chore: import upstream snapshot with attribution

docs/plots/ai.py

@@ -0,0 +1,5 @@
+# Airy function Ai(x), Ai'(x) and int_0^x Ai(t) dt on the real line
+f = airyai
+f_diff = lambda z: airyai(z, derivative=1)
+f_int = lambda z: airyai(z, derivative=-1)
+plot([f, f_diff, f_int], [-10,5])

docs/plots/ai_c.py

@@ -0,0 +1,2 @@
+# Airy function Ai(z) in the complex plane
+cplot(airyai, [-8,8], [-8,8], points=50000)

docs/plots/ber.py

@@ -0,0 +1,6 @@
+# Kelvin functions ber_n(x) and bei_n(x) on the real line for n=0,2
+f0 = lambda x: ber(0,x)
+f1 = lambda x: bei(0,x)
+f2 = lambda x: ber(2,x)
+f3 = lambda x: bei(2,x)
+plot([f0,f1,f2,f3],[0,10],[-10,10])

docs/plots/besseli.py

@@ -0,0 +1,6 @@
+# Modified Bessel function I_n(x) on the real line for n=0,1,2,3
+i0 = lambda x: besseli(0,x)
+i1 = lambda x: besseli(1,x)
+i2 = lambda x: besseli(2,x)
+i3 = lambda x: besseli(3,x)
+plot([i0,i1,i2,i3],[0,5],[0,5])

docs/plots/besseli_c.py

@@ -0,0 +1,2 @@
+# Modified Bessel function I_n(z) in the complex plane
+cplot(lambda z: besseli(1,z), [-8,8], [-8,8], points=50000)

docs/plots/besselj.py

@@ -0,0 +1,6 @@
+# Bessel function J_n(x) on the real line for n=0,1,2,3
+j0 = lambda x: besselj(0,x)
+j1 = lambda x: besselj(1,x)
+j2 = lambda x: besselj(2,x)
+j3 = lambda x: besselj(3,x)
+plot([j0,j1,j2,j3],[0,14])

docs/plots/besselj_c.py

@@ -0,0 +1,2 @@
+# Bessel function J_n(z) in the complex plane
+cplot(lambda z: besselj(1,z), [-8,8], [-8,8], points=50000)

docs/plots/besselk.py

@@ -0,0 +1,6 @@
+# Modified Bessel function of 2nd kind K_n(x) on the real line for n=0,1,2,3
+k0 = lambda x: besselk(0,x)
+k1 = lambda x: besselk(1,x)
+k2 = lambda x: besselk(2,x)
+k3 = lambda x: besselk(3,x)
+plot([k0,k1,k2,k3],[0,8],[0,5])

docs/plots/besselk_c.py

@@ -0,0 +1,2 @@
+# Modified Bessel function of 2nd kind K_n(z) in the complex plane
+cplot(lambda z: besselk(1,z), [-8,8], [-8,8], points=50000)

docs/plots/bessely.py

@@ -0,0 +1,6 @@
+# Bessel function of 2nd kind Y_n(x) on the real line for n=0,1,2,3
+y0 = lambda x: bessely(0,x)
+y1 = lambda x: bessely(1,x)
+y2 = lambda x: bessely(2,x)
+y3 = lambda x: bessely(3,x)
+plot([y0,y1,y2,y3],[0,10],[-4,1])

docs/plots/bessely_c.py

@@ -0,0 +1,2 @@
+# Bessel function of 2nd kind Y_n(z) in the complex plane
+cplot(lambda z: bessely(1,z), [-8,8], [-8,8], points=50000)

docs/plots/bi.py

@@ -0,0 +1,5 @@
+# Airy function Bi(x), Bi'(x) and int_0^x Bi(t) dt on the real line
+f = airybi
+f_diff = lambda z: airybi(z, derivative=1)
+f_int = lambda z: airybi(z, derivative=-1)
+plot([f, f_diff, f_int], [-10,2], [-1,2])

docs/plots/bi_c.py

@@ -0,0 +1,2 @@
+# Airy function Bi(z) in the complex plane
+cplot(airybi, [-8,8], [-8,8], points=50000)

docs/plots/buildplots.py

@@ -0,0 +1,22 @@
+import os.path
+import glob
+
+for f in glob.glob("*.py"):
+    if "buildplots" in f or os.path.exists(f[:-3]+".png"):
+        continue
+    print("Processing", f)
+    code = open(f).readlines()
+    code = ["from mpmath import *; mp.dps=5"] + code
+    for i in range(len(code)):
+        l = code[i].rstrip()
+        if "cplot(" in l:
+            l = l[:-1] + (", dpi=45, file='%s.png', verbose=True)" % f[:-3])
+            code[i] = l
+        elif "splot(" in l:
+            l = l[:-1] + (", dpi=45, file='%s.png')" % f[:-3])
+            code[i] = l
+        elif "plot(" in l:
+            l = l[:-1] + (", dpi=45, file='%s.png')" % f[:-3])
+            code[i] = l
+    code = "\n".join(code)
+    exec(code)

