def testUtily(self):
# Python 2.6.9 on Travis Ubuntu 14.04 produces -0.0
self.test('degrees90(PI_2)', degrees90(PI_2), 90.0)
self.test('degrees90(PI)', degrees90(PI), -180.0) # XXX
self.test('degrees90(PI2)', degrees90(PI2), 0.0)
self.test('degrees90(-PI_2)', degrees90(-PI_2), -90.0)
self.test('degrees90(-PI)', degrees90(-PI), -180.0) # XXX
self.test('degrees90(-PI2)', abs(degrees90(-PI2)), 0.0) # -0.0
self.test('degrees180(PI_2)', degrees180(PI_2), 90.0)
self.test('degrees180(PI)', degrees180(PI), 180.0) # XXX
self.test('degrees180(PI2)', degrees180(PI2), 0.0)
self.test('degrees180(-PI_2)', degrees180(-PI_2), -90.0)
self.test('degrees180(-PI)', degrees180(-PI), -180.0) # XXX
self.test('degrees180(-PI2)', abs(degrees180(-PI2)), 0.0) # -0.0
self.test('degrees360(PI_2)', degrees360(PI_2), 90.0)
self.test('degrees360(PI)', degrees360(PI), 180.0) # XXX
self.test('degrees360(PI2)', degrees360(PI2), 0.0)
self.test('degrees360(-PI_2)', degrees360(-PI_2), 270.0)
self.test('degrees360(-PI)', degrees360(-PI), 180.0) # XXX
self.test('degrees360(-PI2)', abs(degrees360(-PI2)), 0.0) # -0.0
self.test('radiansPI_2(90)', radiansPI_2(90), PI_2)
self.test('radiansPI_2(180)', radiansPI_2(180), -PI)
self.test('radiansPI_2(360)', radiansPI_2(360), 0.0)
self.test('radiansPI_2(-90)', radiansPI_2(-90), -PI_2)
self.test('radiansPI_2(-180)', radiansPI_2(-180), -PI)
self.test('radiansPI_2(-360)', abs(radiansPI_2(-360)), 0.0) # -0.0
self.test('radiansPI(90)', radiansPI(90), PI_2)
self.test('radiansPI(180)', radiansPI(180), PI)
self.test('radiansPI(360)', radiansPI(360), 0.0)
self.test('radiansPI(-90)', radiansPI(-90), -PI_2)
self.test('radiansPI(-180)', radiansPI(-180), -PI)
self.test('radiansPI(-360)', abs(radiansPI(-360)), 0.0) # -0.0
self.test('radiansPI2(90)', radiansPI2(90), PI_2)
self.test('radiansPI2(180)', radiansPI2(180), PI)
self.test('radiansPI2(360)', radiansPI2(360), 0.0)
self.test('radiansPI2(-90)', radiansPI2(-90), PI_2+PI)
self.test('radiansPI2(-180)', radiansPI2(-180), PI)
self.test('radiansPI2(-360)', abs(radiansPI2(-360)), 0.0) # -0.0
self.test('wrap90(90)', wrap90(90), 90)
self.test('wrap90(180)', wrap90(180), -180)
self.test('wrap90(360)', wrap90(360), 0)
self.test('wrap90(-90)', wrap90(-90), -90)
self.test('wrap90(-180)', wrap90(-180), -180)
self.test('wrap90(-360)', wrap90(-360), 0)
self.test('wrap180(90)', wrap180(90), 90)
self.test('wrap180(180)', wrap180(180), 180)
self.test('wrap180(360)', wrap180(360), 0)
self.test('wrap180(-90)', wrap180(-90), -90)
self.test('wrap180(-180)', wrap180(-180), -180)
self.test('wrap180(-360)', wrap180(-360), 0)
self.test('wrap360(90)', wrap360(90), 90)
self.test('wrap360(180)', wrap360(180), 180)
self.test('wrap360(360)', wrap360(360), 0)
self.test('wrap360(-90)', wrap360(-90), 270)
self.test('wrap360(-180)', wrap360(-180), 180)
self.test('wrap360(-360)', wrap360(-360), 0)
self.test('wrapPI_2(PI_2)', wrapPI_2(PI_2), PI_2)
self.test('wrapPI_2(PI)', wrapPI_2(PI), -PI) # XXX
self.test('wrapPI_2(PI2)', wrapPI_2(PI2), 0.0)
self.test('wrapPI_2(-PI_2)', wrapPI_2(-PI_2), -PI_2)
self.test('wrapPI_2(-PI)', wrapPI_2(-PI), -PI) # XXX
self.test('wrapPI_2(-PI2)', abs(wrapPI_2(-PI2)), 0.0)
self.test('wrapPI(PI_2)', wrapPI(PI_2), PI_2)
self.test('wrapPI(PI)', wrapPI(PI), PI) # XXX
self.test('wrapPI(PI2)', wrapPI(PI2), 0.0)
self.test('wrapPI(-PI_2)', wrapPI(-PI_2), -PI_2)
self.test('wrapPI(-PI)', wrapPI(-PI), -PI) # XXX
self.test('wrapPI(-PI2)', abs(wrapPI(-PI2)), 0.0) # -0.0
self.test('wrapPI2(PI_2)', wrapPI2(PI_2), PI_2)
self.test('wrapPI2(PI)', wrapPI2(PI), PI) # XXX
self.test('wrapPI2(PI2)', wrapPI2(PI2), 0.0)
self.test('wrapPI2(-PI_2)', wrapPI2(-PI_2), PI_2+PI)
self.test('wrapPI2(-PI)', wrapPI2(-PI), PI) # XXX
