def NRM_dir_stat(sc):
"""
Function to calculate the NRM direction statistics, DANG, free floating direction and NRMdev.
input: Mdec_free,Minc_free, x, y, z, Yint
output: DANG, NRMdev, dir_vec_free
"""
# input: directional_statistics/ mean_dir_stat[Mdec_free,Minc_free, x, y, z]
# arai_statistics/ intercept_stats[Yint]
# output: directional_statistics/ NRM_dir_stat[DANG, NRMdev, dir_vec_free]
x = sc["directional_statistics"]["mean_dir_stat"]["x"]
y = sc["directional_statistics"]["mean_dir_stat"]["y"]
z = sc["directional_statistics"]["mean_dir_stat"]["z"]
Mdec_free = sc["directional_statistics"]["mean_dir_stat"]["Mdec_free"]
Minc_free = sc["directional_statistics"]["mean_dir_stat"]["Minc_free"]
Yint = sc["arai_statistics"]["intercept_stats"]["Yint"]
mean_x = sum(x) / len(x)
mean_y = sum(y) / len(y)
mean_z = sum(z) / len(z)
center_of_mass = [mean_x, mean_y, mean_z]
# calculate DANG & NRMdev
dir_vec_free = helpers.dir2cart(Mdec_free, Minc_free, 1)
DANG = helpers.get_angle_diff(dir_vec_free, center_of_mass)
NRMdev = ((math.sin(math.radians(DANG)) * helpers.norm(center_of_mass)) / abs(Yint)) * 100
sc["directional_statistics"]["NRM_dir_stat"]["dir_vec_free"] = dir_vec_free
sc["directional_statistics"]["NRM_dir_stat"]["DANG"] = DANG
sc["directional_statistics"]["NRM_dir_stat"]["NRMdev"] = NRMdev
return sc
def best_fit_lines_Zijderveld(sc):
"""
Function to calculate the direction of the Best - Fit lines for the Zijderveld, use the Free floating direction
input: Free-floating direction (Mdec_free, Minc_free) and the center-of-mass vector (CMvec) to calculate the size of the plot
output: The (x,y) coordinates for the horizontal (line_H_) and vertical (line_V_) lines for the Zijderveld diagram, for the two options, Up-North (UpN) or Up-West (UpW)
"""
# input: directional_statistics/ mean_dir_stat[CMvec, Mdec_free, Minc_free ]
# output: best_fit_lines/ best_fit_lines_Zijderveld[line_H_UpN, line_V_UpN, line_H_UpW, line_V_UpW]
CMvec = sc["directional_statistics"]["mean_dir_stat"]["CMvec"]
Mdec_free = sc["directional_statistics"]["mean_dir_stat"]["Mdec_free"]
Minc_free = sc["directional_statistics"]["mean_dir_stat"]["Minc_free"]
# first find in which order of magnitude the point for the lines should be, they should be outside the area of the zijderveld plot
# find the maximum absolute value for the center of mass and take an order of magnitude bigger to be sure to outside of the plot
Abs_CMvec = []
for i in range(len(CMvec)):
Abs_CMvec.append(abs(CMvec[i]))
M = max(Abs_CMvec) * 10
# get the direction vector with the correct magnitude M
Dvec = helpers.dir2cart(Mdec_free, Minc_free, M)
# Center of mass - Direction vector is the first point
P1 = helpers.list_min_list(CMvec, Dvec)
# Center of mass + Direction vector is the second point
P2 = helpers.list_plus_list(CMvec, Dvec)
# North Up
line_H_UpN = [[P1[1], P1[0]], [P2[1], P2[0]]]
line_V_UpN = [[P1[1], -1 * P1[2]], [P2[1], -1 * P2[2]]]
# West Up
line_H_UpW = [[P1[0], -1 * P1[1]], [P2[0], -1 * P2[1]]]
line_V_UpW = [[P1[0], -1 * P1[2]], [P2[0], -1 * P2[2]]]
sc["best_fit_lines"]["best_fit_lines_Zijderveld"][
"line_H_UpN"] = line_H_UpN
sc["best_fit_lines"]["best_fit_lines_Zijderveld"][
"line_V_UpN"] = line_V_UpN
sc["best_fit_lines"]["best_fit_lines_Zijderveld"][
"line_H_UpW"] = line_H_UpW
sc["best_fit_lines"]["best_fit_lines_Zijderveld"][
"line_V_UpW"] = line_V_UpW
return sc
def alpha_stat(sc):
"""
Function to calculate the alpha statistic, the angular difference between the anchored and free-floating best-fit directions
input: free floating direction vector (dir_vec_free), and the anchored direction (Mdec_anc, Minc_anc)
output: alpha
"""
# input: directional_statistics/ mean_dir_stat[Mdec_anc, Minc_anc]
# NRM_dir_stat[dir_vec_free]
# output: directional_statistics/ alpha_stat[alpha]
Mdec_anc = sc["directional_statistics"]["mean_dir_stat"]["Mdec_anc"]
Minc_anc = sc["directional_statistics"]["mean_dir_stat"]["Minc_anc"]