docs/plots/chebyt.py

@@ -0,0 +1,7 @@
+# Chebyshev polynomials T_n(x) on [-1,1] for n=0,1,2,3,4
+f0 = lambda x: chebyt(0,x)
+f1 = lambda x: chebyt(1,x)
+f2 = lambda x: chebyt(2,x)
+f3 = lambda x: chebyt(3,x)
+f4 = lambda x: chebyt(4,x)
+plot([f0,f1,f2,f3,f4],[-1,1])

docs/plots/chebyu.py

@@ -0,0 +1,7 @@
+# Chebyshev polynomials U_n(x) on [-1,1] for n=0,1,2,3,4
+f0 = lambda x: chebyu(0,x)
+f1 = lambda x: chebyu(1,x)
+f2 = lambda x: chebyu(2,x)
+f3 = lambda x: chebyu(3,x)
+f4 = lambda x: chebyu(4,x)
+plot([f0,f1,f2,f3,f4],[-1,1])

docs/plots/coulombf.py

@@ -0,0 +1,7 @@
+# Regular Coulomb wave functions -- equivalent to figure 14.3 in A&S
+F1 = lambda x: coulombf(0,0,x)
+F2 = lambda x: coulombf(0,1,x)
+F3 = lambda x: coulombf(0,5,x)
+F4 = lambda x: coulombf(0,10,x)
+F5 = lambda x: coulombf(0,x/2,x)
+plot([F1,F2,F3,F4,F5], [0,25], [-1.2,1.6])

docs/plots/coulombf_c.py

@@ -0,0 +1,2 @@
+# Regular Coulomb wave function in the complex plane
+cplot(lambda z: coulombf(1,1,z), points=50000)

docs/plots/coulombg.py

@@ -0,0 +1,7 @@
+# Irregular Coulomb wave functions -- equivalent to figure 14.5 in A&S
+F1 = lambda x: coulombg(0,0,x)
+F2 = lambda x: coulombg(0,1,x)
+F3 = lambda x: coulombg(0,5,x)
+F4 = lambda x: coulombg(0,10,x)
+F5 = lambda x: coulombg(0,x/2,x)
+plot([F1,F2,F3,F4,F5], [0,30], [-2,2])

docs/plots/coulombg_c.py

@@ -0,0 +1,2 @@
+# Irregular Coulomb wave function in the complex plane
+cplot(lambda z: coulombg(1,1,z), points=50000)

docs/plots/ellipe.py

@@ -0,0 +1,7 @@
+# Elliptic integral E(z,m) for some different m
+f1 = lambda z: ellipe(z,-2)
+f2 = lambda z: ellipe(z,-1)
+f3 = lambda z: ellipe(z,0)
+f4 = lambda z: ellipe(z,1)
+f5 = lambda z: ellipe(z,2)
+plot([f1,f2,f3,f4,f5], [0,pi], [0,4])

docs/plots/ellipf.py

@@ -0,0 +1,7 @@
+# Elliptic integral F(z,m) for some different m
+f1 = lambda z: ellipf(z,-1)
+f2 = lambda z: ellipf(z,-0.5)
+f3 = lambda z: ellipf(z,0)
+f4 = lambda z: ellipf(z,0.5)
+f5 = lambda z: ellipf(z,1)
+plot([f1,f2,f3,f4,f5], [0,pi], [0,4])

docs/plots/ellipk.py

@@ -0,0 +1,2 @@
+# Complete elliptic integrals K(m) and E(m)
+plot([ellipk, ellipe], [-2,1], [0,3], points=600)

docs/plots/ellippi.py

@@ -0,0 +1,7 @@
+# Elliptic integral Pi(n,z,m) for some different n, m
+f1 = lambda z: ellippi(0.9,z,0.9)
+f2 = lambda z: ellippi(0.5,z,0.5)
+f3 = lambda z: ellippi(-2,z,-0.9)
+f4 = lambda z: ellippi(-0.5,z,0.5)
+f5 = lambda z: ellippi(-1,z,0.5)
+plot([f1,f2,f3,f4,f5], [0,pi], [0,4])

docs/plots/gi.py

@@ -0,0 +1,2 @@
+# Scorer function Gi(x) and Gi'(x) on the real line
+plot([scorergi, diffun(scorergi)], [-10,10])

