class PointCartCovMat(PointCart):
"""class for geodetic coordinates x, y, z
and its covariance matrix"""
__slots__ = ["covmat", "xi", "yi", "zi"]
def __init__(self, id,
x=None, y=None, z=None,
covmat=None,
index=None,
textTable=None):
"""x, y, z ... coordinates
covmat ... covariance matrix
index ... (xi, yi, zi) indexes of rows in covariance matrix
textTable ... TextTable instance
"""
if not textTable:
textTable = coor_var_table()
super(PointCartCovMat, self).__init__(id, x, y, z, textTable=textTable)
if covmat == None:
self.covmat = CovMat(3, 2)
else:
self.covmat = covmat
i = 0
if index == None:
if x == None: self.xi = None
else: self.xi = i; i += 1
if y == None: self.yi = None
else: self.yi = i; i += 1
if z == None: self.zi = None
else: self.zi = i
#self.xi, self.yi, self.zi = 0, 1, 2
else:
self.index = index
def _get_index(self): return [self.xi, self.yi, self.zi]
def _set_index(self, index):
if index == None: self.xi = None; self.yi = None; self.zi = None
if len(index) == 3:
self.xi = index[0]; self.yi = index[1];
self.zi = index[2]
elif len(index) == 2:
self.xi = index[0]; self.yi = index[1];
elif len(index) == 1:
self.zi = index[0]
else:
raise PointCartCovMatError,\
"Index (xi, yi, zi) or (xi, yi) or (zi,) expected"
index = property(_get_index, _set_index)
def get_dim(self):
dim = 0
if self.x != None: dim += 1
if self.y != None: dim += 1
if self.z != None: dim += 1
return dim
# setting of variance and covariance throught managed attributes
def _set_var_x(self, vx):
if self.xi == None:
raise PointCartCovMatError, "Variance index of x coordinate not defined"
self.covmat.set_var(self.xi, vx)
def _set_var_y(self, vy):
if self.yi == None:
raise PointCartCovMatError, "Variance index of y coordinate not defined"
self.covmat.set_var(self.yi, vy)
def _set_var_z(self, vz):
if self.zi == None:
raise PointCartCovMatError, "Variance index of z coordinate not defined"
self.covmat.set_var(self.zi, vz)
def _set_cov_xy(self, cxy):
if self.xi == None or self.yi == None:
raise PointCartCovMatError, "Covariance index of coordinate x and y not defined"
self.covmat.set_cov(self.xi, self.yi, cxy)
def _set_cov_xz(self, cxz):
if self.xi == None or self.zi == None:
raise PointCartCovMatError, "Covariance index of coordinate x and z not defined"
self.covmat.set_cov(self.xi, self.zi, cxz)
def _set_cov_yz(self, cyz):
if self.yi == None or self.zi == None:
raise PointCartCovMatError, "Covariance index of coordinate y and z not defined"
self.covmat.set_cov(self.yi, self.zi, cyz)
def _get_var_x(self):
if self.xi == None:
#raise PointCartCovMatError, "Variance of x coordinate not defined"
return None
return self.covmat.get_var(self.xi)
def _get_var_y(self):
if self.yi == None:
#raise PointCartCovMatError, "Variance of y coordinate not defined"
return None
return self.covmat.get_var(self.yi)
def _get_var_z(self):
if self.zi == None:
#raise PointCartCovMatError, "Variance of z coordinate not defined"
return None
return self.covmat.get_var(self.zi)
def _get_cov_xy(self):
if self.xi == None or self.yi == None:
return None
#raise PointCartCovMatError, "Covariance of coordinate x and y not defined"
return self.covmat.get_cov(self.xi, self.yi)
def _get_cov_xz(self):
if self.xi == None or self.zi == None:
return None
#raise PointCartCovMatError, "Covariance of coordinate x and z not defined"
return self.covmat.get_cov(self.xi, self.zi)
def _get_cov_yz(self):
if self.yi == None or self.zi == None:
return None
#raise PointCartCovMatError, "Covariance of coordinate y and z not defined"
return self.covmat.get_cov(self.yi, self.zi)
def _set_var(self, var):
"""
sets all variances in covariance matrix
var = (varx, vary, varz)
or
var = (varx, vary)
"""
for i, v in zip((self.xi, self.yi, self.zi), var):
if i == None:
raise PointCartCovMatError, "Index for var %e not set" % v
else:
self.covmat.set_var(i, v)
def _set_cov(self, cov):
"""sets all covariances in covariance matrix
cov = (cov_xy, cov_xz, cov_yz)
"""
if type(cov) != tuple and type(cov) != list:
cov = (cov,)
for i, j, c in zip((self.xi, self.xi, self.yi),
(self.yi, self.zi, self.zi), cov):
if i == None or j == None:
raise PointCartCovMatError, "Index for cov %e not set" % c
else:
self.covmat.set_cov(i, j, c)
def _get_var(self):
"""returns list with all variances var_x, var_y, var_z"""
var = []
for i in (self.xi, self.yi, self.zi):
if i == None:
#raise PointCartCovMatError, "variance not set"
var.append(None)
else:
var.append(self.covmat.get_var(i))
return var
def _get_stdev(self):
"""returns list with all standard deviations - sqrt(var)"""
from math import sqrt
return [(var==None and [None] or [sqrt(var)])[0] for var in self._get_var()]
def _get_stdev_x(self):
var = self._get_var_x()
if var == None:
return None
else:
from math import sqrt
return sqrt(var)
def _get_stdev_y(self):
var = self._get_var_y()
if var == None:
return None
else:
from math import sqrt
return sqrt(var)
def _get_stdev_z(self):
var = self._get_var_z()
if var == None:
return None
else:
from math import sqrt
return sqrt(var)
def _get_cov(self):
cov = []
for i,j in ((self.xi, self.yi),\
(self.xi, self.zi),\
(self.yi, self.zi)):
if i == None or j == None:
#raise PointCartCovMatError, "covariance not set"
cov.append(None)
else:
#print "i:%i j:%i" %(i,j)
#yield self.covmat.get_cov(i,j)
cov.append(self.covmat.get_cov(i,j))
return cov
var = property(_get_var, _set_var)
cov = property(_get_cov, _set_cov)
stdev = property(_get_stdev)
varx = property(_get_var_x, _set_var_x)
vary = property(_get_var_y, _set_var_y)
varz = property(_get_var_z, _set_var_z)
covxy = property(_get_cov_xy, _set_cov_xy)
covxz = property(_get_cov_xz, _set_cov_xz)
covyz = property(_get_cov_yz, _set_cov_yz)
stdevx = property(_get_stdev_x)
stdevy = property(_get_stdev_y)
stdevz = property(_get_stdev_z)
def _get_err_ell(self):
"""
returns parameters of standard error ellipse
(a, b, omega)
omega ... clockwise from x axis in radians in interval -pi:pi
"""
if self.x == None or self.y == None:
raise PointCartCovMatError, "Point id=%s: No x, y coordinates set"\
% self.id
vx = self.varx
vy = self.vary
cxy = self.covxy
if vx == None:
raise PointCartCovMatError, "Point id=%s: No varx set" % self.id
if vy == None:
raise PointCartCovMatError, "Point id=%s: No vary set" % self.id
if cxy == None:
raise PointCartCovMatError, "Point id=%s: No covariance xy set" \
% self.id
# test of positive definity
det = vx*vy - cxy*cxy
if det < -1e-4:
raise PointCartCovMatError, "Covariance matrix is not positive definite: det = %e" % det
import math
c = math.sqrt((vx - vy)**2 + 4.0*cxy*cxy)
a = math.sqrt((vx + vy + c)/2.0)
if vx + vy - c < 0.0:
b = 0.0
else:
b = math.sqrt((vx + vy - c)/2.0)
omega = math.atan2(2.0*cxy, vx - vy)/2.0
return [a, b, omega]
errEll = property(_get_err_ell)
def get_point_cov_mat(self, dim=3):
'''
returns covariance matrix
selection of covariance matrix of point from large covariance matrix
dim: dimension of covariance matrix to be returned
'''
if dim > 3 or dim < 1:
raise PointCartCovMatError, "Wrong dimension of covariance matrix."
if self.covmat.dim == dim:
return self.covmat
lcm = self.covmat.empty_copy()
lcm.dim = dim
lcm.band = dim - 1 < self.covmat.band and dim - 1 or self.covmat.band
var = self.var; cov = self.cov
for i,v in enumerate(var[:dim]):
if v != None: lcm.set_var(i,v)
if dim > 1:
if cov[0] != None: lcm.set_cov(0,1,cov[0])
if dim > 2:
if cov[1] != None: lcm.set_cov(0,2,cov[1])
if cov[2] != None: lcm.set_cov(1,2,cov[2])
#import sys
#print >>sys.stderr, "get_point_cov_mat:", self.covmat, lcm
return lcm
# old version
#def set_point_cov_mat(self, covmat=None):
# """
# sets point covariance matrix to covmat
# if covmat is None
# sets CovMat(dim=3, band=2) and makes local copy from large
# covariance matrix
# """
# if covmat is None:
# self.covmat = self.get_point_cov_mat()
# else:
# if covmat.dim == 3:
# self.covmat = covmat
# else:
# raise PointCartCovMatError, \
# "CovMat instance with dim=3 expected"
#def slice_cov_mat(self):
# """
# sets covariance matrix just for this one point
# makes local copy from larg covariance matrix if needed
# """
# if self.covmat.dim != self.get_dim():
# self.covmat = self.get_point_cov_mat(dim=self.get_dim())
def set_point_cov_mat(self, covmat):
"""
sets covariance matrix of point
covmat: CovMat instance with proper dimension
"""
dim = self.get_dim()
if dim != covmat.dim:
raise PointCartCovMatError,\
"Wrong dimension of covariance matrix (%i != %i)" \
% (dim, covmat.dim)
i = 0
if self.x == None: self.xi = None
else: self.xi = i; i += 1
if self.y == None: self.yi = None
else: self.yi = i; i += 1
if self.z == None: self.zi = None
else: self.zi = i
self.covmat = covmat
def tran_(self, tran):
"""
transforms point with its covariance matrix
tran: Tran2D or Tran3D instance
Tran2D transforms points xyz and xy. Covariances xz and yz of xyz point
are left unchanged with this transform. Is this Correct?