self.test('wrapPI2(-PI2)', abs(wrapPI2(-PI2)), 0.0) # -0.0
self.test('unroll180', fStr(unroll180(-90, 110, wrap=True)), '-160.0, -250.0')
self.test('unroll180', fStr(unroll180(-90, 110, wrap=False)), '200.0, 110.0')
self.test('unroll180', fStr(unroll180(-90, 830, wrap=True)), '-160.0, -250.0')
self.test('unroll180', fStr(unroll180(-90, 830, wrap=False)), '920.0, 830.0')
self.test('unroll180', fStr(unroll180(-110, 90, wrap=True)), '-160.0, -270.0')
self.test('unroll180', fStr(unroll180(-110, 90, wrap=False)), '200.0, 90.0')
self.test('unroll180', fStr(unroll180(-830, 90, wrap=True)), '-160.0, -990.0')
self.test('unroll180', fStr(unroll180(-830, 90, wrap=False)), '920.0, 90.0')
e = d = g = f = 0
for a in range(-1000, 1000):
a *= 0.47
r = radians(a)
sr, cr = sin(r), cos(r)
s, c = sincos2(r)
e = max(e, abs(sr - s), abs(cr - c))
sd, cd = sincos2d(a)
d = max(d, abs(sr - sd), abs(cr - cd))
if sincosd: # compare with geographiclib
s, c = sincosd(a)
g = max(g, abs(sr - s), abs(cr - c))
f = max(f, abs(sd - s), abs(cd - c))
EPS_ = EPS * 8
self.test('sincos2', e, EPS, known=e < EPS_)
self.test('sincos2d', d, EPS, known=d < EPS_)
if sincosd:
self.test('sincosd ', g, EPS, known=g < EPS_)
self.test('sincos*d', f, EPS, known=f < EPS_)
a, b = splice(range(10)) # PYCHOK false
self.test('splice', (a, b), map1(type(a), (0, 2, 4, 6, 8), (1, 3, 5, 7, 9)))
a, b, c = splice(range(10), n=3) # PYCHOK false
self.test('splice', (a, b, c), map1(type(a), (0, 3, 6, 9), (1, 4, 7), (2, 5, 8)))
a, b, c = splice(range(10), n=3, fill=-1) # PYCHOK false
self.test('splice', (a, b, c), map1(type(a), (0, 3, 6, 9), (1, 4, 7, -1), (2, 5, 8, -1)))
t = tuple(splice(range(12), n=5)) # PYCHOK false
self.test('splice', t, map1(type(t[0]), (0, 5, 10), (1, 6, 11), (2, 7), (3, 8), (4, 9)))
# <https://www.CivilGeo.com/when-a-foot-isnt-really-a-foot/>
self.test('iFt2m', ft2m(614963.91), 187441, fmt='%.0f')
self.test('iFt2m', ft2m(2483759.84), 757050, fmt='%.0f')
self.test('sFt2m', ft2m(614962.68, usurvey=True), 187441, fmt='%.0f')
self.test('sFt2m', ft2m(2483754.87, usurvey=True), 757050, fmt='%.0f')
self.test('m2iFt', m2ft(187441), 614963.91, fmt='%.0f')
self.test('m2iFt', m2ft(757050), 2483759.84, fmt='%.0f')
self.test('m2sFt', m2ft(187441, usurvey=True), 614962.68, fmt='%.0f')
self.test('m2sFt', m2ft(757050, usurvey=True), 2483754.87, fmt='%.0f')
def testUtily(self):
# Python 2.6.9 on Travis Ubuntu 14.04 produces -0.0
self.test('degrees90(PI_2)', degrees90(PI_2), 90.0)
self.test('degrees90(PI)', degrees90(PI), -180.0) # XXX
self.test('degrees90(PI2)', degrees90(PI2), 0.0)
self.test('degrees90(-PI_2)', degrees90(-PI_2), -90.0)
self.test('degrees90(-PI)', degrees90(-PI), -180.0) # XXX
self.test('degrees90(-PI2)', abs(degrees90(-PI2)), 0.0) # -0.0
self.test('degrees180(PI_2)', degrees180(PI_2), 90.0)
self.test('degrees180(PI)', degrees180(PI), 180.0) # XXX
self.test('degrees180(PI2)', degrees180(PI2), 0.0)
self.test('degrees180(-PI_2)', degrees180(-PI_2), -90.0)
self.test('degrees180(-PI)', degrees180(-PI), -180.0) # XXX
self.test('degrees180(-PI2)', abs(degrees180(-PI2)), 0.0) # -0.0
self.test('degrees360(PI_2)', degrees360(PI_2), 90.0)
self.test('degrees360(PI)', degrees360(PI), 180.0) # XXX
self.test('degrees360(PI2)', degrees360(PI2), 0.0)
self.test('degrees360(-PI_2)', degrees360(-PI_2), 270.0)
self.test('degrees360(-PI)', degrees360(-PI), 180.0) # XXX
self.test('degrees360(-PI2)', abs(degrees360(-PI2)), 0.0) # -0.0
self.test('radiansPI_2(90)', radiansPI_2(90), PI_2)
self.test('radiansPI_2(180)', radiansPI_2(180), -PI)
self.test('radiansPI_2(360)', radiansPI_2(360), 0.0)
self.test('radiansPI_2(-90)', radiansPI_2(-90), -PI_2)
self.test('radiansPI_2(-180)', radiansPI_2(-180), -PI)
self.test('radiansPI_2(-360)', abs(radiansPI_2(-360)), 0.0) # -0.0
