Basic Matrix/Vector Operations
Routines
9.1 Basic Linear Algebra Subprograms (BLAS)
Programming Notes for Level 1 BLAS
Set a vector to a constant value,
xi ← a SSETCopy a vector,
yi ← xi SCOPYScale a vector by a constant,
xi ← axi SSCALSet a vector to a constant multiple of a vector,
yi ← axi SVCALAdd a constant to a vector,
xi ←xi +
a SADDSubtract a vector from a constant,
xi ← a‑ xi SSUBAdd a multiple of one vector to another,
yi ← axi +
yi SAXPYSwap two vectors,
yi↔ xi SSWAPCompute extended precision
xTy or
xHy DSDOTCompute extended precision
a +
xTy or
a +
xHy SDSDOTCompute ACC +
b +
xTy with extended precision accumulator
SDDOTIFind the index
i such that
xi = min
j xj ISMINFind the index
i such that
xi= max
j xj ISMAXFind the first index
i such that |
xi| = min
j |
xj|
ISAMINFind the first index
i such that |
xi| = max
j |
xj|
ISAMAXConstruct a Givens rotation
SROTGApply a Givens rotation
SROTConstruct a modified Givens rotation
SROTMGApply a modified Givens rotation
SROTMProgramming Notes for Level 2 and Level 3 BLAS
Matrix-vector multiply, general
SGEMVMatrix-vector multiply, banded
SGBMVMatrix-vector multiply, Hermitian
CHEMVMatrix-vector multiply, packed Hermitian
CHPMVMatrix-vector multiply, Hermitian and banded
CHBMVMatrix-vector multiply, symmetric and real
SSYMVMatrix-vector multiply, packed symmetric, real
SSPMVMatrix-vector multiply, symmetric and banded
SSBMVMatrix-vector multiply, triangular
STRMVMatrix-vector multiply, triangular and banded
STBMVMatrix-vector solve, triangular
STRSVMatrix-vector solve, triangular and banded
STBSVMatrix-vector multiply, packed triangular
STPMVMatrix-vector solve, packed triangular
STPSVRank-one matrix update, general and real
SGERRank-one matrix update, general, complex,and transpose
CGERURank-one matrix update, general, complex, and conjugate transpose
CGERCRank-one matrix update, Hermitian and conjugate transpose
CHERHermitian, packed and conjugate transpose
CHPRRank-two matrix update, Hermitian and conjugate transpose
CHER2Rank-two matrix update, Hermitian, packed and conjugate transpose
CHPR2Rank-one matrix update, symmetric and real
SSYRRank-one matrix update, packed symmetric and real
SSPRRank-two matrix update, symmetric and real
SSYR2Rank-two matrix update, packed symmetric and real
SSPR2Matrix-matrix multiply, general
SGEMMMatrix-matrix multiply, symmetric
SSYMMMatrix-matrix multiply, Hermitian
CHEMMRank-
k update, symmetric
SSYRKRank-
k update, Hermitian
CHERKRank-2
k update, symmetric
SSYR2KRank-2
k update, Hermitian
CHER2KMatrix-matrix multiply, triangular
STRMMMatrix-matrix solve, triangular
STRSM9.2 Other Matrix/Vector Operations
9.2.1 Matrix Copy
9.2.2 Matrix Conversion
Real general to real band
CRGRBReal band to real general
CRBRGComplex general to complex band
CCGCBComplex band to complex general
CCBCGReal general to complex general
CRGCGReal rectangular to complex rectangular
CRRCRReal band to complex band
CRBCBReal symmetric to real general
CSFRGComplex Hermitian to complex general
CHFCGReal symmetric band to real band
CSBRBComplex Hermitian band to complex band
CHBCBReal rectangular matrix to its transpose
TRNRR9.2.3 Matrix Multiplication
Multiply two real rectangular matrices
MRRRRMultiply two complex rectangular matrices
MCRCRCompute matrix Hadamard product
HRRRRCompute the bilinear form
xTAy BLINFCompute the matrix polynomial
p(
A)
POLRG9.2.4 Matrix-Vector Multiplication
Real rectangular matrix times a real vector
MURRVReal band matrix times a real vector
MURBVComplex rectangular matrix times a complex vector
MUCRVComplex band matrix times a complex vector
MUCBV9.2.5 Matrix Addition
Real band matrix plus a real band matrix
ARBRBComplex band matrix plus a complex band matrix
ACBCB9.2.6 Matrix Norm
∞-norm of a real rectangular matrix
NRIRR 1-norm of a real rectangular matrix
NR1RRFrobenius norm of a real rectangular matrix
NR2RR1-norm of a real band matrix
NR1RB1-norm of a complex band matrix
NR1CB9.2.7 Distance Between Two Points
Euclidean distance
DISL2 119
1-norm distance
DISL1 121
9.2.8 Vector Convolutions
Convolution of real vectors
VCONRConvolution of complex vectors
VCONC9.3 Extended Precision Arithmetic
Initialize a real accumulator,
ACC ←
a DQINIStore a real accumulator,
a ←
ACC DQSTOAdd to a real accumulator,
ACC ←
ACC +
a DQADDAdd a product to a real accumulator,
ACC ← ACC +
ab DQMULInitialize a complex accumulator,
ACC ←
a ZQINIStore a complex accumulator,
a ←
ACC ZQSTOAdd to a complex accumulator,
ACC ←
ACC +
a ZQADDAdd a product to a complex accumulator,
ACC ←
ACC +
ab ZQMULPublished date: 03/19/2020
Last modified date: 03/19/2020