pyblas 0.0.10

Description:

pyblas 0.0.10

🔢 PyBLAS
PyBLAS is a python port of the netlib reference BLAS implementation.
Usage
pip install numpy pyblas

import numpy as np
from pyblas.level1 import dswap

x = np.array([1.2, 2.3, 3.4], dtype=np.double) # A double-precision vector x
y = np.array([5.6, 7.8, 9.0], dtype=np.double) # A double precision vector y
N = len(x) # The length of the vectors x and y
incx = 1 # The index spacing of the vector x
incy = 1 # The index spacing of the vector y

# Swap the values of the vectors x and y
dswap(N, x, incx, y, incy)
print(x, y)

For more details on how to use the PyBLAS library, please consult our docs
What is BLAS
The Basic Linear Algebra Subprograms (BLAS) are a collection of functions which form the basis of many modern numerical computing packages, including numpy, scipy, and matlab.
They provide functions for performing basic calculations on vectors and matrices, which form the basis for more complex calculations such as solving systems of linear equations.
Who is this for?

Maths and computer science students who are learning about linear algebra and want to see how to implement simple operations.
Algorithm developers who want to prototype their calculations in a high level language with the same APIs they will use in C or Fortran.
Data scientists who want to better understand what is going on under the hood of the algorithms they use.
Educators who want an easy to use BLAS implementation when teaching numerical computing courses.

Performance
Optimal performance is not a goal of the PyBLAS project.
The project aim is to have a simple and readable implementation of the BLAS standards.
As such, we often forego optimization opporunities in favour of simplicity.
The project matches overall algorithmic complexity with the reference implementation for all functions.
Accuracy
The project aims to match the numerical accuracy of the reference BLAS implementation.
A future goal is to have benchmarks which can be run against the system BLAS libraries to verify the numerical accuract of the functions
Level 1



single (s)
double (d)
single complex (c)
double complex (z)





scopy
dcopy
ccopy
zcopy
y := x


sswap
dswap
cswap
zswap
x, y := y


sscal
dscal
cscal (csscal)
zscal (zdscal)
x := a*x


saxpy
daxpy
caxpy
zaxpy
y := a*x + y




scabs1
dcabs1
`=>


sasum
dasum


`=> sum(




scasum
dzasum
`=> sum(


sdot (sdsdot, dsdot)
ddot
cdotu
zdotu
=> <x, y>




cdotc
zdotc
=> <x^H, y>


snrm2
dnrm2


=> sqrt(<x, x>)




scnrm2
dznrm2
=> sqrt(<x^H, x>)


srot
drot
csrot
zdrot
[x_i, y_i] := [c s; -s c] * [x_i, y_i]


srotg
drotg
crotg
zrotg
c := a/r, s:= b/r, a :=r, b := "z"


srotm
drotm


[x_i, y_i] := [h_1 h_2; h_3, h_4] * [x_i, y_i]


srotmg
drotmg






Level 2



single (s)
double (d)
single complex (c)
double complex (z)





ssyr
dsyr


A := a*x*x^T + A (sym)




cher
zher
A := a*x*x^H + A (her)


sspr
dspr


A := a*x*x^T + A (sym-packaged)




chpr
zhpr
A := a*x*x^H + A (her-packaged)


sger
dger
cgeru
zgeru
A := a*x*y^T + A




cgerc
zgerc
A := a*x*y^H + A


ssyr2
dsyr2


A := a*x*y^T + a*y*x^T + A (sym)




cher2
zher2
A := a*x*y^H + a^+*y*x^H + A (her)


sspr2
dspr2


A := a*x*y^T + a*y*x^T + A (sym-packed)




chpr2
zhpr2
A := a*x*y^H + a*y*x^H + A (her-packed)



| | | |
| strsv | dtrsv | ctrsv | ztrsv | x := A^-1*b or x := A^[TH]^-1*b (tri) |
| stbsv | dtbsv | ctbsv | ztbsv | x := A^-1*b or x := A^[TH]^-1*b (band) |
| stpsv | dtpsv | ctpsv | ztpsv | x := A^-1*b or x := A^[TH]^-1*b (tri-packed) |
| | | |
| stpmv | dtpmv | ctpmv | ztpmv | x := A^[1TH]*x (sym-packed) |
| stbmv | dtbmv | ctbmv | ztbmv | x := A^[1TH]*x (tri-band) |
| strmv | dtrmv | ctrmv | ztrmv | x := A^[1TH]*x (tri) |
| sgemv | dgemv | cgemv | zgemv | y := a*A^[1TH]*x + b*y |
| | | chemv | zhemv | y := a*A*x + b*y (herm) |
| sgbmv | dgbmv | cgbmv | zgbmv | y := a*A^[1TH]*x + b*y (band) |
| | | chbmv | zhbmv | y := a*A*x + b*y (band-herm) |
| ssymv | dsymv | | y := a*A*x + b*y (sym) |
| sspmv | dspmv | | y := a*A*x + b*y (sym-packed) |
| | | chpmv | zhpmv | y := a*A*x + b*y (her-packed) |
| ssbmv | dsbmv | | | y := a*A*x + b*y (sym-band) |
| isamax | idamax | | | | => argmax(|x_i|) |
| | | icamax |izamax | => argmax(|Re(x_i)| + |Im(x_i)|) |
Level 3