Basic Matrix/Vector Operations

FNLMath : Basic Matrix/Vector Operations

Routines

Basic Linear Algebra Subprograms (BLAS)

Programming Notes for Level 1 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 first index i such that |xi| = minj |xj| ISAMIN

Find the first 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

Programming Notes for Level 2 and Level 3 BLAS

Matrix-vector multiply, general SGEMV

Matrix-vector multiply, banded SGBMV

Matrix-vector multiply, Hermitian CHEMV

Matrix-vector multiply, packed Hermitian CHPMV

Matrix-vector multiply, Hermitian and banded CHBMV

Matrix-vector multiply, symmetric and real SSYMV

Matrix-vector multiply, packed symmetric, real SSPMV

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

Matrix-vector multiply, packed triangular STPMV

Matrix-vector solve, packed triangular STPSV

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

Hermitian, packed and conjugate transpose CHPR

Rank-two matrix update, Hermitian and conjugate transpose CHER2

Rank-two matrix update, Hermitian, packed and conjugate transpose CHPR2

Rank-one matrix update, symmetric and real SSYR

Rank-one matrix update, packed symmetric and real SSPR

Rank-two matrix update, symmetric and real SSYR2

Rank-two matrix update, packed symmetric and real SSPR2

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 X T X MXTXF

Compute X TY MXTYF

Compute XY T 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 119

1-norm distance DISL1 121

∞-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