self.test('radiansPI(90)', radiansPI(90), PI_2)
self.test('radiansPI(180)', radiansPI(180), PI)
self.test('radiansPI(360)', radiansPI(360), 0.0)
self.test('radiansPI(-90)', radiansPI(-90), -PI_2)
self.test('radiansPI(-180)', radiansPI(-180), -PI)
self.test('radiansPI(-360)', abs(radiansPI(-360)), 0.0) # -0.0
self.test('radiansPI2(90)', radiansPI2(90), PI_2)
self.test('radiansPI2(180)', radiansPI2(180), PI)
self.test('radiansPI2(360)', radiansPI2(360), 0.0)
self.test('radiansPI2(-90)', radiansPI2(-90), PI_2 + PI)
self.test('radiansPI2(-180)', radiansPI2(-180), PI)
self.test('radiansPI2(-360)', abs(radiansPI2(-360)), 0.0) # -0.0
self.test('wrap90(90)', wrap90(90), 90)
self.test('wrap90(180)', wrap90(180), -180)
self.test('wrap90(360)', wrap90(360), 0)
self.test('wrap90(-90)', wrap90(-90), -90)
self.test('wrap90(-180)', wrap90(-180), -180)
self.test('wrap90(-360)', wrap90(-360), 0)
self.test('wrap180(90)', wrap180(90), 90)
self.test('wrap180(180)', wrap180(180), 180)
self.test('wrap180(360)', wrap180(360), 0)
self.test('wrap180(-90)', wrap180(-90), -90)
self.test('wrap180(-180)', wrap180(-180), -180)
self.test('wrap180(-360)', wrap180(-360), 0)
self.test('wrap360(90)', wrap360(90), 90)
self.test('wrap360(180)', wrap360(180), 180)
self.test('wrap360(360)', wrap360(360), 0)
self.test('wrap360(-90)', wrap360(-90), 270)
self.test('wrap360(-180)', wrap360(-180), 180)
self.test('wrap360(-360)', wrap360(-360), 0)
self.test('wrapPI_2(PI_2)', wrapPI_2(PI_2), PI_2)
self.test('wrapPI_2(PI)', wrapPI_2(PI), -PI) # XXX
self.test('wrapPI_2(PI2)', wrapPI_2(PI2), 0.0)
self.test('wrapPI_2(-PI_2)', wrapPI_2(-PI_2), -PI_2)
self.test('wrapPI_2(-PI)', wrapPI_2(-PI), -PI) # XXX
self.test('wrapPI_2(-PI2)', abs(wrapPI_2(-PI2)), 0.0)
self.test('wrapPI(PI_2)', wrapPI(PI_2), PI_2)
self.test('wrapPI(PI)', wrapPI(PI), PI) # XXX
self.test('wrapPI(PI2)', wrapPI(PI2), 0.0)
self.test('wrapPI(-PI_2)', wrapPI(-PI_2), -PI_2)
self.test('wrapPI(-PI)', wrapPI(-PI), -PI) # XXX
self.test('wrapPI(-PI2)', abs(wrapPI(-PI2)), 0.0) # -0.0
self.test('wrapPI2(PI_2)', wrapPI2(PI_2), PI_2)
self.test('wrapPI2(PI)', wrapPI2(PI), PI) # XXX
self.test('wrapPI2(PI2)', wrapPI2(PI2), 0.0)
self.test('wrapPI2(-PI_2)', wrapPI2(-PI_2), PI_2 + PI)
self.test('wrapPI2(-PI)', wrapPI2(-PI), PI) # XXX
self.test('wrapPI2(-PI2)', abs(wrapPI2(-PI2)), 0.0) # -0.0
self.test('unroll180', fstr(unroll180(-90, 110, wrap=True)),
'-160.0, -250.0')
self.test('unroll180', fstr(unroll180(-90, 110, wrap=False)),
'200.0, 110.0')
self.test('unroll180', fstr(unroll180(-90, 830, wrap=True)),
'-160.0, -250.0')
self.test('unroll180', fstr(unroll180(-90, 830, wrap=False)),
'920.0, 830.0')
self.test('unroll180', fstr(unroll180(-110, 90, wrap=True)),
'-160.0, -270.0')
self.test('unroll180', fstr(unroll180(-110, 90, wrap=False)),
'200.0, 90.0')
self.test('unroll180', fstr(unroll180(-830, 90, wrap=True)),
'-160.0, -990.0')
self.test('unroll180', fstr(unroll180(-830, 90, wrap=False)),
'920.0, 90.0')
e = d = g = f = 0
for a in range(-1000, 1000):
a *= 0.47
r = radians(a)
sr, cr = sin(r), cos(r)
s, c = sincos2(r)
e = max(e, abs(sr - s), abs(cr - c))
sd, cd = sincos2d(a)
d = max(d, abs(sr - sd), abs(cr - cd))
if sincosd: # compare with geographiclib
s, c = sincosd(a)
g = max(g, abs(sr - s), abs(cr - c))
f = max(f, abs(sd - s), abs(cd - c))
EPS_ = EPS * 8
self.test('sincos2', e, EPS, known=e < EPS_)
self.test('sincos2d', d, EPS, known=d < EPS_)
if sincosd:
self.test('sincosd ', g, EPS, known=g < EPS_)
self.test('sincos*d', f, EPS, known=f < EPS_)
# <https://www.CivilGeo.com/when-a-foot-isnt-really-a-foot/>
self.test('iFt2m', ft2m(614963.91), 187441, fmt='%.0f')
self.test('iFt2m', ft2m(2483759.84), 757050, fmt='%.0f')
