blas

README

Sparse matrix formats

Implementation of sparse BLAS (Basic Linear Algebra Subprograms) routines in Go for sparse matrix arithmetic. See http://www.netlib.org/blas/blast-forum/chapter3.pdf for more details. Includes optimised assembler implementations of key kernel operations (vector dot product and Axpy operations).

Indicative Benchmarks

Operation	Pure Go	Assembler
Dusdot (with increment/stride)	1340 ns/op	978 ns/op
Dusdot (unitary)	1215 ns/op	662 ns/op
Dusaxpy (with increment/stride)	1944 ns/op	1769 ns/op
Dusaxpy (unitary)	1091 ns/op	979 ns/op

Documentation

Overview

Package blas provides implementations of sparse BLAS (Basic Linear Algebra Subprograms) routines for sparse matrix arithmetic and solving sparse linear systems.

See http://www.netlib.org/blas/blast-forum/chapter3.pdf for further information.

Index

• func Dusaxpy(alpha float64, x []float64, indx []int, y []float64, incy int)
• func Dusdot(x []float64, indx []int, y []float64, incy int) (dot float64)
• func Dusga(y []float64, incy int, x []float64, indx []int)
• func Dusgz(y []float64, incy int, x []float64, indx []int)
• func Dusmm(transA bool, k int, alpha float64, a *SparseMatrix, b []float64, ldb int, ...)
• func Dusmv(transA bool, alpha float64, a *SparseMatrix, x []float64, incx int, ...)
• func Dussc(x []float64, y []float64, incy int, indx []int)
• type SparseMatrix
  • func (m *SparseMatrix) At(i, j int) float64
  • func (m *SparseMatrix) Cull(epsilon float64) *SparseMatrix
  • func (m *SparseMatrix) Set(i, j int, v float64)

Functions

func Dusaxpy

func Dusaxpy(alpha float64, x []float64, indx []int, y []float64, incy int)

Dusaxpy (Sparse update (y <- alpha * x + y)) scales the sparse vector x by alpha and adds the result to the dense vector y. indx is used as the index values to gather and incy as the stride for y.

func Dusdot

func Dusdot(x []float64, indx []int, y []float64, incy int) (dot float64)

Dusdot (Sparse dot product (r <- x^T * y)) calculates the dot product of sparse vector x and dense vector y. indx is used as the index values to gather and incy as the stride for y.

func Dusga

func Dusga(y []float64, incy int, x []float64, indx []int)

Dusga (Sparse gather (x <- y|x)) gathers entries from the dense vector y into the sparse vector x using indx as the index values to gather and incy as the stride for y.

func Dusgz

func Dusgz(y []float64, incy int, x []float64, indx []int)

Dusgz (Sparse gather and zero (x <- y|x, y|x <- 0)) gathers entries from the dense vector y into the sparse vector x (as Usga()) and then sets the corresponding elements of y (y[indx[i]]) to 0. indx is used as the index values to gather and incy as the stride for y.

func Dusmm

func Dusmm(transA bool, k int, alpha float64, a *SparseMatrix, b []float64, ldb int, c []float64, ldc int)

Dusmm (Sparse matrix multiply (C <- alpha * A * B + C Or C <- alpha * A^T * B + C)) multiplies a dense matrix B by a sparse matrix A (or its transpose), and adds it to a dense matrix operand C. C is modified to hold the result of operation. k Represents the number of columns in matrices B and C and ldb and ldc are the spans to be used for indexing into matrices B and C respectively.

func Dusmv

func Dusmv(transA bool, alpha float64, a *SparseMatrix, x []float64, incx int, y []float64, incy int)

Dusmv (sparse matrix / vector multiply (y <- alpha * A * x + y Or y <- alpha * A^T * x + y)) multiplies a dense vector x by sparse matrix a (or its transpose), and adds it to the dense vector y. transA is a boolean indicating whether to transpose (true) a. alpha is used to scale a and incx and incy represent the span to be used for indexing into vectors x and y respectively.

func Dussc

func Dussc(x []float64, y []float64, incy int, indx []int)

Dussc (Sparse scatter (y|x <- x)) scatters enries into the dense vector y from the sparse vector x using indx as the index values to scatter to and incy as the stride for y. The function will panic if x and idx are different lengths.

Types

type SparseMatrix

type SparseMatrix struct {
	I, J   int
	Indptr []int
	Ind    []int
	Data   []float64
}

SparseMatrix represents the common structure for representing compressed sparse matrix formats e.g. CSR (Compressed Sparse Row) or CSC (Compressed Sparse Column)

func (*SparseMatrix) At

func (m *SparseMatrix) At(i, j int) float64

At returns the element of the matrix located at coordinate i, j.

func (*SparseMatrix) Cull

func (m *SparseMatrix) Cull(epsilon float64) *SparseMatrix

Cull returns a new SparseMatrix with all entries within epsilon of 0 removed.

func (*SparseMatrix) Set

func (m *SparseMatrix) Set(i, j int, v float64)

Set is a generic method to set a matrix element. Note: setting a non-zero element to zero does not remove the element from the sparcity pattern but will actually store a zero value.