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mir.sparse.blas.gemv

License:

Boost License 1.0.

Authors:

Ilya Yaroshenko

void gemv(CR, CL, SliceKind kind1, T1, I1, J1, SliceKind kind2, Iterator2, SliceKind kind3, Iterator3)(in CR alpha, Slice!(ChopIterator!(J1*, Series!(I1*, T1*)), 1, kind1) a, Slice!(Iterator2, 1, kind2) x, in CL beta, Slice!(Iterator3, 1, kind3) y);

General matrix-vector multiplication.

Parameters:

CR `alpha`	scalar
Slice!(ChopIterator!(J1, Series!(I1, T1*)), 1, kind1) `a`	sparse matrix (CSR format)
Slice!(Iterator2, 1, kind2) `x`	dense vector
CL `beta`	scalar
Slice!(Iterator3, 1, kind3) `y`	dense vector

Returns:

y = alpha * a × x + beta * y if beta does not equal null and y = alpha * a × x otherwise.

Examples:

import mir.ndslice;
import mir.sparse;

auto slice = sparse!double(3, 5);
slice[] =
    [[ 0.0, 2.0,  3.0, 0.0, 0.0],
     [ 6.0, 0.0, 30.0, 8.0, 0.0],
     [ 6.0, 0.0, 30.0, 8.0, 0.0]];
auto alpha = 3.0;
auto a = slice.compress;
auto x =  [ 17.0, 19, 31, 3, 5].sliced;
auto beta = 2.0;
auto y = [1.0, 2, 3].sliced;
auto t = [131.0, 1056.0, 1056.0].sliced;
t[] *= alpha;
import mir.glas.l1: axpy;
axpy(beta, y, t);
gemv(alpha, a, x, beta, y);
assert(t == y);

void gemtv(CR, CL, SliceKind kind1, T1, I1, J1, SliceKind kind2, Iterator2, SliceKind kind3, Iterator3)(in CR alpha, Slice!(ChopIterator!(J1*, Series!(I1*, T1*)), 1, kind1) a, Slice!(Iterator2, 1, kind2) x, in CL beta, Slice!(Iterator3, 1, kind3) y);

General matrix-vector multiplication with transposition.

Parameters:

CR `alpha`	scalar
Slice!(ChopIterator!(J1, Series!(I1, T1*)), 1, kind1) `a`	sparse matrix (CSR format)
Slice!(Iterator2, 1, kind2) `x`	dense vector
CL `beta`	scalar
Slice!(Iterator3, 1, kind3) `y`	dense vector

Returns:

y = alpha * aᵀ × x + beta * y if beta does not equal null and y = alpha * aᵀ × x otherwise.

Examples:

import mir.ndslice;
import mir.sparse;

auto slice = sparse!double(5, 3);
slice[] =
    [[0.0,  6.0,  6.0],
     [2.0,  0.0,  0.0],
     [3.0, 30.0, 30.0],
     [0.0,  8.0,  8.0],
     [0.0,  0.0,  0.0]];
auto alpha = 3.0;
auto a = slice.compress;
auto x =  [ 17.0, 19, 31, 3, 5].sliced;
auto beta = 2.0;
auto y = [1.0, 2, 3].sliced;
auto t = [131.0, 1056.0, 1056.0].sliced;
t[] *= alpha;
import mir.glas.l1: axpy;
axpy(beta, y, t);
gemtv(alpha, a, x, beta, y);
assert(t == y);

void gemv(CR, CL, SliceKind kind1, Iterator1, T2, I2, SliceKind kind3, Iterator3)(in CR alpha, Slice!(Iterator1, 2, kind1) a, Series!(I2*, T2*) x, in CL beta, Slice!(Iterator3, 1, kind3) y);

General matrix-vector multiplication for sparse vectors.

Parameters:

CR `alpha`	scalar
Slice!(Iterator1, 2, kind1) `a`	dense matrix
Series!(I2, T2) `x`	sparse vector
CL `beta`	scalar
Slice!(Iterator3, 1, kind3) `y`	dense vector

Returns:

y = alpha * a × x + beta * y if beta does not equal null and y = alpha * a × x otherwise.

Examples:

import mir.ndslice;
import mir.sparse;

auto slice = sparse!double(3, 5);
slice[] =
    [[ 0.0, 2.0,  3.0, 0.0, 0.0],
     [ 6.0, 0.0, 30.0, 8.0, 0.0],
     [ 6.0, 0.0, 30.0, 8.0, 0.0]];
auto alpha = 3.0;
auto a = slice.compress;
auto x =  [ 17.0, 19, 31, 3, 5].sliced;
auto beta = 2.0;
auto y = [1.0, 2, 3].sliced;
auto t = [131.0, 1056.0, 1056.0].sliced;
t[] *= alpha;
import mir.glas.l1: axpy;
axpy(beta, y, t);
gemv(alpha, a, x, beta, y);
assert(t == y);

void selectiveGemv(string op = "", SliceKind kind1, SliceKind kind2, T, T3, I3)(Slice!(T*, 2, kind1) a, Slice!(T*, 1, kind2) x, Series!(I3*, T3*) y);

Selective general matrix-vector multiplication with a selector sparse vector.

Parameters:

Slice!(T*, 2, kind1) `a`	dense matrix
Slice!(T*, 1, kind2) `x`	dense vector
Series!(I3, T3) `y`	sparse vector (compressed)

Returns:

y[available indexes] <op>= (alpha * a × x)[available indexes].

Library Reference

mir.sparse.blas.gemv