Merge pull request #19 from NFFT/develop

Develop

Manifest.toml

@@ -2,7 +2,7 @@
 
 julia_version = "1.10.4"
 manifest_format = "2.0"
-project_hash = "6a0dbf49b9f181ea3bc8882243fdc78ded95cdb7"
+project_hash = "d9ad1fa52dc8a8a415fe050e4fcf94ccb8acb79a"
 
 [[deps.Aqua]]
 deps = ["Compat", "Pkg", "Test"]
@@ -88,6 +88,22 @@ uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[[deps.LinearMaps]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "ee79c3208e55786de58f8dcccca098ced79f743f"
+uuid = "7a12625a-238d-50fd-b39a-03d52299707e"
+version = "3.11.3"
+
+    [deps.LinearMaps.extensions]
+    LinearMapsChainRulesCoreExt = "ChainRulesCore"
+    LinearMapsSparseArraysExt = "SparseArrays"
+    LinearMapsStatisticsExt = "Statistics"
+
+    [deps.LinearMaps.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 

Project.toml

@@ -7,11 +7,13 @@ version = "1.2.2"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 CpuId = "adafc99b-e345-5852-983c-f28acb93d879"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearMaps = "7a12625a-238d-50fd-b39a-03d52299707e"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 Aqua = "0.5 - 0.8"
 CpuId = "0.3"
 LinearAlgebra = "1"
+LinearMaps = "3"
 Test = "1"
 julia = "1"

deps/build.jl

@@ -3,12 +3,22 @@ using CpuId
 # file ending for OS
 ending = ".so"
 path = "/../src/lib/"
+glibcversion = ""
 
 if Sys.iswindows()
     ending = ".dll"
     path = "\\..\\src\\lib\\"
 elseif Sys.isapple()
     ending = ".dylib"
+else
+    glibcversion = "glibc2.40/"
+    if VersionNumber(
+        unsafe_string(
+            @ccall string(@__DIR__, path, "glibc-version.so").glibc_version()::Cstring
+        ),
+    ) < v"2.35"
+        glibcversion = "glibc2.22/"
+    end
 end
 
 if cpufeature(:AVX2)
@@ -19,12 +29,12 @@ else
     flag = "SSE2/"
 end
 
-lib_path_nfft = string(@__DIR__, path, flag, "libnfftjulia", ending)
-lib_path_nfct = string(@__DIR__, path, flag, "libnfctjulia", ending)
-lib_path_nfst = string(@__DIR__, path, flag, "libnfstjulia", ending)
-lib_path_fastsum = string(@__DIR__, path, flag, "libfastsumjulia", ending)
+lib_path_nfft = string(@__DIR__, path, flag, glibcversion, "libnfftjulia", ending)
+lib_path_nfct = string(@__DIR__, path, flag, glibcversion, "libnfctjulia", ending)
+lib_path_nfst = string(@__DIR__, path, flag, glibcversion, "libnfstjulia", ending)
+lib_path_fastsum = string(@__DIR__, path, flag, glibcversion, "libfastsumjulia", ending)
 
-println( lib_path_nfft )
+println(lib_path_nfft)
 
 chmod(lib_path_nfft, filemode(lib_path_nfft) | 0o755)
 chmod(lib_path_nfct, filemode(lib_path_nfct) | 0o755)

docs/make.jl

@@ -7,11 +7,13 @@ makedocs(
     pages = [
         "Home" => "index.md",
         "About" => "about.md",
-        "Transformations" =>
-            ["NFFT" => "NFFT.md", "NFST" => "NFST.md", "NFCT" => "NFCT.md"],
-        "Applications" =>
-            ["fastsum" => "fastsum.md",],
-        "Flags" => "Flags.md",
+        "Transformations" => [
+            "NFFT" => "NFFT.md",
+            "NFST" => "NFST.md",
+            "NFCT" => "NFCT.md",
+            "NFMT" => "NFMT.md",
+        ],
+        "Applications" => ["fastsum" => "fastsum.md"],
     ],
 )
 