self.test('sFt2m', ft2m(614962.68, usurvey=True), 187441, fmt='%.0f')
self.test('sFt2m', ft2m(2483754.87, usurvey=True), 757050, fmt='%.0f')
self.test('m2iFt', m2ft(187441), 614963.91, fmt='%.0f')
self.test('m2iFt', m2ft(757050), 2483759.84, fmt='%.0f')
self.test('m2sFt', m2ft(187441, usurvey=True), 614962.68, fmt='%.0f')
self.test('m2sFt', m2ft(757050, usurvey=True), 2483754.87, fmt='%.0f')
self.test('degrees2m', fstr(degrees2m(90), prec=4), '10007557.1761')
self.test('degrees2m', fstr(degrees2m(90, lat=30), prec=4),
'8666798.7443')
self.test('m2degrees', fstr(m2degrees(degrees2m(90)), prec=1), '90.0')
self.test('degrees2m', fstr(degrees2m(180), prec=4), '20015114.3522')
self.test('degrees2m', fstr(degrees2m(180, lat=3 - 0), prec=4),
'19987684.3336')
self.test('m2degrees', fstr(m2degrees(degrees2m(180)), prec=1),
'180.0')
for a in range(0, 90, 7):
d = m2degrees(degrees2m(45, lat=a), lat=a)
self.test('m2-degrees-2m(%s, lat=%s)' % (45, a),
d,
'45.00',
fmt='%.2f')
self.test('isPoints2', isPoints2(None), False)
def testElliptic(self):
RC = elliptic._RC
RD = elliptic._RD
RF = elliptic._RF
RG = elliptic._RG
RJ = elliptic._RJ
eps4 = EPS * 4
self.test('eps4', eps4, eps4, fmt='%.9e')
y = 0.1
for x in range(2, 100):
x *= 0.01
rc = RC(x, y)
rf = RF(x, y, y)
k = abs(rc - rf) < eps4
t = 'RC, RF(%.3f, ...)' % (x, )
self.test(t, rc, rf, fmt='%.12f', known=k)
y = x
for kp2 in range(1, 100):
kp2 *= 0.01
rd = RD(0, kp2, 1)
rj = RJ(0, kp2, 1, 1)
k = abs(rd - rj) < eps4
t = 'RD, RJ(%.3f, ...)' % (kp2, )
self.test(t, rd, rj, fmt='%.12f', known=k)
self.test('eps4', eps4, eps4, fmt='%.9e', nl=1)
# <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1EllipticFunction.html>
e = elliptic.Elliptic(0.1)
self.test('cK', e.cK, '1.612441349', fmt='%.9f')
self.test('cE', e.cE, '1.530757637', fmt='%.9f')
self.test('eps', e.eps, '0.0263340', fmt='%.7f')
phi = radians(20)
sn, cn = sincos2(phi)
self.test('fE(phi)', e.fE(phi), '0.348372822', fmt='%.9f')
dn = e.fDelta(sn, cn)
self.test('fDelta(sn, cn)', dn, '0.994133906', fmt='%.9f')
self.test('fD(sn, cn, dn)',
e.fD(sn, cn, dn),
'0.013885234',
fmt='%.9f')
self.test('fE(sn, cn, dn)',
e.fE(sn, cn, dn),
'0.348372822',
fmt='%.9f')
self.test('fEd(PI_2)', e.fEd(PI_2), '0.027415224', fmt='%.9f')
self.test('fEinv(PI_2)', e.fEinv(PI_2), '1.612999420', fmt='%.9f')
self.test('fF(sn, cn, dn)',
e.fF(sn, cn, dn),
'0.349761345',
fmt='%.9f')
self.test('fG(sn, cn, dn)',
e.fG(sn, cn, dn),
'0.348372822',
fmt='%.9f')
self.test('fH(sn, cn, dn)',
e.fH(sn, cn, dn),
'0.363646580',
fmt='%.9f')
self.test('fPi(sn, cn, dn)',
e.fPi(sn, cn, dn),
'0.349761345',
fmt='%.9f')
try:
t = e.fPi(0, None, 1)
except EllipticError as x:
t = str(x)
self.test('fPi(sn, None, dn)', t,
'invokation Elliptic.fPi(0, None, 1): invalid')
try:
t = e.fPi(0, 1, None)
except EllipticError as x:
t = str(x)
self.test('fPi(sn, dn, None)', t,
'invokation Elliptic.fPi(0, 1, None): invalid')
self.test('deltaD(sn, cn, dn)',
e.deltaD(sn, cn, dn),
'-0.3223642',
fmt='%.7f',
nl=1)
self.test('deltaE(sn, cn, dn)',
e.deltaE(sn, cn, dn),
'0.0084191',
fmt='%.7f')
self.test('deltaEinv(sn, cn)',
e.deltaEinv(sn, cn),
'-0.0082518',
fmt='%.7f')
self.test('deltaF(sn, cn, dn)',
e.deltaF(sn, cn, dn),
'-0.0083379',
fmt='%.7f')
self.test('deltaG(sn, cn, dn)',
e.deltaG(sn, cn, dn),
'0.0084191',
fmt='%.7f')
self.test('deltaH(sn, cn, dn)',
e.deltaH(sn, cn, dn),
'0.3688975',
fmt='%.7f')
self.test('deltaPi(sn, cn, dn)',
e.deltaPi(sn, cn, dn),
'-0.0083379',
fmt='%.7f')
try:
t = e.deltaPi(0, None, 1)
except EllipticError as x:
t = str(x)
self.test('deltaPi(sn, None, dn)', t,
'invokation Elliptic.deltaPi(0, None, 1): invalid')
try:
t = e.deltaPi(0, 1, None)
except EllipticError as x:
t = str(x)
self.test('deltaPi(sn, dn, None)', t,
