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julia> conv(u, v)
2×3 Matrix{ComplexF64}:
-5.0+0.0im -7.0+0.0im -9.0+0.0im
-5.0+0.0im -7.0+0.0im -9.0+0.0im</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/convolutions.jl#L5-L59">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.ccorr" href="#FourierTools.ccorr"><code>FourierTools.ccorr</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">ccorr(u, v[, dims]; centered=false)</code></pre><p>Calculates the cross-correlation between <code>u</code> and <code>v</code> along <code>dims</code>. <code>centered=true</code> moves the output of the cross-correlation to the Fourier center.</p><p>If <code>u</code> and <code>v</code> are both a real valued array we use <code>rfft</code> and hence the output is real as well. If either <code>u</code> or <code>v</code> is complex we use <code>fft</code> and output is hence complex.</p><p>Per default the correlation is performed along <code>min(ndims(u), ndims(v))</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; ccorr([1,1,0,0], [1,1,0,0], centered=true)
-5.0+0.0im -7.0+0.0im -9.0+0.0im</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/convolutions.jl#L5-L59">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.ccorr" href="#FourierTools.ccorr"><code>FourierTools.ccorr</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">ccorr(u, v[, dims]; centered=false)</code></pre><p>Calculates the cross-correlation between <code>u</code> and <code>v</code> along <code>dims</code>. <code>centered=true</code> moves the output of the cross-correlation to the Fourier center.</p><p>If <code>u</code> and <code>v</code> are both a real valued array we use <code>rfft</code> and hence the output is real as well. If either <code>u</code> or <code>v</code> is complex we use <code>fft</code> and output is hence complex.</p><p>Per default the correlation is performed along <code>min(ndims(u), ndims(v))</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; ccorr([1,1,0,0], [1,1,0,0], centered=true)
4-element Vector{Float64}:
0.0
1.0
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0.0 + 0.0im
1.0 + 0.0im
0.0 + 0.0im
0.0 + 0.0im</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/correlations.jl#L3-L44">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.conv_psf" href="#FourierTools.conv_psf"><code>FourierTools.conv_psf</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">conv_psf(u, psf[, dims])</code></pre><p><code>conv_psf</code> is a shorthand for <code>conv(u,ifftshift(psf))</code>. For examples see <code>conv</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/convolutions.jl#L68-L72">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv" href="#FourierTools.plan_conv"><code>FourierTools.plan_conv</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv(u, v [, dims]; kwargs...)</code></pre><p>Pre-plan an optimized convolution for arrays shaped like <code>u</code> and <code>v</code> (based on pre-plan FFT) along the given dimenions <code>dims</code>. <code>dims = 1:ndims(u)</code> per default. The 0 frequency of <code>u</code> must be located at the first entry.</p><p>We return two arguments: The first one is <code>v_ft</code> (obtained by <code>fft(v)</code> or <code>rfft(v)</code>). The second return is the convolution function <code>pconv</code>. <code>pconv</code> itself has two arguments. <code>pconv(u, v_ft=v_ft)</code> where <code>u</code> is the object and <code>v_ft</code> the v_ft. This function achieves faster convolution than <code>conv(u, u)</code>. Depending whether <code>u</code> is real or complex we do <code>fft</code>s or <code>rfft</code>s Additionally, it is possible to provide <code>flags=FFTW.MEASURE</code> as <code>kwargs</code> to change the planning of the FFT.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; u = [1 2 3 4 5]
0.0 + 0.0im</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/correlations.jl#L3-L44">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.conv_psf" href="#FourierTools.conv_psf"><code>FourierTools.conv_psf</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">conv_psf(u, psf[, dims])</code></pre><p><code>conv_psf</code> is a shorthand for <code>conv(u,ifftshift(psf))</code>. For examples see <code>conv</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/convolutions.jl#L68-L72">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv" href="#FourierTools.plan_conv"><code>FourierTools.plan_conv</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv(u, v [, dims]; kwargs...)</code></pre><p>Pre-plan an optimized convolution for arrays shaped like <code>u</code> and <code>v</code> (based on pre-plan FFT) along the given dimenions <code>dims</code>. <code>dims = 1:ndims(u)</code> per default. The 0 frequency of <code>u</code> must be located at the first entry.