Basic Linear Algebra Subprograms (BLAS)

Set a vector to a constant value, xi ← a..................................................................... SSET

Copy a vector, yi ← xi........................................................................................... SCOPY

Scale a vector by a constant, xi ← axi.................................................................... SSCAL

Set a vector to a constant multiple of a vector, yi ← axi............................................ SVCAL

Add a constant to a vector, xi ←xi + a...................................................................... SADD

Subtract a vector from a constant, xi ← a - xi............................................................ SSUB

Add a multiple of one vector to another, yi ← axi + yi................................................. SAXPY

Swap two vectors, yi↔ xi..................................................................................... SSWAP

Compute xTy or xHy................................................................................................. SDOT

Compute extended precision xTy or xHy................................................................... DSDOT

Compute extended precision a + xTy or a + xHy..................................................... SDSDOT

Compute ACC + b + xTy
with extended precision accumulator..................................................................... SDDOTI

Compute zi ← xiyi............................................................................................... SHPROD

Compute Σ xiyizi....................................................................................................... SXYZ

Compute Σ xi......................................................................................................... SSUM

Compute Σ |xi|...................................................................................................... SASUM

Compute ||x||2....................................................................................................... SNRM2

Compute ∏ xi.................................................................................................... SPRDCT

Find the index i such that xi = minj xj......................................................................... ISMIN

Find the index i such that xi= maxj xj........................................................................ ISMAX

Find the index i such that |xi| = minj |xj|.................................................................... ISAMIN

Find the index i such that |xi| = maxj |xj|.................................................................. ISAMAX

Construct a Givens rotation................................................................................... SROTG

Apply a Givens rotation........................................................................................... SROT

Construct a modified Givens rotation................................................................... SROTMG

Apply a modified Givens rotation........................................................................... SROTM

Matrix-vector multiply, general.............................................................................. SGEMV

Matrix-vector multiply, banded.............................................................................. SGBMV

Matrix-vector multiply, Hermitian........................................................................... CHEMV

Matrix-vector multiply, Hermitian and banded......................................................... CHBMV

Matrix-vector multiply, symmetric and real............................................................. SSYMV

Matrix-vector multiply, symmetric and banded........................................................ SSBMV

Matrix-vector multiply, triangular............................................................................ STRMV

Matrix-vector multiply, triangular and banded.......................................................... STBMV

Matrix-vector solve, triangular................................................................................ STRSV

Matrix-vector solve, triangular and banded............................................................... STBSV

Rank-one matrix update, general and real................................................................ SGER

Rank-one matrix update, general, complex,
and transpose..................................................................................................... CGERU

Rank-one matrix update, general, complex,
and conjugate transpose...................................................................................... CGERC

Rank-one matrix update,
Hermitian and conjugate transpose.......................................................................... CHER

Rank-two matrix update,
Hermitian and conjugate transpose........................................................................ CHER2

Rank-one matrix update, symmetric and real............................................................ SSYR

Rank-two matrix update, symmetric and real.......................................................... SSYR2

Matrix-matrix multiply, general............................................................................. SGEMM

Matrix-matrix multiply, symmetric........................................................................ SSYMM

Matrix-matrix multiply, Hermitian.......................................................................... CHEMM

Rank-k update, symmetric.................................................................................... SSYRK

Rank-k update, Hermitian..................................................................................... CHERK

Rank-2k update, symmetric................................................................................ SSYR2K

Rank-2k update, Hermitian.................................................................................. CHER2K

Matrix-matrix multiply, triangular........................................................................... STRMM

Matrix-matrix solve, triangular............................................................................... STRSM

Other Matrix/Vector Operations

Matrix Copy

Real general....................................................................................................... CRGRG

Complex general................................................................................................. CCGCG

Real band........................................................................................................... CRBRB

Complex band..................................................................................................... CCBCB

Matrix Conversion

Real general to real band...................................................................................... CRGRB

Real band to real general...................................................................................... CRBRG

Complex general to complex band........................................................................ CCGCB

Complex band to complex general........................................................................ CCBCG

Real general to complex general........................................................................... CRGCG

Real rectangular to complex rectangular................................................................ CRRCR

Real band to complex band.................................................................................. CRBCB

Real symmetric to real general.............................................................................. CSFRG

Complex Hermitian to complex general.................................................................. CHFCG

Real symmetric band to real band......................................................................... CSBRB

Complex Hermitian band to complex band............................................................. CHBCB

Real rectangular matrix to its transpose................................................................. TRNRR

Matrix Multiplication

Compute XT X....................................................................................................... MXTXF

Compute XT Y...................................................................................................... MXTYF

Compute XYT........................................................................................................ MXYTF

Multiply two real rectangular matrices................................................................... MRRRR

Multiply two complex rectangular matrices............................................................ MCRCR

Compute matrix Hadamard product....................................................................... HRRRR

Compute the bilinear form xTAy................................................................................ BLINF

Compute the matrix polynomial p(A)...................................................................... POLRG

Matrix-Vector Multiplication

Real rectangular matrix times a real vector............................................................ MURRV

Real band matrix times a real vector..................................................................... MURBV

Complex rectangular matrix times a complex vector............................................... MUCRV

Complex band matrix times a complex vector........................................................ MUCBV

Matrix Addition

Real band matrix plus a real band matrix............................................................... ARBRB

Complex band matrix plus a complex band matrix.................................................. ACBCB

Matrix Norm

∞-norm of a real rectangular matrix......................................................................... NRIRR

1-norm of a real rectangular matrix......................................................................... NR1RR

Frobenius norm of a real rectangular matrix............................................................ NR2RR

1-norm of a real band matrix.................................................................................. NR1RB

1-norm of a complex band matrix........................................................................... NR1CB

Distance Between Two Points

Euclidean distance................................................................................................. DISL2

1-norm distance..................................................................................................... DISL1

∞-norm distance..................................................................................................... DISLI

Vector Convolutions

Convolution of real vectors.................................................................................... VCONR

Convolution of complex vectors............................................................................. VCONC

Extended Precision Arithmetic

Initialize a real accumulator, ACC ← a....................................................................... DQINI

Store a real accumulator, a ← ACC........................................................................ DQSTO

Add to a real accumulator, ACC ← ACC + a............................................................. DQADD

Add a product to a real accumulator, ACC ← ACC + ab.............................................. DQMUL

Initialize a complex accumulator, ACC ← a................................................................ ZQINI

Store a complex accumulator, a ← ACC.................................................................. ZQSTO

Add to a complex accumulator, ACC ←ACC + a....................................................... ZQADD

Add a product to a complex accumulator,
ACC ← ACC + ab................................................................................................... ZQMUL

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