If you spot a problem with this page, click here to create a GitHub issue.

Quickly fork, edit online, and submit a pull request for this page. Requires a signed-in GitHub account. This works well for small changes. If you'd like to make larger changes you may want to consider using a local clone.

mir.glas.l1

Level 1

This is a submodule of mir.glas.

The Level 1 GLAS perform vector and vector-vector operations.

Vector-vector operations
rot	apply Givens rotation
axpy	constant times a vector plus a vector
dot	dot product
dotc	dot product, conjugating the first vector

Vector operations
Function Name	Description
nrm2	Euclidean norm
sqnrm2	square of Euclidean norm
asum	sum of absolute values
iamax	index of max abs value
amax	max abs value

All functions except iamax work with multidimensional tensors.

GLAS does not provide swap, scal, and copy functions. This functionality is part of ndslice package. Examples can be found below.

License:

Boost License 1.0.

Authors:

Ilya Yaroshenko

Examples:

SWAP

import std.algorithm.mutation: swap;
import mir.ndslice.allocation: slice;
import mir.algorithm.iteration: each;
import std.typecons: Yes;
auto x = slice!double(4);
auto y = slice!double(4);
x[] = [0, 1, 2, 3];
y[] = [4, 5, 6, 7];
each!(swap)(x, y);
assert(x == [4, 5, 6, 7]);
assert(y == [0, 1, 2, 3]);

Examples:

SCAL

import mir.ndslice.allocation: slice;
import std.typecons: Yes;
auto x = slice!double(4);
x[] = [0, 1, 2, 3];
x[] *= 2.0;
assert(x == [0, 2, 4, 6]);

Examples:

COPY

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
auto y = slice!double(4);
x[] = [0, 1, 2, 3];
y[] = x;
assert(y == [0, 1, 2, 3]);

void rot(C, S, SliceKind kind1, SliceKind kind2, size_t N, Iterator1, Iterator2)(in C c, in S s, Slice!(Iterator1, N, kind1) x, Slice!(Iterator2, N, kind2) y);

Applies a plane rotation, where the c (cos) and s (sin) are scalars. Uses unrolled loops for strides equal to one.

Parameters:

C `c`	cos scalar
S `s`	sin scalar
Slice!(Iterator1, N, kind1) `x`	first n-dimensional tensor
Slice!(Iterator2, N, kind2) `y`	second n-dimensional tensor

BLAS SROT, DROT, CROT, ZROT, CSROT, ZDROTF

Examples:

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
auto y = slice!double(4);
auto a = slice!double(4);
auto b = slice!double(4);
double cos = 3.0 / 5;
double sin = 4.0 / 5;
x[] = [0, 1, 2, 3];
y[] = [4, 5, 6, 7];
foreach (i; 0 .. 4)
{
    a[i] = cos * x[i] + sin * y[i];
    b[i] = cos * y[i] - sin * x[i];
}
rot(cos, sin, x, y);
assert(x == a);
assert(y == b);

void axpy(A, SliceKind kind1, SliceKind kind2, size_t N, Iterator1, Iterator2)(in A a, Slice!(Iterator1, N, kind1) x, Slice!(Iterator2, N, kind2) y);

Constant times a vector plus a vector. Uses unrolled loops for strides equal to one.

Parameters:

A `a`	scale parameter
Slice!(Iterator1, N, kind1) `x`	first n-dimensional tensor
Slice!(Iterator2, N, kind2) `y`	second n-dimensional tensor

BLAS SAXPY, DAXPY, CAXPY, ZAXPY

Examples:

SAXPY, DAXPY

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
auto y = slice!double(4);
x[] = [0, 1, 2, 3];
y[] = [4, 5, 6, 7];
axpy(2.0, x, y);
assert(y == [4, 7, 10, 13]);

Examples:

SAXPY, DAXPY

import mir.ndslice.allocation: slice;

auto a = 3 + 4i;
auto x = slice!cdouble(2);
auto y = slice!cdouble(2);
x[] = [0 + 1i, 2 + 3i];
y[] = [4 + 5i, 6 + 7i];
axpy(a, x, y);
assert(y == [a * (0 + 1i) + (4 + 5i), a * (2 + 3i) + (6 + 7i)]);

F dot(F, SliceKind kind1, SliceKind kind2, size_t N, Iterator1, Iterator2)(Slice!(Iterator1, N, kind1) x, Slice!(Iterator2, N, kind2) y); auto dot(SliceKind kind1, SliceKind kind2, size_t N, Iterator1, Iterator2)(Slice!(Iterator1, N, kind1) x, Slice!(Iterator2, N, kind2) y);

Forms the dot product of two vectors. Uses unrolled loops for strides equal to one.