'invokation Elliptic.deltaPi(0, 1, None): invalid')
# U{Carlson<https://ArXiv.org/pdf/math/9409227.pdf>} 3 Numerical checks
self.test('RF(1, 2, 0)',
RF(1, 2, 0),
'1.3110287771461',
fmt='%.13f',
nl=1)
self.test('RF(2, 3, 4)', RF(2, 3, 4), '0.58408284167715', fmt='%.14f')
self.test('RC(0, 1/4)', RC(0, 0.25), '3.1415926535898',
fmt='%.13f') # PI
self.test('RC(9/4, 2)', RC(2.25, 2), '0.69314718055995',
fmt='%.14f') # ln(2)
self.test('RJ(0, 1, 2, 3)',
RJ(0, 1, 2, 3),
'0.77688623778582',
fmt='%.14f')
self.test('RJ(2, 3, 4, 5)',
RJ(2, 3, 4, 5),
'0.14297579667157',
fmt='%.14f')
self.test('RD(0, 2, 1)', RD(0, 2, 1), '1.7972103521034', fmt='%.13f')
self.test('RD(2, 3, 4)', RD(2, 3, 4), '0.16510527294261', fmt='%.14f')
self.test('RG(0, 16, 16)',
RG(0, 16, 16),
'3.1415926535898',
fmt='%.13f') # PI
self.test('RG(2, 3, 4)', RG(2, 3, 4), '1.7255030280692', fmt='%.13f')
self.test('RG(0, 0.0796, 4)',
RG(0, 0.0796, 4),
'1.0284758090288',
fmt='%.13f')
e.reset(0, 0)
self.test('sncndn(x)',
fstr(e.sncndn(0), prec=9),
'0.0, 1.0, 1.0',
nl=1)
self.test('sncndn(x)',
fstr(e.sncndn(PI_2), prec=9),
'1.0, -0.0, 1.0',
known=True)
e.reset(1, 1)
self.test('sncndn(x)', fstr(e.sncndn(0), prec=9), '0.0, 1.0, 1.0')
self.test('sncndn(x)', fstr(e.sncndn(PI_2), prec=9),
'0.917152336, 0.398536815, 0.398536815')
self.test('sncndn(x)', type(e.sncndn(PI_4)), elliptic.Elliptic3Tuple)
self.testCopy(e)
for f in range(4): # coverage
t = (f / 4.0, ) * 4
e = elliptic.Elliptic(*t)
s = 'k2 alpha2 kp2 alphap2'
e = tuple(getattr(e, a) for a in s.split())
t = tuple(Scalar(f, name=n) for n, f in zip(s.split(), t))
self.test(s, e, t)
def testElliptic(self):
_RC = elliptic._RC
_RD = elliptic._RD
_RF = elliptic._RF
_RG = elliptic._RG
_RJ = elliptic._RJ
eps = EPS * 4
self.test('eps', eps, eps, fmt='%.12e')
y = 0.1
for x in range(2, 100):
x *= 0.01
rc = _RC(x, y)
rf = _RF(x, y, y)
k = abs(rc - rf) < eps
t = '_RC, _RF(%.3f, ...)' % (x, )
self.test(t, rc, rf, fmt='%.12f', known=k)
y = x
for kp2 in range(1, 100):
kp2 *= 0.01
rd = _RD(0, kp2, 1)
rj = _RJ(0, kp2, 1, 1)
k = abs(rd - rj) < eps
t = '_RD, _RJ(%.3f, ...)' % (kp2, )
self.test(t, rd, rj, fmt='%.12f', known=k)
self.test('eps', eps, eps, fmt='%.12e')
# <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1EllipticFunction.html>
e = elliptic.Elliptic(0.1)
self.test('cK', e.cK, '1.612441349', fmt='%.9f')
self.test('cE', e.cE, '1.530757637', fmt='%.9f')
phi = radians(20)
sn, cn = sincos2(phi)
self.test('fE(phi)', e.fE(phi), '0.348372822', fmt='%.9f')
dn = e.fDelta(sn, cn)
self.test('fDelta', dn, '0.994133906', fmt='%.9f')
self.test('fE(sn, cn, Delta)',
e.fE(sn, cn, dn),
'0.348372822',
fmt='%.9f')
self.test('fEd(PI_2)', e.fEd(PI_2), '0.027415224', fmt='%.9f')
self.test('fEinv(PI_2)', e.fEinv(PI_2), '1.612999420', fmt='%.9f')
self.test('fF(sn, cn, dn)',
e.fF(sn, cn, dn),
'0.349761345',
fmt='%.9f')
self.test('fG(sn, cn, dn)',
e.fG(sn, cn, dn),
'0.348372822',
fmt='%.9f')
self.test('fH(sn, cn, dn)',
e.fH(sn, cn, dn),
'0.363646580',
fmt='%.9f')
self.test('fPi(sn, cn, dn)',
e.fPi(sn, cn, dn),
'0.349761345',
fmt='%.9f')
self.test('_RF(1, 2, 0)', _RF(1, 2, 0), '1.311028777', fmt='%.9f')
self.test('_RF(2, 3, 4)', _RF(2, 3, 4), '0.584082842', fmt='%.9f')
self.test('_RC(0, 1/4)', _RC(0, 0.25), '3.141592654', fmt='%.9f')
self.test('_RC(9/4, 2)', _RC(2.25, 2), '0.693147181', fmt='%.9f')
self.test('_RC(1/4,-2)', _RC(0.25, -2), '0.231049060', fmt='%.9f')
self.test('_RJ(0, 1, 2, 3)',
_RJ(0, 1, 2, 3),
'0.776886238',
fmt='%.9f')
self.test('_RJ(2, 3, 4, 5)',
_RJ(2, 3, 4, 5),
'0.142975797',
fmt='%.9f')
self.test('_RD(0, 2, 1)', _RD(0, 2, 1), '1.797210352', fmt='%.9f')
self.test('_RD(2, 3, 4)', _RD(2, 3, 4), '0.165105273', fmt='%.9f')
self.test('_RG(0, 16, 16)', _RG(0, 16, 16), '3.141592654', fmt='%.9f')
