switching to high quality piper tts and added label translations

2026-01-29 23:48:19 +01:00
commit d80c619df9
3934 changed files with 1451600 additions and 0 deletions
@@ -0,0 +1,216 @@
+import pytest
+from mpmath import *
+
+def test_approximation():
+    mp.dps = 15
+    f = lambda x: cos(2-2*x)/x
+    p, err = chebyfit(f, [2, 4], 8, error=True)
+    assert err < 1e-5
+    for i in range(10):
+        x = 2 + i/5.
+        assert abs(polyval(p, x) - f(x)) < err
+
+def test_limits():
+    mp.dps = 15
+    assert limit(lambda x: (x-sin(x))/x**3, 0).ae(mpf(1)/6)
+    assert limit(lambda n: (1+1/n)**n, inf).ae(e)
+
+def test_polyval():
+    assert polyval([], 3) == 0
+    assert polyval([0], 3) == 0
+    assert polyval([5], 3) == 5
+    # 4x^3 - 2x + 5
+    p = [4, 0, -2, 5]
+    assert polyval(p,4) == 253
+    assert polyval(p,4,derivative=True) == (253, 190)
+
+def test_polyroots():
+    p = polyroots([1,-4])
+    assert p[0].ae(4)
+    p, q = polyroots([1,2,3])
+    assert p.ae(-1 - sqrt(2)*j)
+    assert q.ae(-1 + sqrt(2)*j)
+    #this is not a real test, it only tests a specific case
+    assert polyroots([1]) == []
+    pytest.raises(ValueError, lambda: polyroots([0]))
+
+def test_polyroots_legendre():
+    n = 64
+    coeffs = [11975573020964041433067793888190275875, 0,
+        -190100434726484311252477736051902332000, 0,
+        1437919688271127330313741595496589239248, 0,
+        -6897338342113537600691931230430793911840, 0,
+        23556405536185284408974715545252277554280, 0,
+        -60969520211303089058522793175947071316960, 0,
+        124284021969194758465450309166353645376880, 0,
+        -204721258548015217049921875719981284186016, 0,
+        277415422258095841688223780704620656114900, 0,
+        -313237834141273382807123548182995095192800, 0,
+        297432255354328395601259515935229287637200, 0,
+        -239057700565161140389797367947941296605600, 0,
+        163356095386193445933028201431093219347160, 0,
+        -95158890516229191805647495979277603503200, 0,
+        47310254620162038075933656063247634556400, 0,
+        -20071017111583894941305187420771723751200, 0,
+        7255051932731034189479516844750603752850, 0,
+        -2228176940331017311443863996901733412640, 0,
+        579006552594977616773047095969088431600, 0,
+        -126584428502545713788439446082310831200, 0,
+        23112325428835593809686977515028663000, 0,
+        -3491517141958743235617737161547844000, 0,
+        431305058712550634988073414073557200, 0,
+        -42927166660756742088912492757452000, 0,
+        3378527005707706553294038781836500, 0,
+        -205277590220215081719131470288800, 0,
+        9330799555464321896324157740400, 0,
+        -304114948474392713657972548576, 0,
+        6695289961520387531608984680, 0,
+        -91048139350447232095702560, 0,
+        659769125727878493447120, 0,
+        -1905929106580294155360, 0,
+        916312070471295267]
+
+    with mp.workdps(3):
+        with pytest.raises(mp.NoConvergence):
+            polyroots(coeffs, maxsteps=5, cleanup=True, error=False,
+                      extraprec=n*10)
+
+        roots = polyroots(coeffs, maxsteps=50, cleanup=True, error=False,
+                    extraprec=n*10)
+        roots = [str(r) for r in roots]
+        assert roots == \
+            ['-0.999', '-0.996', '-0.991', '-0.983', '-0.973', '-0.961',
+            '-0.946', '-0.93', '-0.911', '-0.889', '-0.866', '-0.841',
+            '-0.813', '-0.784', '-0.753', '-0.72', '-0.685', '-0.649',
+            '-0.611', '-0.572', '-0.531', '-0.489', '-0.446', '-0.402',
+            '-0.357', '-0.311', '-0.265', '-0.217', '-0.17', '-0.121',
+            '-0.073', '-0.0243', '0.0243', '0.073', '0.121', '0.17', '0.217',
+            '0.265', '0.311', '0.357', '0.402', '0.446', '0.489', '0.531',
+            '0.572', '0.611', '0.649', '0.685', '0.72', '0.753', '0.784',
+            '0.813', '0.841', '0.866', '0.889', '0.911', '0.93', '0.946',
+            '0.961', '0.973', '0.983', '0.991', '0.996', '0.999']
+
+def test_polyroots_legendre_init():
+    extra_prec = 100
+    coeffs = [11975573020964041433067793888190275875, 0,
+        -190100434726484311252477736051902332000, 0,
+        1437919688271127330313741595496589239248, 0,
+        -6897338342113537600691931230430793911840, 0,
+        23556405536185284408974715545252277554280, 0,
+        -60969520211303089058522793175947071316960, 0,
+        124284021969194758465450309166353645376880, 0,
+        -204721258548015217049921875719981284186016, 0,
+        277415422258095841688223780704620656114900, 0,
+        -313237834141273382807123548182995095192800, 0,
+        297432255354328395601259515935229287637200, 0,
+        -239057700565161140389797367947941296605600, 0,
+        163356095386193445933028201431093219347160, 0,
