def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def critical_friction(sig1, sig3, pp):
"""
A function that computes the critical friction coefficient
that would induce slip for the given combination of minimum
and maximum principal stress and pore pressure
Parameters
----------
sig1 : float or array_like
The maximum (most compressive) principal stress. If `sig1` is
array_like then `sig3` must be a scalar of type float
sig3 : float or array_like
The minimum (least compressive) principal stress. If `sig3` is
array_like then `sig1` must be a scalar of type float
pp : float
The pore pressure
Returns
-------
mu_c : float or array_like
The critical friction coefficient. If either sig1 or sig3 are
array_like then the result will be an array containing the
critical friction coefficient for each entry in the array.
"""
arg = (sig1 - sig3) / (sig1 + sig3 - 2.0 * pp)
phic = ma.arcsin(arg)
muc = ma.tan(phic)
return muc
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def transform_non_affine(self, a):
# With safeguards
# TODO: Can improve this?
a = np.deg2rad(a) # convert to radians
m = ma.masked_where((a < -self._thresh) | (a > self._thresh), a)
if m.mask.any():
return ma.log(np.abs(ma.tan(m) + 1 / ma.cos(m)))
else:
return np.log(np.abs(np.tan(a) + 1 / np.cos(a)))
def transform_non_affine(self, a):
# NOTE: Critical to truncate valid range inside transform *and*
# in limit_range_for_scale or get weird duplicate tick labels. This
# is not necessary for positive-only scales because it is harder to
# run up right against the scale boundaries.
with np.errstate(divide='ignore', invalid='ignore'):
m = ma.masked_where((a <= -90) | (a >= 90), a)
if m.mask.any():
m = np.deg2rad(m)
return ma.log(ma.abs(ma.tan(m) + 1 / ma.cos(m)))
else:
a = np.deg2rad(a)
return np.log(np.abs(np.tan(a) + 1 / np.cos(a)))
def transform_non_affine(self, a):
"""
This transform takes a numpy array and returns a transformed copy.
Since the range of the Mercator scale is limited by the
user-specified threshold, the input array must be masked to
contain only valid values. Matplotlib will handle masked arrays
and remove the out-of-range data from the plot. However, the
returned array *must* have the same shape as the input array, since
these values need to remain synchronized with values in the other
dimension.
"""
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1 / np.cos(a)))
def transform_non_affine(self, a):
"""
This transform takes an Nx1 ``numpy`` array and returns a
transformed copy. Since the range of the Mercator scale
is limited by the user-specified threshold, the input
array must be masked to contain only valid values.
``matplotlib`` will handle masked arrays and remove the
out-of-range data from the plot. Importantly, the
``transform`` method *must* return an array that is the
same shape as the input array, since these values need to
remain synchronized with values in the other dimension.
"""
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def calc_PA(self) :
"""Calculates the telescope PA. requires LST to be either a field or
previously calculated array
Outputs an array of PA values for each time in radians.
This requires the fields Ra = 'CRVAL2', Dec = 'CRVAL3' and 'DATE-OBS'
to be set.
"""
self.PA = sp.zeros(self.dims[0])
for ii in range(self.dims[0]) :
RA = self.field['CRVAL2'][ii]
DEC = self.field['CRVAL3'][ii]
LST = utils.LSTatGBT(self.field['DATE-OBS'][ii])
H = LST-RA
Latit = 38.0+26.0/60
tanPA = ma.sin(H*sp.pi/180)/(ma.cos(DEC*sp.pi/180)*ma.tan(Latit*sp.pi/180)-ma.sin(DEC*sp.pi/180)*ma.cos(H*sp.pi/180))
self.PA[ii] = ma.arctan(tanPA)
def transform(self, a):
"""
This transform takes an Nx1 ``numpy`` array and returns a
transformed copy. Since the range of the Mercator scale
is limited by the user-specified threshold, the input
array must be masked to contain only valid values.
``matplotlib`` will handle masked arrays and remove the
out-of-range data from the plot. Importantly, the
``transform`` method *must* return an array that is the
same shape as the input array, since these values need to
remain synchronized with values in the other dimension.
"""
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def calc_PA(self):
"""Calculates the telescope PA. requires LST to be either a field or
previously calculated array
Outputs an array of PA values for each time in radians.
This requires the fields Ra = 'CRVAL2', Dec = 'CRVAL3' and 'DATE-OBS'
to be set.
"""
self.PA = sp.zeros(self.dims[0])
for ii in range(self.dims[0]):
RA = self.field['CRVAL2'][ii]
DEC = self.field['CRVAL3'][ii]
LST = utils.LSTatGBT(self.field['DATE-OBS'][ii])
H = LST - RA
Latit = 38.0 + 26.0 / 60
tanPA = ma.sin(H * sp.pi / 180) / (
ma.cos(DEC * sp.pi / 180) * ma.tan(Latit * sp.pi / 180) -
ma.sin(DEC * sp.pi / 180) * ma.cos(H * sp.pi / 180))
self.PA[ii] = ma.arctan(tanPA)
def func(x):
return (1 - sec(x)) / (tan(x)**2)
def transform_non_affine(self, a):
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
