Rename Quadratures

Analysis/LegendreSeries.m

@@ -1,7 +1,7 @@
 function [c, Q] = LegendreSeries(f, a, b, n)
 % Calculates the Legendre expansion of f over the interval [a,b].
 % Additionally returns the equivalent polynomial.
-[x, w]=GaussLegendre(-1, 1, n+1);
+[x, w]=gauleg(-1, 1, n+1);
 P=Legendre(n);
 y1=Horner(P, x);
 y2=f(((b-a)*x+b+a)/2);

Analysis/hermSeries.m

@@ -1,6 +1,6 @@
 function [ c ] = hermSeries(f, n)
 sig=1/sqrt(2);
-[x,w]=GaussHermite(n,0,sig);
+[x,w]=gauherm(n,0,sig);
 Psi=zeros(n);
 a=zeros(n,1); a(end)=1;
 for i=1:n

Integration/ClenshawCurtis.m

@@ -1,9 +1,9 @@
 function [x, w] = ClenshawCurtis(a, b, n)
 % Returns abscissas and weights for the corresponding Clenshaw-Curtis
-% (n+1)-point quadrature over the interval [a, b].
-th=(0:n)*pi/n;
+% n-point quadrature over the interval [a, b].
+th=(0:n-1)*pi/(n-1);
 x=(b-a)/2*cos(th)+(b+a)/2;
-d=1./(1-(0:2:n).^2);
-c=ifft([d, d(ceil(n/2):-1:2)], 'symmetric');
-w=(b-a)*[c(1)/2, c(2:n), c(1)/2];
+d=1./(1-(0:2:n-1).^2);
+c=ifft([d, d(ceil((n-1)/2):-1:2)], 'symmetric');
+w=(b-a)*[c(1)/2, c(2:n-1), c(1)/2];
 end

Integration/GaussChebyshev.m → Integration/gaucheb.m

@@ -1,4 +1,4 @@
-function [x, w] = GaussChebyshev(a, b, n)
+function [x, w] = gaucheb(a, b, n)
 % Returns abscissas and weights for the Gauss-Chebyshev n-point quadrature
 % over the interval [a, b].
 th=pi*(1:2:2*n-1)/(2*n);

Integration/GaussHermite.m → Integration/gauherm.m

@@ -1,4 +1,4 @@
-function [x, w] = GaussHermite(n, mu, sigma)
+function [x, w] = gauherm(n, mu, sigma)
 % Returns abscissas and weights for the Gauss-Hermite n-point quadrature 
 % over the interval [-inf, inf] using the Golub-Welsch Algorithm.
 E=sqrt((1:n-1)/2);

Integration/GaussJacobi.m → Integration/gaujac.m

@@ -1,6 +1,6 @@
-function [x, w] = GaussJacobi(a,b,n)
+function [x, w] = gaujac(a,b,n)
 % Returns abscissas and weights for the Gauss-Jacobi n-point quadrature 
-% over the interval [-1, 1] using the Golub-Welsch Algorithm.
+% over the interval [a, b] using the Golub-Welsch Algorithm.
 k=1:n;
 c=2*k+a+b;
 D=(b^2-a^2)./(c.*(c-2)+(b^2==a^2));

Integration/GaussLaguerre.m → Integration/gaulag.m

@@ -1,6 +1,6 @@
-function [x, w] = GaussLaguerre(alpha, n)
+function [x, w] = gaulag(alpha, n)
 % Returns abscissas and weights for the Gauss-Laguerre n-point quadrature
-% over the interval [0, inf] using the Golub-Welsch Algorithm.
+% over the interval [0, inf) using the Golub-Welsch Algorithm.
 k=(1:n);
 D=2*k-1+alpha;
 E=sqrt(k.*(k+alpha));

Integration/GaussLegendre.m → Integration/gauleg.m

@@ -1,4 +1,4 @@
-function [x, w] = GaussLegendre(a, b, n)
+function [x, w] = gauleg(a, b, n)
 % Returns abscissas and weights for the Gauss-Legendre n-point quadrature 
 % over the interval [a, b] using the Golub-Welsch Algorithm.
 k=1:n-1;

PDE/heatExp.m

@@ -1,7 +1,7 @@
 function [] = heatExp( N )
 dt=0.001;
 