self.test('_RG(2, 3, 4)', _RG(2, 3, 4), '1.725503028', fmt='%.9f')
self.test('_RG(0, 0.0796, 4)',
_RG(0, 0.0796, 4),
'1.028475809',
fmt='%.9f')
e.reset(0, 0)
self.test('sncndn(x)', fStr(e.sncndn(0), prec=9), '0.0, 1.0, 1.0')
self.test('sncndn(x)',
fStr(e.sncndn(PI_2), prec=9),
'1.0, -0.0, 1.0',
known=True)
e.reset(1, 1)
self.test('sncndn(x)', fStr(e.sncndn(0), prec=9), '0.0, 1.0, 1.0')
self.test('sncndn(x)', fStr(e.sncndn(PI_2), prec=9),
'0.917152336, 0.398536815, 0.398536815')
def testUtily(self):
# Python 2.6.9 on Travis Ubuntu 14.04 produces -0.0
self.test('degrees90(PI_2)', degrees90(PI_2), 90.0)
self.test('degrees90(PI)', degrees90(PI), -180.0) # XXX
self.test('degrees90(PI2)', degrees90(PI2), 0.0)
self.test('degrees90(-PI_2)', degrees90(-PI_2), -90.0)
self.test('degrees90(-PI)', degrees90(-PI), -180.0) # XXX
self.test('degrees90(-PI2)', abs(degrees90(-PI2)), 0.0) # -0.0
self.test('degrees180(PI_2)', degrees180(PI_2), 90.0)
self.test('degrees180(PI)', degrees180(PI), 180.0) # XXX
self.test('degrees180(PI2)', degrees180(PI2), 0.0)
self.test('degrees180(-PI_2)', degrees180(-PI_2), -90.0)
self.test('degrees180(-PI)', degrees180(-PI), -180.0) # XXX
self.test('degrees180(-PI2)', abs(degrees180(-PI2)), 0.0) # -0.0
self.test('degrees360(PI_2)', degrees360(PI_2), 90.0)
self.test('degrees360(PI)', degrees360(PI), 180.0) # XXX
self.test('degrees360(PI2)', degrees360(PI2), 0.0)
self.test('degrees360(-PI_2)', degrees360(-PI_2), 270.0)
self.test('degrees360(-PI)', degrees360(-PI), 180.0) # XXX
self.test('degrees360(-PI2)', abs(degrees360(-PI2)), 0.0) # -0.0
self.test('radiansPI_2(90)', radiansPI_2(90), PI_2)
self.test('radiansPI_2(180)', radiansPI_2(180), -PI)
self.test('radiansPI_2(360)', radiansPI_2(360), 0.0)
self.test('radiansPI_2(-90)', radiansPI_2(-90), -PI_2)
self.test('radiansPI_2(-180)', radiansPI_2(-180), -PI)
self.test('radiansPI_2(-360)', abs(radiansPI_2(-360)), 0.0) # -0.0
self.test('radiansPI(90)', radiansPI(90), PI_2)
self.test('radiansPI(180)', radiansPI(180), PI)
self.test('radiansPI(360)', radiansPI(360), 0.0)
self.test('radiansPI(-90)', radiansPI(-90), -PI_2)
self.test('radiansPI(-180)', radiansPI(-180), -PI)
self.test('radiansPI(-360)', abs(radiansPI(-360)), 0.0) # -0.0
self.test('radiansPI2(90)', radiansPI2(90), PI_2)
self.test('radiansPI2(180)', radiansPI2(180), PI)
self.test('radiansPI2(360)', radiansPI2(360), 0.0)
self.test('radiansPI2(-90)', radiansPI2(-90), PI_2 + PI)
self.test('radiansPI2(-180)', radiansPI2(-180), PI)
self.test('radiansPI2(-360)', abs(radiansPI2(-360)), 0.0) # -0.0
self.test('wrap90(90)', wrap90(90), 90.0)
self.test('wrap90(180)', wrap90(180), -180.0)
self.test('wrap90(360)', wrap90(360), 0.0)
self.test('wrap90(-90)', wrap90(-90), -90.0)
self.test('wrap90(-180)', wrap90(-180), -180.0)
self.test('wrap90(-360)', wrap90(-360), 0.0)
self.test('wrap180(90)', wrap180(90), 90.0)
self.test('wrap180(180)', wrap180(180), 180.0)
self.test('wrap180(360)', wrap180(360), 0.0)
self.test('wrap180(-90)', wrap180(-90), -90.0)
self.test('wrap180(-180)', wrap180(-180), -180.0)
self.test('wrap180(-360)', wrap180(-360), 0.0)
self.test('wrap360(90)', wrap360(90), 90.0)
self.test('wrap360(180)', wrap360(180), 180.0)
self.test('wrap360(360)', wrap360(360), 0.0)
self.test('wrap360(-90)', wrap360(-90), 270.0)
self.test('wrap360(-180)', wrap360(-180), 180.0)
self.test('wrap360(-360)', wrap360(-360), 0.0)
self.test('wrapPI_2(PI_2)', wrapPI_2(PI_2), PI_2)
self.test('wrapPI_2(PI)', wrapPI_2(PI), -PI) # XXX
self.test('wrapPI_2(PI2)', wrapPI_2(PI2), 0.0)
self.test('wrapPI_2(-PI_2)', wrapPI_2(-PI_2), -PI_2)
self.test('wrapPI_2(-PI)', wrapPI_2(-PI), -PI) # XXX
self.test('wrapPI_2(-PI2)', abs(wrapPI_2(-PI2)), 0.0)