docs/src/NFMT.md

@@ -0,0 +1,61 @@
+# [Nonequispaced Fast Cosine Transform (NFMT)](@id NFMT_site)
+
+```@meta
+    CurrentModule = NFFT3
+```
+
+## NDMT and NFMT
+
+We consider for $\pmb{d}\in\{\exp,\cos,\mathrm{alg}\}^d$ the trigonometric polynomial
+
+$$f^{\pmb{d}}(\pmb{x}) \coloneqq \sum_{\pmb{k} \in I_{\pmb{N},\pmb{d}}^d} \hat{f}_{\pmb{k}}^{\pmb{d}} \, \phi_{\pmb{k}}^{\pmb{d}}(\pmb{x}), \quad \pmb{x} \in \mathbb{R}^d,$$
+
+with 
+
+$$\phi_{\pmb{k}}^{\pmb{d}}(\pmb{x})=\prod_{j=1}^d\begin{cases}1,&k_j=0\\\exp(2\pi\mathrm{i}k_jx_j),&d_j=\exp,\;k_j\neq0\\
+\sqrt{2}\cos(\pi k_jx_j),&d_j=\cos,\;k_j\neq0\\
+\sqrt{2}\cos(k_j\arccos(2x_j-1)),&d_j=\mathrm{alg},\;k_j\neq0\end{cases} $$
+
+and multibandlimit $\pmb{N} \in (2\mathbb{N})^d$ and index set
+
+$$I_{\pmb{N},\pmb{d}}^d \coloneqq \overset{d}{\underset{j=1}{\vphantom{\mathop{\raisebox{-.5ex}{\hbox{\huge{$\times$}}}}}⨉}}\begin{cases}\Big\{-\frac{N_j}{2},-\frac{N_j}{2}+1,\ldots,\frac{N_j}{2}\Big\},&d_j=\exp\\\Big\{0,1,\ldots,\frac{N_j}{2}\Big\},&d_j\neq\exp\end{cases}.$$
+
+The NDMT is the evaluation of
+
+$$f^{\pmb{d}}(\pmb{x}_j) \coloneqq \sum_{\pmb{k} \in I_{\pmb{N},\pmb{d}}^d} \hat{f}_{\pmb{k}}^{\pmb{d}} \, \phi_{\pmb{k}}^{\pmb{d}}(\pmb{x}_j)$$
+
+at arbitrary nodes $\pmb{x}_j \in [0,1]^d$ for given coefficients $\hat{f}_{\pmb{k}}^{\pmb{d}} \in \mathbb{R}, \pmb{k} \in I_{\pmb{N},\pmb{d}}^d$. Similarly to the NDFT, the transposed NDMT is the evaluation of
+
+$$\hat{h}^{\pmb{d}}_{\pmb{k}} = \sum_{j=1}^M f^{\pmb{d}}_j \, \phi_{\pmb{k}}^{\pmb{d}}(\pmb{x}_j)$$
+
+for the frequencies $\pmb{k} \in I_{\pmb{N},\pmb{d}}^d$ with given coefficients $f^{\pmb{d}}_j \in \mathbb{R}, j = 1,2,\ldots,M$.
+
+We modify the [NFFT](@ref NFFT_site) in order to derive a fast algorithm for the computation of the NDMT and transposed NDMT, obtaining the NFMT and its transposed counterpart. For details we refer to [[Potts, Schröter, 2024](#PottsSchröter2024)].
+
+## Plan structure
+
+```@docs
+    NFMT{D}
+```
+
+## Functions
+
+```@docs
+    nfmt_trafo
+    nfmt_trafo_direct
+    nfmt_transposed
+    nfmt_transposed_direct
+  	nfmt_finalize_plan
+    nfmt_init
+```
+
+## Literature
+
+```@raw html
+<ul>
+<li id="PottsSchröetr2024">[<a>Potts, Schröter, 2024</a>]
+  D. Potts, P.Schröter. Linear Algebra Appl.</emph>
+  arXiv: <a href="https://arxiv.org/abs/2306.09174">2306.09174</a>.
+</li>
+</ul>
+```

docs/src/fastsum.md

@@ -100,6 +100,46 @@ where the inner sum can be computed by an adjoint NFFT which is then followed by
     fastsum_trafo_exact
 ```
 
+## Supported kernel functions
+
+- `gaussian`
+$${K}(x)=\exp\Big(-\frac{x^2}{c^2}\Big)$$
+- `multiquadratic`
+$${K}(x)=\sqrt{x^2+c^2}$$
+- `inverse_multiquadratic`
+$${K}(x)=\sqrt{\frac{1}{x^2+c^2}}$$
+- `logarithm`
+$${K}(x)=\log(\vert x\vert)$$
+- `thinplate_spline`
+$${K}(x)=x^2\log(\vert x\vert)$$
+- `one_over_square`
+$${K}(x)=\frac{1}{x^2}$$
+- `one_over_modulus`
+$${K}(x)=\frac{1}{\vert x\vert}$$
+- `one_over_x`
+$${K}(x)=\frac{1}{x}$$
+- `one_over_multiquadric3`
+$${K}(x)=\Big(\frac{1}{x^2+c^2}\Big)^\frac{3}{2}$$
+- `sinc_kernel`
+$${K}(x)=\frac{\sin(cx)}{x}$$
+- `cosc`
+$${K}(x)=\frac{\cos(cx)}{x}$$
+- `kcot`
+$${K}(x)=\cot(cx)$$
+- `one_over_cube`
+$${K}(x)=\frac{1}{x^3}$$
+- `log_sin`
+$${K}(x)=\log(\vert\sin(cx)\vert)$$
+- `laplacian_rbf`
+$${K}(x)=\exp\Big(-\frac{\vert x\vert}{c}\Big)$$
+- `der_laplacian_rbf`
+$${K}(x)=\frac{\vert x\vert}{c}\exp\Big(-\frac{\vert x\vert}{c}\Big)$$
+- `xx_gaussian`
+$${K}(x)=\frac{x^2}{c^2}\exp\Big(-\frac{x^2}{c^2}\Big)$$
+- `absx`
+$${K}(x)=\vert x\vert$$
+
+
 ## Literature
 
 ```@raw html