</p><p>We return two arguments: The first one is <code>v_ft</code> (obtained by <code>fft(v)</code> or <code>rfft(v)</code>). The second return is the convolution function <code>pconv</code>. <code>pconv</code> itself has two arguments. <code>pconv(u, v_ft=v_ft)</code> where <code>u</code> is the object and <code>v_ft</code> the v_ft. This function achieves faster convolution than <code>conv(u, u)</code>. Depending whether <code>u</code> is real or complex we do <code>fft</code>s or <code>rfft</code>s Additionally, it is possible to provide <code>flags=FFTW.MEASURE</code> as <code>kwargs</code> to change the planning of the FFT.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; u = [1 2 3 4 5]
1×5 Matrix{Int64}:
1 2 3 4 5

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julia&gt; pconv(u)
1×5 Matrix{Float64}:
1.0 2.0 3.0 4.0 5.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/convolutions.jl#L79-L117">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv_psf" href="#FourierTools.plan_conv_psf"><code>FourierTools.plan_conv_psf</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv_psf(u, psf [, dims]; kwargs...) where {T, N}</code></pre><p><code>plan_conv_psf</code> is a shorthand for <code>plan_conv(u, ifftshift(psf))</code>. For examples see <code>plan_conv</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/convolutions.jl#L196-L200">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv_buffer" href="#FourierTools.plan_conv_buffer"><code>FourierTools.plan_conv_buffer</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv_buffer(u, v [, dims]; kwargs...)</code></pre><p>Similar to <a href="#FourierTools.plan_conv"><code>plan_conv</code></a> but instead uses buffers to prevent memory allocations. Not AD friendly!</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/convolutions.jl#L147-L153">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv_psf_buffer" href="#FourierTools.plan_conv_psf_buffer"><code>FourierTools.plan_conv_psf_buffer</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv_psf_buffer(u, psf [, dims]; kwargs...) where {T, N}</code></pre><p><code>plan_conv_psf_buffer</code> is a shorthand for <code>plan_conv_buffer(u, ifftshift(psf))</code>. For examples see <code>plan_conv</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/58c675e01d9c1c5bd79df056e7853ae7e15e7c16/src/convolutions.jl#L184-L188">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../helpers/">« FFT Helpers</a><a class="docs-footer-nextpage" href="../resampling/">Resampling (sinc Interpolation) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 23 September 2024 15:26">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
1.0 2.0 3.0 4.0 5.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/convolutions.jl#L79-L117">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv_psf" href="#FourierTools.plan_conv_psf"><code>FourierTools.plan_conv_psf</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv_psf(u, psf [, dims]; kwargs...) where {T, N}</code></pre><p><code>plan_conv_psf</code> is a shorthand for <code>plan_conv(u, ifftshift(psf))</code>. For examples see <code>plan_conv</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/convolutions.jl#L196-L200">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv_buffer" href="#FourierTools.plan_conv_buffer"><code>FourierTools.plan_conv_buffer</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv_buffer(u, v [, dims]; kwargs...)</code></pre><p>Similar to <a href="#FourierTools.plan_conv"><code>plan_conv</code></a> but instead uses buffers to prevent memory allocations. Not AD friendly!</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/convolutions.jl#L147-L153">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FourierTools.plan_conv_psf_buffer" href="#FourierTools.plan_conv_psf_buffer"><code>FourierTools.plan_conv_psf_buffer</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">plan_conv_psf_buffer(u, psf [, dims]; kwargs...) where {T, N}</code></pre><p><code>plan_conv_psf_buffer</code> is a shorthand for <code>plan_conv_buffer(u, ifftshift(psf))</code>. For examples see <code>plan_conv</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/bionanoimaging/FourierTools.jl/blob/3697e743847d7806ae8fff3f2d62b6adcf2ec9d5/src/convolutions.jl#L184-L188">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../helpers/">« FFT Helpers</a><a class="docs-footer-nextpage" href="../resampling/">Resampling (sinc Interpolation) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 25 September 2024 11:52">Wednesday 25 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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