docs/plots/gi_c.py

@@ -0,0 +1,2 @@
+# Scorer function Gi(z) in the complex plane
+cplot(scorergi, [-8,8], [-8,8], points=50000)

docs/plots/hankel1.py

@@ -0,0 +1,6 @@
+# Hankel function H1_n(x) on the real line for n=0,1,2,3
+h0 = lambda x: hankel1(0,x)
+h1 = lambda x: hankel1(1,x)
+h2 = lambda x: hankel1(2,x)
+h3 = lambda x: hankel1(3,x)
+plot([h0,h1,h2,h3],[0,6],[-2,1])

docs/plots/hankel1_c.py

@@ -0,0 +1,2 @@
+# Hankel function H1_n(z) in the complex plane
+cplot(lambda z: hankel1(1,z), [-8,8], [-8,8], points=50000)

docs/plots/hankel2.py

@@ -0,0 +1,6 @@
+# Hankel function H2_n(x) on the real line for n=0,1,2,3
+h0 = lambda x: hankel2(0,x)
+h1 = lambda x: hankel2(1,x)
+h2 = lambda x: hankel2(2,x)
+h3 = lambda x: hankel2(3,x)
+plot([h0,h1,h2,h3],[0,6],[-1,2])

docs/plots/hankel2_c.py

@@ -0,0 +1,2 @@
+# Hankel function H2_n(z) in the complex plane
+cplot(lambda z: hankel2(1,z), [-8,8], [-8,8], points=50000)

docs/plots/hermite.py

@@ -0,0 +1,7 @@
+# Hermite polynomials H_n(x) on the real line for n=0,1,2,3,4
+f0 = lambda x: hermite(0,x)
+f1 = lambda x: hermite(1,x)
+f2 = lambda x: hermite(2,x)
+f3 = lambda x: hermite(3,x)
+f4 = lambda x: hermite(4,x)
+plot([f0,f1,f2,f3,f4],[-2,2],[-25,25])

docs/plots/hi.py

@@ -0,0 +1,2 @@
+# Scorer function Hi(x) and Hi'(x) on the real line
+plot([scorerhi, diffun(scorerhi)], [-10,2], [0,2])

docs/plots/hi_c.py

@@ -0,0 +1,2 @@
+# Scorer function Hi(z) in the complex plane
+cplot(scorerhi, [-8,8], [-8,8], points=50000)

docs/plots/ker.py

@@ -0,0 +1,6 @@
+# Kelvin functions ker_n(x) and kei_n(x) on the real line for n=0,2
+f0 = lambda x: ker(0,x)
+f1 = lambda x: kei(0,x)
+f2 = lambda x: ker(2,x)
+f3 = lambda x: kei(2,x)
+plot([f0,f1,f2,f3],[0,5],[-1,4])

docs/plots/kleinj.py

@@ -0,0 +1,2 @@
+# Klein J-function as function of the number-theoretic nome
+fp.cplot(lambda q: fp.kleinj(qbar=q), [-1,1], [-1,1], points=50000)

docs/plots/kleinj2.py

@@ -0,0 +1,2 @@
+# Klein J-function as function of the half-period ratio
+fp.cplot(lambda t: fp.kleinj(tau=t), [-1,2], [0,1.5], points=50000)

docs/plots/laguerre.py

@@ -0,0 +1,7 @@
+# Hermite polynomials L_n(x) on the real line for n=0,1,2,3,4
+f0 = lambda x: laguerre(0,0,x)
+f1 = lambda x: laguerre(1,0,x)
+f2 = lambda x: laguerre(2,0,x)
+f3 = lambda x: laguerre(3,0,x)
+f4 = lambda x: laguerre(4,0,x)
+plot([f0,f1,f2,f3,f4],[0,10],[-10,10])

docs/plots/lambertw.py

@@ -0,0 +1,2 @@
+# Branches 0 and -1 of the Lambert W function
+plot([lambertw, lambda x: lambertw(x,-1)], [-2,2], [-5,2], points=2000)

docs/plots/lambertw_c.py

@@ -0,0 +1,2 @@
+# Principal branch of the Lambert W function W(z)
+cplot(lambertw, [-1,1], [-1,1], points=50000)

docs/plots/legendre.py

@@ -0,0 +1,7 @@
+# Legendre polynomials P_n(x) on [-1,1] for n=0,1,2,3,4
+f0 = lambda x: legendre(0,x)
+f1 = lambda x: legendre(1,x)
+f2 = lambda x: legendre(2,x)
+f3 = lambda x: legendre(3,x)
+f4 = lambda x: legendre(4,x)
+plot([f0,f1,f2,f3,f4],[-1,1])