self.test('wrapPI(PI_2)', wrapPI(PI_2), PI_2)
self.test('wrapPI(PI)', wrapPI(PI), PI) # XXX
self.test('wrapPI(PI2)', wrapPI(PI2), 0.0)
self.test('wrapPI(-PI_2)', wrapPI(-PI_2), -PI_2)
self.test('wrapPI(-PI)', wrapPI(-PI), -PI) # XXX
self.test('wrapPI(-PI2)', abs(wrapPI(-PI2)), 0.0) # -0.0
self.test('wrapPI2(PI_2)', wrapPI2(PI_2), PI_2)
self.test('wrapPI2(PI)', wrapPI2(PI), PI) # XXX
self.test('wrapPI2(PI2)', wrapPI2(PI2), 0.0)
self.test('wrapPI2(-PI_2)', wrapPI2(-PI_2), PI_2 + PI)
self.test('wrapPI2(-PI)', wrapPI2(-PI), PI) # XXX
self.test('wrapPI2(-PI2)', abs(wrapPI2(-PI2)), 0.0) # -0.0
self.test('unroll180', fstr(unroll180(-90, 110, wrap=True)),
'-160.0, -250.0')
self.test('unroll180', fstr(unroll180(-90, 110, wrap=False)),
'200.0, 110.0')
self.test('unroll180', fstr(unroll180(-90, 830, wrap=True)),
'-160.0, -250.0')
self.test('unroll180', fstr(unroll180(-90, 830, wrap=False)),
'920.0, 830.0')
self.test('unroll180', fstr(unroll180(-110, 90, wrap=True)),
'-160.0, -270.0')
self.test('unroll180', fstr(unroll180(-110, 90, wrap=False)),
'200.0, 90.0')
self.test('unroll180', fstr(unroll180(-830, 90, wrap=True)),
'-160.0, -990.0')
self.test('unroll180', fstr(unroll180(-830, 90, wrap=False)),
'920.0, 90.0')
e = d = g = f = t = 0
for a in range(-1000, 1000, 2):
a *= 0.47
r = radians(a)
sr, cr = sin(r), cos(r)
s, c = sincos2(r)
e = max(e, abs(sr - s), abs(cr - c))
sd, cd = sincos2d(a)
d = max(d, abs(sr - sd), abs(cr - cd))
if Math: # compare with geographiclib
t = max(t, abs(atan2d(sr, cr) - atand(sr, cr)))
s, c = sincosd(a)
g = max(g, abs(sr - s), abs(cr - c))
f = max(f, abs(sd - s), abs(cd - c))
EPS_ = EPS * 8
self.test('sincos2', e, EPS_, known=e < EPS_)
self.test('sincos2d', d, EPS_, known=d < EPS_)
if Math:
self.test('atand', t, EPS, known=t < EPS)
self.test('sincosd ', g, EPS_, known=g < EPS_)
self.test('sincos*d', f, EPS_, known=f < EPS_)
# <https://www.CivilGeo.com/when-a-foot-isnt-really-a-foot/>
self.test('iFt2m', ft2m(614963.91), 187441, fmt='%.0f')
self.test('iFt2m', ft2m(2483759.84), 757050, fmt='%.0f')
self.test('sFt2m', ft2m(614962.68, usurvey=True), 187441, fmt='%.0f')
self.test('sFt2m', ft2m(2483754.87, usurvey=True), 757050, fmt='%.0f')
self.test('m2iFt', m2ft(187441), 614963.91, prec=2)
self.test('m2iFt', m2ft(757050), 2483759.84, prec=2)
self.test('m2sFt', m2ft(187441, usurvey=True), 614962.68, prec=2)
self.test('m2sFt', m2ft(757050, usurvey=True), 2483754.87, prec=2)
for f, m in ((m2yard, '1.093613'), (acre2ha, '0.404686'),
(acre2m2, '4046.856422'), (chain2m, '20.116800'),
(fathom2m, '1.828800'), (furlong2m, '201.168000'),
(yard2m, '0.914400')):
self.test(f.__name__, f(1), m, prec=6)
self.test('degrees2m', fstr(degrees2m(90), prec=4), '10007557.1761')
self.test('degrees2m', fstr(degrees2m(90, lat=30), prec=4),
'8666798.7443')
self.test('m2degrees', fstr(m2degrees(degrees2m(90)), prec=1), '90.0')
self.test('degrees2m', fstr(degrees2m(180), prec=4), '20015114.3522')
self.test('degrees2m', fstr(degrees2m(180, lat=3 - 0), prec=4),
'19987684.3336')
self.test('m2degrees', fstr(m2degrees(degrees2m(180)), prec=1),
'180.0')
t = 'm2degrees2m(%s, lat=%s)'
for a in range(0, 90, 7):
d = m2degrees(degrees2m(45, lat=a), lat=a)
self.test(t % (45, a), d, '45.00', prec=2)
self.test('isPoints2', isPoints2(None), False)
def testElliptic(self):
_RC = elliptic._RC
_RD = elliptic._RD
_RF = elliptic._RF
_RG = elliptic._RG
_RJ = elliptic._RJ
eps4 = EPS * 4
self.test('eps4', eps4, eps4, fmt='%.9e')
y = 0.1
for x in range(2, 100):
x *= 0.01
rc = _RC(x, y)
rf = _RF(x, y, y)
k = abs(rc - rf) < eps4
t = '_RC, _RF(%.3f, ...)' % (x, )
self.test(t, rc, rf, fmt='%.12f', known=k)
y = x
for kp2 in range(1, 100):
kp2 *= 0.01
rd = _RD(0, kp2, 1)
rj = _RJ(0, kp2, 1, 1)