Tran3D transforms only points xyz.
"""
if isinstance(tran, Tran2D):
if self.is_set_xyz():
# transform xyz point with 2D transformation
self.x, self.y = tran.transform_xy(self.x, self.y)
cm3 = self.get_point_cov_mat(dim=3)
cm2 = self.get_point_cov_mat(dim=2)
cm2.transform_(tran)
cm3.set_var(0, cm2.get_var(0))
cm3.set_var(1, cm2.get_var(1))
cm3.set_cov(0, 1, cm2.get_cov(0, 1))
self.set_point_cov_mat(cm3)
elif self.is_set_xy():
self.x, self.y = tran.transform_xy(self.x, self.y)
cm = self.get_point_cov_mat(dim=2)
cm.transform_(tran)
self.set_point_cov_mat(cm)
else:
import sys
print >>sys.stderr, "point id=%s not transformed" % self.id
elif isinstance(tran, Tran3D):
if self.is_set_xyz():
self.x, self.y, self.z = \
tran.transform_xyz(self.x, self.y, self.z)
cm = self.get_point_cov_mat(dim=3)
cm.transform_(tran)
self.set_point_cov_mat(cm)
else:
import sys
print >>sys.stderr, "point id=%s not transformed" % self.id
else:
raise PointListError, "Tran2D or Tran3D instance expected"
def __add__(self, other):
'''addition of two points with covariance matrix'''
if not isinstance(other, PointCartCovMat):
raise PointCartCovMatError, \
"Addition of two PointCartCovMat instances supported"
x, y, z = None, None, None
if self.x != None and other.x != None: x = self.x + other.x
if self.y != None and other.y != None: y = self.y + other.y
if self.z != None and other.z != None: z = self.z + other.z
#id = " ".join([self.id, "+", other.id])
#co = PointCartCovMat(id=self.id, x=x, y=y, z=z, textTable=self.textTable)
# covariance matrix
if self.covmat.dim == 3:
lcm = self.covmat
else:
lcm = self.get_point_cov_mat()
if other.covmat.dim == 3:
ocm = other.covmat
else:
ocm = other.get_point_cov_mat()
import copy
p = copy.deepcopy(self)
p.x = x; p.y = y; p.z = z; p.covmat = lcm + ocm
if x == None: p.xi = None
else: p.xi = 0
if y == None: p.yi = None
else: p.yi = 1
if z == None: p.zi = None
else: p.zi = 2
return p
def __sub__(self, other):
'''subtraction of two points with covariance matrix'''
if not isinstance(other, PointCartCovMat):
raise PointCartCovMatError, \
"Subtraction of two PointCartCovMat instances supported"
x, y, z = None, None, None
if self.x != None and other.x != None: x = self.x - other.x
if self.y != None and other.y != None: y = self.y - other.y
if self.z != None and other.z != None: z = self.z - other.z
# covariance matrix
if self.covmat.dim == 3:
lcm = self.covmat
else:
lcm = self.get_point_cov_mat()
if other.covmat.dim == 3:
ocm = other.covmat
else:
ocm = other.get_point_cov_mat()
import copy
p = copy.deepcopy(self)
p.x = x; p.y = y; p.z = z; p.covmat = lcm + ocm
if x == None: p.xi = None
else: p.xi = 0
if y == None: p.yi = None
else: p.yi = 1
if z == None: p.zi = None
else: p.zi = 2
return p
def __mul__(self, scalar):
"""
returns multiplication of point coordinates with scalar
"""
return super(PointCartCovMat, self).__mul__(scalar)
# multiplication of variances and covariances
var = self.var
cov = self.cov
for i in xrange(3):
if var[i] is not None:
var[i] *= scalar*scalar
if cov[i] is not None:
cov[i] *= scalar*scalar
self.var = var
self.cov = cov
def make_table_row(self):
row = [self.id, self.x, self.y, self.z]
ncols = self.textTable.get_num_of_col()
#print ncols
if ncols > 4:
row.extend(self.var)
if ncols > 4 + 3:
row.extend(self.cov)
return self.textTable.make_table_row(row)
def plot_error_ellipse(self, figure):
"plots error ellipse from covariance matrix of point"
if self.x != None and self.y != None:
figure.plot_point_error_ellipse(self)
def plot_error_z(self, figure):
"""
plots confidence interval of z coordinate
at coordinates x, y
"""
if self.x is not None and self.y is not None and self.z is not None:
figure.plot_point_error_z(self)
def plot_x_stdev(self, figure, x):
"""
plots interval of standard deviation of x coordinate
along vertical axis
x: horizontal coordinate
confScale: confidence scale factor
"""
if self.x != None:
figure.plot_point_x_stdev(self, x)
def plot_y_stdev(self, figure, x):
if self.y != None:
figure.plot_point_y_stdev(self, x)
def plot_z_stdev(self, figure, x):
if self.z != None:
figure.plot_point_z_stdev(self, x)