dir_vec_free = sc["directional_statistics"]["NRM_dir_stat"]["dir_vec_free"]
dir_vec_anc = []
dir_vec_anc = helpers.dir2cart(Mdec_anc, Minc_anc, 1)
alpha = helpers.get_angle_diff(dir_vec_free, dir_vec_anc)
sc["directional_statistics"]["alpha_stat"]["alpha"] = alpha
return sc
def field_basics_pTh(sc):
"""
Function to write the field basics to the suitcase for pseudo-Thellier. Only difference here w.r.t. the field_basics function above is that the "infield_steps" are now the ARM_aqc_steps for the NAA format, for pTh-GF (generic format) this is still the infieldstep. The lab field strength (Blab), and the direction of the labfield as provided by the user in the input (field_dir_vec_initial). The labfield direction is chcked with the direction of the last ptrm_step to check if the field_dir_vec_initial is correct or if it should be anti-parallel to that.
input: the ptrm_gained_vec from the basisc, the infield_steps and the ARM_acq_steps from the measurements
output: the field basics: Blab, field_dir_vec_initial, field_dir_vec
"""
# input: preprocessed/ msrmnts [infield_steps, ARM_acq_steps]
# basics [ptrm_gained_vec]
# output: preprocessed/ field_basics [Blab, field_dir_vec_initial, field_dir_vec]
infield_steps = sc["preprocessed"]["msrmnts"]["infield_steps"]
ARM_acq_steps = sc["preprocessed"]["msrmnts"]["ARM_acq_steps"]
ptrm_gained_vec = sc["preprocessed"]["basics"]["ptrm_gained_vec"]
# make extra if statement
if len(infield_steps) == 0:
infield_steps = ARM_acq_steps
# get lab field strength and direction of applied labfield
Blab = infield_steps[0]["lab_field"]
field_dir_vec_initial = helpers.dir2cart(infield_steps[0]["lab_field_dec"],
infield_steps[0]["lab_field_inc"],
1)
# check the field_dir_vec_initial, in an experiment the specimen could have been rotated so that field dir vec should be negative
# check this by comparing the direction of the ptrm with field_dir_vec_initial
vecl = ptrm_gained_vec[len(ptrm_gained_vec) - 1] # last ptrm gained step
vecl_abs = [] # make this vector absolute
for i in range(len(vecl)):
vecl_abs.append(abs(vecl[i]))
# check field direction, and make it positive or negative is necessary, only works for fields applied along principal axis
if field_dir_vec_initial[2] == 1 or field_dir_vec_initial[2] == -1:
if field_dir_vec_initial[0] == 0 and field_dir_vec_initial[1] == 0:
# then you have [0,0,1] or [0,0,-1]
if (max(vecl) - max(vecl_abs)) < 0:
field_dir_vec = [0, 0, -1]
else:
field_dir_vec = [0, 0, 1]
else: # [x,x,1] en x != 0
field_dir_vec = field_dir_vec_initial
elif field_dir_vec_initial[1] == 1 or field_dir_vec_initial[1] == -1:
if field_dir_vec_initial[0] == 0 and field_dir_vec_initial[2] == 0:
# then you have [0,1,0] or [0,-1,0]
if (max(vecl) - max(vecl_abs)) < 0:
field_dir_vec = [0, -1, 0]
else:
field_dir_vec = [0, 1, 0]
else: # [x,1,x] en x != 0
field_dir_vec = field_dir_vec_initial
elif field_dir_vec_initial[0] == 1 or field_dir_vec_initial[0] == -1:
if field_dir_vec_initial[1] == 0 and field_dir_vec_initial[2] == 0:
# then you have [1,0,0] or [-1,0,0]
if (max(vecl) - max(vecl_abs)) < 0:
field_dir_vec = [-1, 0, 0]
else:
field_dir_vec = [1, 0, 0]
else: # [1,x,x] with x != 0
field_dir_vec = field_dir_vec_initial
else: # All other field directions that are not principal axis
field_dir_vec = field_dir_vec_initial
sc["preprocessed"]["field_basics"]["Blab"] = Blab
sc["preprocessed"]["field_basics"][
"field_dir_vec_initial"] = field_dir_vec_initial
sc["preprocessed"]["field_basics"]["field_dir_vec"] = field_dir_vec
return sc
def anisotropy_calc(sc):
"""
Function that calculates the paleointensity correction factor when anisotropy data is available. It uses the previously calculated s-tensor. First the direction of the NRM for the selected part of the Arai plot is determined to give Mhat_ChRM. Which is used to get the anisotropy correction c. The anisotropy correction in multiplied with Banc to get Banc_aniso_corr.