docs/plots/lommels1.py

@@ -0,0 +1,6 @@
+# Lommel function s_(u,v)(x) on the real line for a few different u,v
+f1 = lambda x: lommels1(-1,2.5,x)
+f2 = lambda x: lommels1(0,0.5,x)
+f3 = lambda x: lommels1(0,6,x)
+f4 = lambda x: lommels1(0.5,3,x)
+plot([f1,f2,f3,f4], [0,20])

docs/plots/lommels2.py

@@ -0,0 +1,6 @@
+# Lommel function S_(u,v)(x) on the real line for a few different u,v
+f1 = lambda x: lommels2(-1,2.5,x)
+f2 = lambda x: lommels2(1.5,2,x)
+f3 = lambda x: lommels2(2.5,1,x)
+f4 = lambda x: lommels2(3.5,-0.5,x)
+plot([f1,f2,f3,f4], [0,8], [-8,8])

docs/plots/pcfd.py

@@ -0,0 +1,7 @@
+# Parabolic cylinder function D_n(x) on the real line for n=0,1,2,3,4
+d0 = lambda x: pcfd(0,x)
+d1 = lambda x: pcfd(1,x)
+d2 = lambda x: pcfd(2,x)
+d3 = lambda x: pcfd(3,x)
+d4 = lambda x: pcfd(4,x)
+plot([d0,d1,d2,d3,d4],[-7,7])

docs/plots/spherharm40.py

@@ -0,0 +1,15 @@
+# Real part of spherical harmonic Y_(4,0)(theta,phi)
+def Y(l,m):
+    def g(theta,phi):
+        R = abs(fp.re(fp.spherharm(l,m,theta,phi)))
+        x = R*fp.cos(phi)*fp.sin(theta)
+        y = R*fp.sin(phi)*fp.sin(theta)
+        z = R*fp.cos(theta)
+        return [x,y,z]
+    return g
+
+fp.splot(Y(4,0), [0,fp.pi], [0,2*fp.pi], points=300)
+# fp.splot(Y(4,0), [0,fp.pi], [0,2*fp.pi], points=300)
+# fp.splot(Y(4,1), [0,fp.pi], [0,2*fp.pi], points=300)
+# fp.splot(Y(4,2), [0,fp.pi], [0,2*fp.pi], points=300)
+# fp.splot(Y(4,3), [0,fp.pi], [0,2*fp.pi], points=300)

docs/plots/spherharm41.py

@@ -0,0 +1,11 @@
+# Real part of spherical harmonic Y_(4,1)(theta,phi)
+def Y(l,m):
+    def g(theta,phi):
+        R = abs(fp.re(fp.spherharm(l,m,theta,phi)))
+        x = R*fp.cos(phi)*fp.sin(theta)
+        y = R*fp.sin(phi)*fp.sin(theta)
+        z = R*fp.cos(theta)
+        return [x,y,z]
+    return g
+
+fp.splot(Y(4,1), [0,fp.pi], [0,2*fp.pi], points=300)

docs/plots/spherharm42.py

@@ -0,0 +1,11 @@
+# Real part of spherical harmonic Y_(4,2)(theta,phi)
+def Y(l,m):
+    def g(theta,phi):
+        R = abs(fp.re(fp.spherharm(l,m,theta,phi)))
+        x = R*fp.cos(phi)*fp.sin(theta)
+        y = R*fp.sin(phi)*fp.sin(theta)
+        z = R*fp.cos(theta)
+        return [x,y,z]
+    return g
+
+fp.splot(Y(4,2), [0,fp.pi], [0,2*fp.pi], points=300)

docs/plots/spherharm43.py

@@ -0,0 +1,11 @@
+# Real part of spherical harmonic Y_(4,3)(theta,phi)
+def Y(l,m):
+    def g(theta,phi):
+        R = abs(fp.re(fp.spherharm(l,m,theta,phi)))
+        x = R*fp.cos(phi)*fp.sin(theta)
+        y = R*fp.sin(phi)*fp.sin(theta)
+        z = R*fp.cos(theta)
+        return [x,y,z]
+    return g
+
+fp.splot(Y(4,3), [0,fp.pi], [0,2*fp.pi], points=300)

docs/plots/spherharm44.py

@@ -0,0 +1,14 @@
+from mpmath import fp
+
+# Real part of spherical harmonic Y_(4,4)(theta,phi)
+def Y(l,m):
+    def g(theta,phi):
+        R = abs(fp.re(fp.spherharm(l,m,theta,phi)))
+        x = R*fp.cos(phi)*fp.sin(theta)
+        y = R*fp.sin(phi)*fp.sin(theta)
+        z = R*fp.cos(theta)
+        return [x,y,z]
+    return g
+
+fp.splot(Y(4,4), [0,fp.pi], [0,2*fp.pi], points=300,
+    dpi=45, file="spherharm44.png")