def multiplymatrices_incl_errors(inmatrix1,
inmatrix2,
inmatrix1_err=None,
inmatrix2_err=None):
if inmatrix1 is None or inmatrix2 is None:
raise MTex.MTpyError_inputarguments(
'ERROR - two 2x2 arrays needed as input')
if inmatrix1.shape != inmatrix2.shape:
raise MTex.MTpyError_inputarguments(
'ERROR - two 2x2 arrays with same dimensions needed as input')
prod = np.array(np.dot(np.matrix(inmatrix1), np.matrix(inmatrix2)))
if (inmatrix1_err is None) or (inmatrix1_err is None):
return prod, None
var = np.zeros((2, 2))
var[0,0] = (inmatrix1_err[0,0] * inmatrix2[0,0])**2 + (inmatrix1_err[0,1] * inmatrix2[1,0])**2+\
(inmatrix2_err[0,0] * inmatrix1[0,0])**2 + (inmatrix2_err[1,0] * inmatrix1[0,1])**2
var[0,1] = (inmatrix1_err[0,0] * inmatrix2[0,1])**2 + (inmatrix1_err[0,1] * inmatrix2[1,1])**2+\
(inmatrix2_err[0,1] * inmatrix1[0,0])**2 + (inmatrix2_err[1,1] * inmatrix1[0,1])**2
var[1,0] = (inmatrix1_err[1,0] * inmatrix2[0,0])**2 + (inmatrix1_err[1,1] * inmatrix2[1,0])**2+\
(inmatrix2_err[0,0] * inmatrix1[1,0])**2 + (inmatrix2_err[1,0] * inmatrix1[1,1])**2
var[1,1] = (inmatrix1_err[1,0] * inmatrix2[0,1])**2 + (inmatrix1_err[1,1] * inmatrix2[1,1])**2+\
(inmatrix2_err[0,1] * inmatrix1[1,0])**2 + (inmatrix2_err[1,1] * inmatrix1[1,1])**2
return prod, np.sqrt(var)
def rotatematrix_incl_errors(inmatrix, angle, inmatrix_err=None):
if inmatrix is None:
raise MTex.MTpyError_inputarguments(
'Matrix AND eror matrix must be defined')
if (inmatrix_err is not None) and (inmatrix.shape != inmatrix_err.shape):
raise MTex.MTpyError_inputarguments(
'Matrix and err-matrix shapes do not match: %s - %s' %
(str(inmatrix.shape), str(inmatrix_err.shape)))
try:
degreeangle = angle % 360
except:
raise MTex.MTpyError_inputarguments(
'"Angle" must be a valid number (in degrees)')
phi = math.radians(degreeangle)
cphi = np.cos(phi)
sphi = np.sin(phi)
# JP: Changed the rotation matrix to be formulated to rotate
# counter clockwise, I cannot find a good reason for this except that
# when you plot the strike and phase tensors the look correct with this
# formulation.
rotmat = np.array([[cphi, sphi], [-sphi, cphi]])
# rotmat = np.array([[ cphi, -sphi], [sphi, cphi]])
rotated_matrix = np.dot(np.dot(rotmat, inmatrix), np.linalg.inv(rotmat))
errmat = None
if (inmatrix_err is not None):
err_orig = np.real(inmatrix_err)
errmat = np.zeros_like(inmatrix_err)
# standard propagation of errors:
errmat[0,0] = np.sqrt( (cphi**2 * err_orig[0,0])**2 + \
(cphi * sphi * err_orig[0,1])**2 + \
(cphi * sphi * err_orig[1,0])**2 + \
(sphi**2 * err_orig[1,1])**2 )
errmat[0,1] = np.sqrt( (cphi**2 * err_orig[0,1])**2 + \
(cphi * sphi * err_orig[1,1])**2 + \
(cphi * sphi * err_orig[0,0])**2 + \
(sphi**2 * err_orig[1,0])**2 )
errmat[1,0] = np.sqrt( (cphi**2 * err_orig[1,0])**2 + \
(cphi * sphi * err_orig[1,1])**2 +\
(cphi * sphi * err_orig[0,0])**2 + \
(sphi**2 * err_orig[0,1])**2 )
errmat[1,1] = np.sqrt( (cphi**2 * err_orig[1,1])**2 + \
(cphi * sphi * err_orig[0,1])**2 + \
(cphi * sphi * err_orig[1,0])**2 + \
(sphi**2 * err_orig[0,0])**2 )
return rotated_matrix, errmat
def rhophi2z(rho, phi, freq):
"""
Convert impedance-style information given in Rho/Phi format into complex valued Z.