k = abs(rd - rj) < eps4
t = '_RD, _RJ(%.3f, ...)' % (kp2, )
self.test(t, rd, rj, fmt='%.12f', known=k)
self.test('eps4', eps4, eps4, fmt='%.9e')
# <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1EllipticFunction.html>
e = elliptic.Elliptic(0.1)
self.test('cK', e.cK, '1.612441349', fmt='%.9f')
self.test('cE', e.cE, '1.530757637', fmt='%.9f')
self.test('eps', e.eps, '0.0263340', fmt='%.7f')
phi = radians(20)
sn, cn = sincos2(phi)
self.test('fE(phi)', e.fE(phi), '0.348372822', fmt='%.9f')
dn = e.fDelta(sn, cn)
self.test('fDelta(sn, cn)', dn, '0.994133906', fmt='%.9f')
self.test('fD(sn, cn, dn)',
e.fD(sn, cn, dn),
'0.013885234',
fmt='%.9f')
self.test('fE(sn, cn, dn)',
e.fE(sn, cn, dn),
'0.348372822',
fmt='%.9f')
self.test('fEd(PI_2)', e.fEd(PI_2), '0.027415224', fmt='%.9f')
self.test('fEinv(PI_2)', e.fEinv(PI_2), '1.612999420', fmt='%.9f')
self.test('fF(sn, cn, dn)',
e.fF(sn, cn, dn),
'0.349761345',
fmt='%.9f')
self.test('fG(sn, cn, dn)',
e.fG(sn, cn, dn),
'0.348372822',
fmt='%.9f')
self.test('fH(sn, cn, dn)',
e.fH(sn, cn, dn),
'0.363646580',
fmt='%.9f')
self.test('fPi(sn, cn, dn)',
e.fPi(sn, cn, dn),
'0.349761345',
fmt='%.9f')
try:
t = e.fPi(0, None, 1)
except EllipticError as x:
t = str(x)
self.test('fPi(sn, None, dn)', t,
'invokation invalid: Elliptic.fPi(0, None, 1)')
try:
t = e.fPi(0, 1, None)
except EllipticError as x:
t = str(x)
self.test('fPi(sn, dn, None)', t,
'invokation invalid: Elliptic.fPi(0, 1, None)')
self.test('deltaD(sn, cn, dn)',
e.deltaD(sn, cn, dn),
'-0.3223642',
fmt='%.7f')
self.test('deltaE(sn, cn, dn)',
e.deltaE(sn, cn, dn),
'0.0084191',
fmt='%.7f')
self.test('deltaEinv(sn, cn)',
e.deltaEinv(sn, cn),
'-0.0082518',
fmt='%.7f')
self.test('deltaF(sn, cn, dn)',
e.deltaF(sn, cn, dn),
'-0.0083379',
fmt='%.7f')
self.test('deltaG(sn, cn, dn)',
e.deltaG(sn, cn, dn),
'0.0084191',
fmt='%.7f')
self.test('deltaH(sn, cn, dn)',
e.deltaH(sn, cn, dn),
'0.3688975',
fmt='%.7f')
self.test('deltaPi(sn, cn, dn)',
e.deltaPi(sn, cn, dn),
'-0.0083379',
fmt='%.7f')
try:
t = e.deltaPi(0, None, 1)
except EllipticError as x:
t = str(x)
self.test('deltaPi(sn, None, dn)', t,
'invokation invalid: Elliptic.deltaPi(0, None, 1)')
try:
t = e.deltaPi(0, 1, None)
except EllipticError as x:
t = str(x)
self.test('deltaPi(sn, dn, None)', t,
'invokation invalid: Elliptic.deltaPi(0, 1, None)')
self.test('_RF(1, 2, 0)', _RF(1, 2, 0), '1.311028777', fmt='%.9f')
self.test('_RF(2, 3, 4)', _RF(2, 3, 4), '0.584082842', fmt='%.9f')
self.test('_RC(0, 1/4)', _RC(0, 0.25), '3.141592654', fmt='%.9f')
self.test('_RC(9/4, 2)', _RC(2.25, 2), '0.693147181', fmt='%.9f')
self.test('_RC(1/4,-2)', _RC(0.25, -2), '0.231049060', fmt='%.9f')
self.test('_RJ(0, 1, 2, 3)',
_RJ(0, 1, 2, 3),
'0.776886238',
fmt='%.9f')
self.test('_RJ(2, 3, 4, 5)',
_RJ(2, 3, 4, 5),
'0.142975797',
fmt='%.9f')
self.test('_RD(0, 2, 1)', _RD(0, 2, 1), '1.797210352', fmt='%.9f')
self.test('_RD(2, 3, 4)', _RD(2, 3, 4), '0.165105273', fmt='%.9f')
self.test('_RG(0, 16, 16)', _RG(0, 16, 16), '3.141592654', fmt='%.9f')
self.test('_RG(2, 3, 4)', _RG(2, 3, 4), '1.725503028', fmt='%.9f')
self.test('_RG(0, 0.0796, 4)',
_RG(0, 0.0796, 4),
'1.028475809',
fmt='%.9f')
e.reset(0, 0)
self.test('sncndn(x)', fStr(e.sncndn(0), prec=9), '0.0, 1.0, 1.0')
self.test('sncndn(x)',
fStr(e.sncndn(PI_2), prec=9),
'1.0, -0.0, 1.0',
known=True)
e.reset(1, 1)
self.test('sncndn(x)', fStr(e.sncndn(0), prec=9), '0.0, 1.0, 1.0')
self.test('sncndn(x)', fStr(e.sncndn(PI_2), prec=9),
'0.917152336, 0.398536815, 0.398536815')
self.test('sncndn(x)', type(e.sncndn(PI_4)), elliptic.Elliptic3Tuple)
self.testCopy(e)
for t in range(4): # coverage
t = (t / 4.0, ) * 4
e = elliptic.Elliptic(*t)
self.test('k2, alpha2, kp2, alphap2',
(e.k2, e.alpha2, e.kp2, e.alphap2), t)