-[x,w]=GaussLegendre(-1,1,N); x=x(:); w=w(:);
+[x,w]=gauleg(-1,1,N); x=x(:); w=w(:);
 V=exp(1i*pi/2*x*(-N/2:N/2-1))/sqrt(2);
 L=-pi^2/4*(-N/2:N/2-1)'.^2;
 

Physics/brachistochrone.m

@@ -2,7 +2,7 @@
 global D x w y1 y2 h;
 L=20;
 
-[~,w]=ClenshawCurtis(-1,1,n-1); w=w(:);
+[~,w]=ClenshawCurtis(-1,1,n); w=w(:);
 [D,x]=chebD(n);
 
 y1=0;

Physics/schrodCayley.m

@@ -10,7 +10,7 @@
 
 Psi=(-(r-R1).*(r-R2).*(r-(R1+R2)/2))*sin(3*th.^2/(2*pi));
 
-[x,w]=ClenshawCurtis(R1,R2,N-1);
+[x,w]=ClenshawCurtis(R1,R2,N);
 W=diag(w);
 Psi=Psi/sqrt(sum(r'*W*abs(Psi).^2)*(2*pi/N));
 

Physics/schrodExp.m

@@ -1,6 +1,6 @@
 function [] = schrodExp( N )
 [D,x]=chebD(N);
-[~,w]=ClenshawCurtis(-1,1,N-1);
+[~,w]=ClenshawCurtis(-1,1,N);
 
 dt=0.001;
 V0=1000;

Physics/schrodPolar.m

@@ -20,7 +20,7 @@
 mu=diag(mu);
 Phi=Phi/sqrt(2*pi/N);
 
-[x,w]=ClenshawCurtis(R1,R2,N-1);
+[x,w]=ClenshawCurtis(R1,R2,N);
 W=diag(w(2:end-1));
 
 E=zeros(k,k);

Sandbox/besselPlot.m

@@ -1,7 +1,7 @@
 m=0;
 rlim=100;
 r=linspace(-rlim,rlim,2048)';
-[tau,w]=GaussLegendre(-pi,pi,256);
+[tau,w]=gauleg(-pi,pi,256);
 f=exp(1i*(m*ones(size(r))*tau-r*sin(tau)));
 J=1/(2*pi)*f*w';
 

Sandbox/eigKernel.m

@@ -1,5 +1,5 @@
 n=512; p=0; a=-4; b=4;
-[x,w]=GaussLegendre(a,b,n);
+[x,w]=gauleg(a,b,n);
 
 x2 = x.^2;
 r=exp(0.5i*x2);

Solitons/nlsecheb.m

@@ -5,7 +5,7 @@
 % Domain substitution x=tan(th), u=sec(th).*w
 [Dt,th]=chebD(N); th=pi/2*th; Dt=2/pi*Dt;
 x=tan(th);
-[~,w]=ClenshawCurtis(-pi/2,pi/2,N-1);
+[~,w]=ClenshawCurtis(-pi/2,pi/2,N);
 w=(sec(th).^2).*w(:);
 
 T=-1/2*diag(cos(th).^4)*(eye(N)+Dt*Dt);

Spectral/hermD.m

@@ -1,9 +1,11 @@
 function [D, x, w] = hermD(N)
 % Hermite spectral differentiation matrix
-[x,w]=GaussHermite(N,0,1/sqrt(2));
-x=x(:); w=w(:).*exp(x.^2);
+[x,w]=gauherm(N,0,1/sqrt(2));
+x=x(:);
 a(N)=1;
+h=HermitePsi(a,x);
 X=repmat(x,[1, N]);
-H=repmat(HermitePsi(a,x),[1, N]);
+H=repmat(h,[1, N]);
 D=(H./H'-eye(N))./(X-X'+eye(N));
+w=1./(N*h.^2);
 end

Spectral/lagD.m

@@ -1,6 +1,6 @@
 function [D,x,w] = lagD(N)
 % Laguerre spectral differentiation matrix
-[x,w]=GaussLaguerre(1,N-1); x=x(:); w=w(:);
+[x,w]=gaulag(1,N-1); x=x(:); w=w(:);
 X=repmat([0;x], [1, N]);
 c(N-1)=1;
 L=[N; -x.*LaguerreL(c,2,x).*exp(-x/2)];