Input:
rho - 2x2 array (real) - in Ohm m
phi - 2x2 array (real) - in degrees
freq - scalar - frequency in Hz
Output:
Z - 2x2 array (complex)
"""
try:
if rho.shape != (2, 2) or phi.shape != (2, 2):
raise
if not (rho.dtype in ['float', 'int']
and phi.dtype in ['float', 'int']):
raise
except:
raise MTex.MTpyError_inputarguments(
'ERROR - arguments must be two 2x2 arrays (real)')
z = np.zeros((2, 2), 'complex')
for i in range(2):
for j in range(2):
abs_z = np.sqrt(5 * freq * rho[i, j])
z[i, j] = cmath.rect(abs_z, math.radians(phi[i, j]))
return z
def rotatevector_incl_errors(invector, angle, invector_err=None):
#check for row or column vector
if invector is None:
raise MTex.MTpyError_inputarguments(
'Vector AND error-vector must be defined')
if (invector_err is not None) and (invector.shape != invector_err.shape):
raise MTex.MTpyError_inputarguments(
'Vector and errror-vector shapes do not match: %s - %s' %
(str(invector.shape), str(invector_err.shape)))
try:
degreeangle = angle % 360
except:
raise MTex.MTpyError_inputarguments(
'"Angle" must be a valid number (in degrees)')
phi = math.radians(degreeangle)
cphi = np.cos(phi)
sphi = np.sin(phi)
# JP: Changed the rotation matrix to be formulated to rotate
# counter clockwise, I cannot find a good reason for this except that
# when you plot the strike and phase tensors the look correct with this
# formulation.
rotmat = np.array([[cphi, sphi], [-sphi, cphi]])
# rotmat = np.array([[ cphi, -sphi],[sphi, cphi]])
if invector.shape == (1, 2):
rotated_vector = np.dot(invector, np.linalg.inv(rotmat))
else:
rotated_vector = np.dot(rotmat, invector)
errvec = None
if (invector_err is not None):
errvec = np.zeros_like(invector_err)
if invector_err.shape == (1, 2):
errvec = np.dot(invector_err, np.abs(np.linalg.inv(rotmat)))
else:
errvec = np.dot(np.abs(rotmat), invector_err)
return rotated_vector, errvec
def invertmatrix_incl_errors(inmatrix, inmatrix_err=None):
if inmatrix is None:
raise MTex.MTpyError_inputarguments('Matrix must be defined')
if (inmatrix_err is not None) and (inmatrix.shape != inmatrix_err.shape):
raise MTex.MTpyError_inputarguments(
'Matrix and err-matrix shapes do not match: %s - %s' %
(str(inmatrix.shape), str(inmatrix_err.shape)))
if (inmatrix.shape[-2] != inmatrix.shape[-1]):
raise MTex.MTpyError_inputarguments('Matrices must be square!')
if (inmatrix_err is not None) and (inmatrix_err.shape[-2] !=
inmatrix_err.shape[-1]):
raise MTex.MTpyError_inputarguments('Matrices must be square!')
dim = inmatrix.shape[-1]
det = np.linalg.det(inmatrix)
if det == 0:
raise MTex.MTpyError_inputarguments(
'Matrix is singular - I cannot invert that!')
inv_matrix = np.zeros_like(inmatrix)
if dim != 2:
raise MTex.MTpyError_inputarguments('Only 2D matrices supported yet')
inv_matrix = np.linalg.inv(inmatrix)
inv_matrix_err = None
if (inmatrix_err is not None):
inmatrix_err = np.real(inmatrix_err)
inv_matrix_err = np.zeros_like(inmatrix_err)
for i in range(2):
for j in range(2):
#looping over the entries of the error matrix
err = 0.
for k in range(2):
for l in range(2):
#each entry has 4 summands
err += np.abs(-inv_matrix[i, k] * inv_matrix[l, j] *
inmatrix_err[k, l])
inv_matrix_err[i, j] = err
return inv_matrix, inv_matrix_err
def reorient_data2D(x_values, y_values, x_sensor_angle=0, y_sensor_angle=90):
"""
Re-orient time series data of a sensor pair, which has not been in default (x=0, y=90) orientation.
Input:
- x-values - Numpy array
- y-values - Numpy array
Note: same length for both! - If not, the shorter length is taken
Optional:
- Angle of the x-sensor - measured in degrees, clockwise from North (0)
- Angle of the y-sensor - measured in degrees, clockwise from North (0)
Output:
- corrected x-values (North)
- corrected y-values (East)
"""
x_values = np.array(x_values)
y_values = np.array(y_values)
try:
if x_values.dtype not in ['complex', 'float', 'int']:
raise
if len(x_values) != len(y_values):
raise
except:
raise MTex.MTpyError_inputarguments(
'ERROR - both input arrays must be of same length')
if len(x_values) != len(y_values):
l = min(len(x_values), len(y_values))
x_values = x_values[:l]
y_values = y_values[:l]
in_array = np.zeros((len(x_values), 2), x_values.dtype)
in_array[:, 0] = x_values
in_array[:, 1] = y_values
try:
x_angle = math.radians(x_sensor_angle)
y_angle = math.radians(y_sensor_angle)
except:
raise MTex.MTpyError_inputarguments(
'ERROR - both angles must be of type int or float')
T = np.matrix(
[[np.real(cmath.rect(1, x_angle)),
np.imag(cmath.rect(1, x_angle))],
[np.real(cmath.rect(1, y_angle)),
np.imag(cmath.rect(1, y_angle))]])
try:
new_array = np.dot(in_array, T.I)
except:
raise MTex.MTpyError_inputarguments(
'ERROR - angles must define independent axes to span 2D')
#print new_array.shape
return new_array[:, 0], new_array[:, 1]