input: s-tensor, the direction of the applied labfield, direction of the data selection, the original Banc
output: the anisotropy correction anis_c, the anisotropy corrected paleointensity estimate Banc_aniso_corr
"""
# input: preprocessed/ field_basics [field_dir_vec]
# s_tensor [s1_list, s2_list, s3_list, s4_list, s5_list, s6_list, scheck_list]
# arai_statistics/ PI_Banc_est [B_anc]
# directional_statistics/ mean_dir_stat [Mdec_free, Minc_free]
# output: anisotropy_statistics/ Anisotropy_Correction [anis_c, Banc_aniso_corr]
Mdec_free = sc["directional_statistics"]["mean_dir_stat"]["Mdec_free"]
Minc_free = sc["directional_statistics"]["mean_dir_stat"]["Minc_free"]
field_dir_vec = sc["preprocessed"]["field_basics"]["field_dir_vec"]
B_anc = sc["arai_statistics"]["PI_Banc_est"]["B_anc"]
Xp_list = sc["preprocessed"]["aniso_trm"]["x+"]
s_tensor = sc["anisotropy_statistics"]["Aniso_tensor"]["s_tensor"]
if Xp_list != None: # then there is anisotropy data, do calculations, if no anisotropy data present do nothing
anis_c = []
# the direction of the NRM, should be determined from the selected Arai plot
# this is the Mdec_free & Minc_free, the unit vecotr of this gives -> Mhat_ChRM
# get mean unit vector
Mhat_ChRM = helpers.dir2cart(Mdec_free, Minc_free, 1)
Blab_orient = field_dir_vec # it was: helpers.dir2cart(Mdec_free, Minc_free, 1), that is wrong!! (13 feb 2020)
s1 = s_tensor[0]
s2 = s_tensor[1]
s3 = s_tensor[2]
s4 = s_tensor[3]
s5 = s_tensor[4]
s6 = s_tensor[5]
A1 = [s1, s4, s6]
A2 = [s4, s2, s5]
A3 = [s6, s5, s3]
A = [A1, A2, A3]
# make A and Mhat_ChRM into a numpy arrays (1)
A = numpy.array(A)
Mhat_ChRM = numpy.array(Mhat_ChRM)
# do numpy calculation (2)
Hanc = numpy.linalg.solve(A, Mhat_ChRM)
# back to python lists (3)
A = A.tolist()
Mhat_ChRM = Mhat_ChRM.tolist()
Hanc = Hanc.tolist()
# unit vector in the direction of the ancient field
Hanc_hat = helpers.list_div_num(Hanc, helpers.norm(Hanc))
Manc = []
Mlab = []
for i in range(len(A)):
Manc.append(helpers.dot_product(A[i], Hanc_hat))
Mlab.append(helpers.dot_product(A[i], field_dir_vec))
aniso_c = helpers.norm(Mlab) / helpers.norm(Manc)
Banc_aniso_corr = aniso_c * B_anc
sc["anisotropy_statistics"]["Anisotropy_Correction"][
"aniso_c"] = aniso_c
sc["anisotropy_statistics"]["Anisotropy_Correction"][
"Banc_aniso_corr"] = Banc_aniso_corr
return (sc)