+        -95158890516229191805647495979277603503200, 0,
+        47310254620162038075933656063247634556400, 0,
+        -20071017111583894941305187420771723751200, 0,
+        7255051932731034189479516844750603752850, 0,
+        -2228176940331017311443863996901733412640, 0,
+        579006552594977616773047095969088431600, 0,
+        -126584428502545713788439446082310831200, 0,
+        23112325428835593809686977515028663000, 0,
+        -3491517141958743235617737161547844000, 0,
+        431305058712550634988073414073557200, 0,
+        -42927166660756742088912492757452000, 0,
+        3378527005707706553294038781836500, 0,
+        -205277590220215081719131470288800, 0,
+        9330799555464321896324157740400, 0,
+        -304114948474392713657972548576, 0,
+        6695289961520387531608984680, 0,
+        -91048139350447232095702560, 0,
+        659769125727878493447120, 0,
+        -1905929106580294155360, 0,
+        916312070471295267]
+
+    roots_init =  matrix(['-0.999', '-0.996',  '-0.991', '-0.983', '-0.973',
+                          '-0.961', '-0.946',  '-0.93',  '-0.911', '-0.889',
+                          '-0.866', '-0.841',  '-0.813', '-0.784', '-0.753',
+                          '-0.72',  '-0.685',  '-0.649', '-0.611', '-0.572',
+                          '-0.531', '-0.489',  '-0.446', '-0.402', '-0.357',
+                          '-0.311', '-0.265',  '-0.217', '-0.17',  '-0.121',
+                          '-0.073', '-0.0243',  '0.0243', '0.073',  '0.121',
+                          '0.17',    '0.217',   '0.265', ' 0.311',  '0.357',
+                          '0.402',   '0.446',   '0.489',  '0.531',  '0.572',
+                          '0.611',   '0.649',   '0.685',  '0.72',   '0.753',
+                          '0.784',   '0.813',   '0.841',  '0.866',  '0.889',
+                          '0.911',   '0.93',    '0.946',  '0.961',  '0.973',
+                          '0.983',   '0.991',   '0.996',  '0.999',  '1.0'])
+    with mp.workdps(2*mp.dps):
+        roots_exact = polyroots(coeffs, maxsteps=50, cleanup=True, error=False,
+                                extraprec=2*extra_prec)
+    with pytest.raises(mp.NoConvergence):
+        polyroots(coeffs, maxsteps=5, cleanup=True, error=False,
+                  extraprec=extra_prec)
+    roots,err = polyroots(coeffs, maxsteps=5, cleanup=True, error=True,
+                          extraprec=extra_prec,roots_init=roots_init)
+    assert max(matrix(roots_exact)-matrix(roots).apply(abs)) < err
+    roots1,err1 = polyroots(coeffs, maxsteps=25, cleanup=True, error=True,
+                            extraprec=extra_prec,roots_init=roots_init[:60])
+    assert max(matrix(roots_exact)-matrix(roots1).apply(abs)) < err1
+
+def test_pade():
+    one = mpf(1)
+    mp.dps = 20
+    N = 10
+    a = [one]
+    k = 1
+    for i in range(1, N+1):
+        k *= i
+        a.append(one/k)
+    p, q = pade(a, N//2, N//2)
+    for x in arange(0, 1, 0.1):
+        r = polyval(p[::-1], x)/polyval(q[::-1], x)
+        assert(r.ae(exp(x), 1.0e-10))
+    mp.dps = 15
+
+def test_fourier():
+    mp.dps = 15
+    c, s = fourier(lambda x: x+1, [-1, 2], 2)
+    #plot([lambda x: x+1, lambda x: fourierval((c, s), [-1, 2], x)], [-1, 2])
+    assert c[0].ae(1.5)
+    assert c[1].ae(-3*sqrt(3)/(2*pi))
+    assert c[2].ae(3*sqrt(3)/(4*pi))
+    assert s[0] == 0
+    assert s[1].ae(3/(2*pi))
+    assert s[2].ae(3/(4*pi))
+    assert fourierval((c, s), [-1, 2], 1).ae(1.9134966715663442)
+
+def test_differint():
+    mp.dps = 15
+    assert differint(lambda t: t, 2, -0.5).ae(8*sqrt(2/pi)/3)
+
+def test_invlap():
+    mp.dps = 15
+    t = 0.01
+    fp = lambda p: 1/(p+1)**2
+    ft = lambda t: t*exp(-t)
+    ftt = ft(t)
+    assert invertlaplace(fp,t,method='talbot').ae(ftt)
+    assert invertlaplace(fp,t,method='stehfest').ae(ftt)
+    assert invertlaplace(fp,t,method='dehoog').ae(ftt)
+    assert invertlaplace(fp,t,method='cohen').ae(ftt)
+    t = 1.0
+    ftt = ft(t)
+    assert invertlaplace(fp,t,method='talbot').ae(ftt)
+    assert invertlaplace(fp,t,method='stehfest').ae(ftt)
+    assert invertlaplace(fp,t,method='dehoog').ae(ftt)
+    assert invertlaplace(fp,t,method='cohen').ae(ftt)
+
+    t = 0.01
+    fp = lambda p: log(p)/p
+    ft = lambda t: -euler-log(t)
+    ftt = ft(t)
+    assert invertlaplace(fp,t,method='talbot').ae(ftt)
+    assert invertlaplace(fp,t,method='stehfest').ae(ftt)
+    assert invertlaplace(fp,t,method='dehoog').ae(ftt)
+    assert invertlaplace(fp,t,method='cohen').ae(ftt)
+    t = 1.0
+    ftt = ft(t)
+    assert invertlaplace(fp,t,method='talbot').ae(ftt)
+    assert invertlaplace(fp,t,method='stehfest').ae(ftt)
+    assert invertlaplace(fp,t,method='dehoog').ae(ftt)
+    assert invertlaplace(fp,t,method='cohen').ae(ftt)