Name	Short- Precision Subprogram	Long- Precision Subprogram	Page
Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude	ISAMAX^&^¤ ICAMAX^&^¤	IDAMAX^&^¤ IZAMAX^&^¤	ISAMAX, IDAMAX, ICAMAX, and IZAMAX--Position of the First or Last Occurrence of the Vector Element Having the Largest Magnitude
Position of the First or Last Occurrence of the Vector Element Having Minimum Absolute Value	ISAMIN^&	IDAMIN^&	ISAMIN and IDAMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Absolute Value
Position of the First or Last Occurrence of the Vector Element Having Maximum Value	ISMAX^&	IDMAX^&	ISMAX and IDMAX--Position of the First or Last Occurrence of the Vector Element Having the Maximum Value
Position of the First or Last Occurrence of the Vector Element Having Minimum Value	ISMIN^&	IDMIN^&	ISMIN and IDMIN--Position of the First or Last Occurrence of the Vector Element Having Minimum Value
Sum of the Magnitudes of the Elements in a Vector	SASUM^&^¤ SCASUM^&^¤	DASUM^&^¤ DZASUM^&^¤	SASUM, DASUM, SCASUM, and DZASUM--Sum of the Magnitudes of the Elements in a Vector
Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y	SAXPY^¤ CAXPY^¤	DAXPY^¤ ZAXPY^¤	SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y
Copy a Vector	SCOPY^¤ CCOPY^¤	DCOPY^¤ ZCOPY^¤	SCOPY, DCOPY, CCOPY, and ZCOPY--Copy a Vector
Dot Product of Two Vectors	SDOT^&^¤ CDOTU^&^¤ CDOTC^&^¤	DDOT^&^¤ ZDOTU^&^¤ ZDOTC^&^¤	SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors
Compute SAXPY or DAXPY N Times	SNAXPY	DNAXPY	SNAXPY and DNAXPY--Compute SAXPY or DAXPY N Times
Compute Special Dot Products N Times	SNDOT	DNDOT	SNDOT and DNDOT--Compute Special Dot Products N Times
Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow	SNRM2^&^¤ SCNRM2^&^¤	DNRM2^&^¤ DZNRM2^&^¤	SNRM2, DNRM2, SCNRM2, and DZNRM2--Euclidean Length of a Vector with Scaling of Input to Avoid Destructive Underflow and Overflow
Euclidean Length of a Vector with No Scaling of Input	SNORM2^& CNORM2^&	DNORM2^& ZNORM2^&	SNORM2, DNORM2, CNORM2, and ZNORM2--Euclidean Length of a Vector with No Scaling of Input
Construct a Givens Plane Rotation	SROTG^¤ CROTG^¤	DROTG^¤ ZROTG^¤	SROTG, DROTG, CROTG, and ZROTG--Construct a Givens Plane Rotation
Apply a Plane Rotation	SROT^¤ CROT^¤ CSROT^¤	DROT^¤ ZROT^¤ ZDROT^¤	SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation
Multiply a Vector X by a Scalar and Store in the Vector X	SSCAL^¤ CSCAL^¤ CSSCAL^¤	DSCAL^¤ ZSCAL^¤ ZDSCAL^¤	SSCAL, DSCAL, CSCAL, ZSCAL, CSSCAL, and ZDSCAL--Multiply a Vector X by a Scalar and Store in the Vector X
Interchange the Elements of Two Vectors	SSWAP^¤ CSWAP^¤	DSWAP^¤ ZSWAP^¤	SSWAP, DSWAP, CSWAP, and ZSWAP--Interchange the Elements of Two Vectors
Add a Vector X to a Vector Y and Store in a Vector Z	SVEA CVEA	DVEA ZVEA	SVEA, DVEA, CVEA, and ZVEA--Add a Vector X to a Vector Y and Store in a Vector Z
Subtract a Vector Y from a Vector X and Store in a Vector Z	SVES CVES	DVES ZVES	SVES, DVES, CVES, and ZVES--Subtract a Vector Y from a Vector X and Store in a Vector Z
Multiply a Vector X by a Vector Y and Store in a Vector Z	SVEM CVEM	DVEM ZVEM	SVEM, DVEM, CVEM, and ZVEM--Multiply a Vector X by a Vector Y and Store in a Vector Z
Multiply a Vector X by a Scalar and Store in a Vector Y	SYAX CYAX CSYAX	DYAX ZYAX ZDYAX	SYAX, DYAX, CYAX, ZYAX, CSYAX, and ZDYAX--Multiply a Vector X by a Scalar and Store in a Vector Y
Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z	SZAXPY CZAXPY	DZAXPY ZZAXPY	SZAXPY, DZAXPY, CZAXPY, and ZZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in a Vector Z
^& This subprogram is invoked as a function in a Fortran program. ^¤ Level 1 BLAS