FNLMath : Basic Matrix/Vector Operations
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
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, ACCa DQINI
Store a real accumulator, aACC DQSTO
Add to a real accumulator, ACCACC + a DQADD
Add a product to a real accumulator, ACC ACC + ab DQMUL
Initialize a complex accumulator, ACCa ZQINI
Store a complex accumulator, aACC ZQSTO
Add to a complex accumulator, ACCACC + a ZQADD
Add a product to a complex accumulator, ACCACC + ab ZQMUL