Returns:

dot product conj(xᐪ) × y

Parameters:

F	type for summation (optional template parameter)
Slice!(Iterator1, N, kind1) `x`	first n-dimensional tensor
Slice!(Iterator2, N, kind2) `y`	second n-dimensional tensor

BLAS SDOT, DDOT, SDSDOT, DSDOT, CDOTC, ZDOTC

Examples:

SDOT, DDOT

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
auto y = slice!double(4);
x[] = [0, 1, 2, 3];
y[] = [4, 5, 6, 7];
assert(dot(x, y) == 5 + 12 + 21);

Examples:

SDOT, DDOT

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
auto y = slice!double(4);
x[] = [0, 1, 2, 3];
y[] = [4, 5, 6, 7];
assert(dot(x, y) == 5 + 12 + 21);

Examples:

SDSDOT, DSDOT

import mir.ndslice.allocation: slice;
auto x = slice!float(4);
auto y = slice!float(4);
x[] = [0, 1, 2, 3];
y[] = [4, 5, 6, 7];
assert(dot!real(x, y) == 5 + 12 + 21); // 80-bit FP for x86 CPUs

Examples:

CDOTU, ZDOTU

import mir.ndslice.allocation: slice;

auto x = slice!cdouble(2);
auto y = slice!cdouble(2);
x[] = [0 + 1i, 2 + 3i];
y[] = [4 + 5i, 6 + 7i];
version(LDC) // DMD Internal error: backend/cgxmm.c 628
assert(dot(x, y) == (0 + 1i) * (4 + 5i) + (2 + 3i) * (6 + 7i));

F dotc(F, SliceKind kind1, SliceKind kind2, size_t N, Iterator1, Iterator2)(Slice!(Iterator1, N, kind1) x, Slice!(Iterator2, N, kind2) y) if (isComplex!(DeepElementType!(typeof(x))) && isComplex!(DeepElementType!(typeof(y)))); auto dotc(SliceKind kind1, SliceKind kind2, size_t N, Iterator1, Iterator2)(Slice!(Iterator1, N, kind1) x, Slice!(Iterator2, N, kind2) y);

Forms the dot product of two complex vectors. Uses unrolled loops for strides equal to one.

Returns:

dot product xᐪ × y

Parameters:

F	type for summation (optional template parameter)
Slice!(Iterator1, N, kind1) `x`	first n-dimensional tensor
Slice!(Iterator2, N, kind2) `y`	second n-dimensional tensor

BLAS CDOTU, ZDOTU

Examples:

CDOTC, ZDOTC

import mir.ndslice.allocation: slice;

auto x = slice!cdouble(2);
auto y = slice!cdouble(2);
x[] = [0 + 1i, 2 + 3i];
y[] = [4 + 5i, 6 + 7i];
version(LDC) // DMD Internal error: backend/cgxmm.c 628
assert(dotc(x, y) == (0 + -1i) * (4 + 5i) + (2 + -3i) * (6 + 7i));

F nrm2(F, SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x); auto nrm2(SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x);

Returns the euclidean norm of a vector. Uses unrolled loops for stride equal to one.

