add GramMatrix

Author: MikaelSlevinsky

Project.toml

@@ -4,12 +4,14 @@ version = "0.16.6"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"
 FastTransforms_jll = "34b6f7d7-08f9-5794-9e10-3819e4c7e49a"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 GenericFFT = "a8297547-1b15-4a5a-a998-a2ac5f1cef28"
+LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
 Libdl = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 RecurrenceRelationships = "807425ed-42ea-44d6-a357-6771516d7b2c"
@@ -19,12 +21,14 @@ ToeplitzMatrices = "c751599d-da0a-543b-9d20-d0a503d91d24"
 
 [compat]
 AbstractFFTs = "1.0"
+ArrayLayouts = "1.10"
 BandedMatrices = "1.5"
 FFTW = "1.7"
 FastGaussQuadrature = "0.4, 0.5, 1"
 FastTransforms_jll = "0.6.2"
 FillArrays = "0.9, 0.10, 0.11, 0.12, 0.13, 1"
 GenericFFT = "0.1"
+LazyArrays = "2.2"
 RecurrenceRelationships = "0.1"
 Reexport = "0.2, 1.0"
 SpecialFunctions = "0.10, 1, 2"

docs/src/index.md

@@ -10,6 +10,20 @@ This package provides a Julia wrapper for the [C library](https://github.com/Mik
 
 For this documentation, please see the documentation for [FastTransforms](https://github.com/MikaelSlevinsky/FastTransforms). Most transforms have separate forward and inverse plans. In some instances, however, the inverse is in the sense of least-squares, and therefore only the forward transform is planned.
 
+### Fast Cholesky factorization of the Gram matrix
+
+```@docs
+AbstractGramMatrix
+```
+
+```@docs
+GramMatrix
+```
+
+```@docs
+ChebyshevGramMatrix
+```
+
 ## Nonuniform fast Fourier transforms
 
 ```@docs

src/FastTransforms.jl

@@ -1,6 +1,6 @@
 module FastTransforms
 
-using BandedMatrices, FastGaussQuadrature, FillArrays, LinearAlgebra,
+using ArrayLayouts, BandedMatrices, FastGaussQuadrature, FillArrays, LazyArrays, LinearAlgebra,
       Reexport, SpecialFunctions, ToeplitzMatrices, RecurrenceRelationships
 
 @reexport using AbstractFFTs
@@ -19,6 +19,8 @@ import AbstractFFTs: Plan, ScaledPlan,
                      fftshift, ifftshift, rfft_output_size, brfft_output_size,
                      normalization
 
+import ArrayLayouts: colsupport, LayoutMatrix, MemoryLayout, AbstractBandedLayout
+
 import BandedMatrices: bandwidths
 
 import FFTW: dct, dct!, idct, idct!, plan_dct!, plan_idct!,
@@ -28,7 +30,7 @@ import FastGaussQuadrature: unweightedgausshermite
 
 import FillArrays: AbstractFill, getindex_value
 
-import LinearAlgebra: mul!, lmul!, ldiv!, cholesky
+import LinearAlgebra: cholesky, issymmetric, isposdef, mul!, lmul!, ldiv!
 
 import GenericFFT: interlace # imported in downstream packages
 
@@ -98,14 +100,18 @@ export plan_clenshawcurtis, plan_fejer1, plan_fejer2
 include("clenshawcurtis.jl")
 include("fejer.jl")
 
-export weightedhermitetransform, iweightedhermitetransform
-
-include("hermite.jl")
-
 export gaunt
 
 include("gaunt.jl")
 
+export GramMatrix, ChebyshevGramMatrix
+
+include("GramMatrix.jl")
+
+export weightedhermitetransform, iweightedhermitetransform
+
+include("hermite.jl")
+
 export sphones, sphzeros, sphrand, sphrandn, sphevaluate,
        sphvones, sphvzeros, sphvrand, sphvrandn,
        diskones, diskzeros, diskrand, diskrandn,