Returns:

euclidean norm sqrt(conj(xᐪ) × x)

Parameters:

F	type for summation (optional template parameter)
Slice!(Iterator, N, kind) `x`	n-dimensional tensor

BLAS SNRM2, DNRM2, SCNRM2, DZNRM2

Examples:

SNRM2, DNRM2

import mir.ndslice.allocation: slice;
import std.math: sqrt, approxEqual;
auto x = slice!double(4);
x[] = [0, 1, 2, 3];
assert(nrm2(x).approxEqual(sqrt(1.0 + 4 + 9)));

Examples:

SCNRM2, DZNRM2

import mir.ndslice.allocation: slice;
import std.math: sqrt, approxEqual;

auto x = slice!cdouble(2);
x[] = [0 + 1i, 2 + 3i];

assert(nrm2(x).approxEqual(sqrt(1.0 + 4 + 9)));

F sqnrm2(F, SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x); auto sqnrm2(SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x);

Forms the square of the euclidean norm. Uses unrolled loops for stride equal to one.

Returns:

conj(xᐪ) × x

Parameters:

F	type for summation (optional template parameter)
Slice!(Iterator, N, kind) `x`	n-dimensional tensor

Examples:

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
x[] = [0, 1, 2, 3];
assert(sqnrm2(x) == 1.0 + 4 + 9);

Examples:

import mir.ndslice.allocation: slice;

auto x = slice!cdouble(2);
x[] = [0 + 1i, 2 + 3i];

assert(sqnrm2(x) == 1.0 + 4 + 9);

F asum(F, SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x); auto asum(SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x);

Takes the sum of the |Re(.)| + |Im(.)|'s of a vector and returns a single precision result.

Returns:

sum of the |Re(.)| + |Im(.)|'s

Parameters:

F	type for summation (optional template parameter)
Slice!(Iterator, N, kind) `x`	n-dimensional tensor

BLAS SASUM, DASUM, SCASUM, DZASUM

Examples:

SASUM, DASUM

import mir.ndslice.allocation: slice;
auto x = slice!double(4);
x[] = [0, -1, -2, 3];
assert(asum(x) == 1 + 2 + 3);

Examples:

SCASUM, DZASUM

import mir.ndslice.allocation: slice;

auto x = slice!cdouble(2);
x[] = [0 - 1i, -2 + 3i];

assert(asum(x) == 1 + 2 + 3);

sizediff_t iamax(Iterator, SliceKind kind)(Slice!(Iterator, 1, kind) x);

Finds the index of the first element having maximum |Re(.)| + |Im(.)|.

Return index of the first element having maximum |Re(.)| + |Im(.)|

Parameters:

Slice!(Iterator, 1, kind) x 1-dimensional tensor

BLAS ISAMAX, IDAMAX, ICAMAX, IZAMAX

Examples:

ISAMAX, IDAMAX

import mir.ndslice.allocation: slice;
auto x = slice!double(6);
//     0  1   2   3   4  5
x[] = [0, -1, -2, -3, 3, 2];
assert(iamax(x) == 3);
// -1 for empty vectors
assert(iamax(x[0 .. 0]) == -1);

Examples:

ICAMAX, IZAMAX

import mir.ndslice.allocation: slice;

auto x = slice!cdouble(4);
//        0          1          2         3
x[] = [0 + -1i, -2 + 3i, 2 + 3i, 2 + 2i];

assert(iamax(x) == 1);
// -1 for empty vectors
assert(iamax(x[$ .. $]) == -1);

auto amax(SliceKind kind, size_t N, Iterator)(Slice!(Iterator, N, kind) x);

Takes the sum of the |Re(.)| + |Im(.)|'s of a vector and returns a single precision result.

Returns:

sum of the |Re(.)| + |Im(.)|'s

Parameters:

Slice!(Iterator, N, kind) x n-dimensional tensor

BLAS SASUM, DASUM, SCASUM, DZASUM

Examples:

import mir.ndslice.allocation: slice;
auto x = slice!double(6);
x[] = [0, -1, -2, -7, 6, 2];
assert(amax(x) == 7);
// 0 for empty vectors
assert(amax(x[0 .. 0]) == 0);

Examples:

import mir.ndslice.allocation: slice;

auto x = slice!cdouble(4);
x[] = [0 + -1i, -7 + 3i, 2 + 3i, 2 + 2i];

assert(amax(x) == 10);
// 0 for empty vectors
assert(amax(x[$ .. $]) == 0);

Library Reference

mir.glas.l1

Level 1

Vector-vector operations

Vector operations