What does Y-axis mean when displaying a complex image using ShowImage()? - dm-script

I made a 1-D complex image "c" as below and used ShowImage to display it. My question is how to understand the Y-axis.
For pixel 1 (30+40i), it looks like the value in Y-axis represents log(modulus(30+40i))=3.9. But it does not seem to follow this rule in pixel 3 (0.3+0.4i).
ComplexImage c := ComplexImage("c", 8, 3, 1)
c[0, 0, 1, 1] = complex(30, 40)
c[0, 1, 1, 2] = complex(3, 4)
c[0, 2, 1, 3] = complex(0.3, 0.4)
ShowImage(c)

While not actually a scripting question, a very interesting observation! It turns out, that the plotted or displayed values for "Log of modulus" really is doing:
log( modulus( C ) + 1 )
And it is important to know, that the script-command log() is taking the natural logarithm. To command log10() would do the one to the base 10.
complexNumber c1 = complex(30,40)
complexNumber c2 = complex(3,4)
complexNumber c3 = complex(0.3,0.4)
result("\n Complex values:\n" )
result( "c1 = \t"+c1+"\n")
result( "c2 = \t"+c2+"\n")
result( "c3 = \t"+c3+"\n")
result("\n Modulus values:\n" )
result( "c1 = \t"+modulus(c1)+"\n")
result( "c2 = \t"+modulus(c2)+"\n")
result( "c3 = \t"+modulus(c3)+"\n")
result("\n Log of Modulus values:\n" )
result( "c1 = \t"+log10(modulus(c1))+"\n")
result( "c2 = \t"+log10(modulus(c2))+"\n")
result( "c3 = \t"+log10(modulus(c3))+"\n")
result("\n Log of Modulus + 1 values:\n" )
result( "c1 = \t"+log(modulus(c1) + 1)+"\n")
result( "c2 = \t"+log(modulus(c2) + 1)+"\n")
result( "c3 = \t"+log(modulus(c3) + 1)+"\n")
This gives you:
Complex values:
c1 = 30 + 40 i
c2 = 3 + 4 i
c3 = 0.3 + 0.4 i
Modulus values:
c1 = 50
c2 = 5
c3 = 0.5
Log of Modulus values:
c1 = 1.69897
c2 = 0.69897
c3 = -0.30103
Log of Modulus +1 values:
c1 = 3.93183
c2 = 1.79176
c3 = 0.405465

compleximage ComplexImage( string title, number size,
number width, number height )
width and height are in pixels
number x = 512, y = 512
compleximage myImage := ComplexImage( "My Image", 16, x, y )
myImage = complex( irow, icol )
ShowImage( myImage )
This example creates an 512 x 512 pixel, 16 byte complex image with the title
"My Image". It then sets all pixels in the image to the expression complex(
irow, icol ). This expression is a complex image expression where the real part is the row number of every pixel and the imaginary part is the column
number of every pixel. Finally it shows the image.

Related

Getting the charge of a single atom, per loop in MD Analysis

I have been trying to use the partial charge of one particular ion to go through a calculation within mdanalysis.
I have tried(This is just a snippet from the code that I know is throwing the error):
Cl = u.select_atoms('resname CLA and prop z <= 79.14')
Lz = 79.14 #Determined from system set-up
Q_sum = 0
COM = 38.42979431152344 #Determined from VMD
file_object1 = open(fors, 'a')
print(dcd, file = file_object1)
for ts in u.trajectory[200:]:
frame = u.trajectory.frame
time = u.trajectory.time
for coord in Cl.positions:
q= Cl.total_charge(Cl.position[coord][2])
coords = coord - (Lz/COM)
q_prof = q * (coords + (Lz / 2)) / Lz
Q_sum = Q_sum + q_prof
print(q)
But I keep getting an error associated with this.
How would I go about selecting this particular atom as it goes through the loop to get the charge of it in MD Analysis? Before I was setting q to equal a constant and the code ran fine so I know it is only this line that is throwing the error:
q = Cl.total_charge(Cl.position[coord][2])
Thanks for the help!
I figured it out with:
def Q_code(dcd, topo):
Lz = u.dimensions[2]
Q_sum = 0
count = 0
CLAs = u.select_atoms('segid IONS or segid PROA or segid PROB or segid MEMB')
ini_frames = -200
n_frames = len(u.trajectory[ini_frames:])
for ts in u.trajectory[ini_frames:]:
count += 1
membrane = u.select_atoms('segid PROA or segid PROB or segid MEMB')
COM = membrane.atoms.center_of_mass()[2]
q_prof = CLAs.atoms.charges * (CLAs.positions[:,2] + (Lz/2 - COM))/Lz
Q_instant = np.sum(q_prof)
Q_sum += Q_instant
Q_av = Q_sum / n_frames
with open('Q_av.txt', 'a') as f:
print('The Q_av for {} is {}'.format(s, Q_av), file = f)
return Q_av

Offset rotation matrix

I'm working with 2 imu's. I need to offset all frames with the first frame from the sensor. I have created a fictive scenario, where I precisely know the rotation and the wanted result. I need the two sensors to show the same result when their initial (start) orientation is subtracted.
import numpy as np
# Sensor 0,1 and 2 start orientation in degrees
s0_x = 30
s0_y = 0
s0_z = 0
s1_x = 0
s1_y = 40
s1_z = 0
s2_x = 10
s2_y = 40
s2_z= -10
# Change from start frame 1
x1 = 20
y1 = 10
z1 = 0
# Change from start frame 2
x2 = 60
y2 = 30
z2 = 30
GCS= [[1,0,0],[0,1,0],[0,0,1]]
sensor0 = [[s0_x, s0_y, s0_z], [s0_x, s0_y, s0_z], [s0_x, s0_y, s0_z]]
sensor1 = [[s1_x, s1_y, s1_z], [s1_x + x1, s1_y + y1, s1_z + z1],[s1_x + x1 + x2, s1_y + y1+ y2, s1_z + z1+ z2]]
sensor2 = [[s2_x, s2_y, s2_z], [s2_x + x1, s2_y + y1, s2_z + z1], [s2_x + x1+ x2, s2_y + y1+ y2, s2_z + z1+ z2]]
def Rot_Mat_X(theta):
r = np.array([[1,0,0],[0,np.cos(np.deg2rad(theta)),-np.sin(np.deg2rad(theta))],[0,np.sin(np.deg2rad(theta)),np.cos(np.deg2rad(theta))]])
return r
# rotation the rotation matrix around the Y axis (input in deg)
def Rot_Mat_Y(theta):
r = np.array([[np.cos(np.deg2rad(theta)),0,np.sin(np.deg2rad(theta))],
[0,1,0],
[-np.sin(np.deg2rad(theta)),0,np.cos(np.deg2rad(theta))]])
return r
# rotation the rotation matrix around the Z axis (input in deg)
def Rot_Mat_Z(theta):
r = np.array([[np.cos(np.deg2rad(theta)),-np.sin(np.deg2rad(theta)),0],
[np.sin(np.deg2rad(theta)),np.cos(np.deg2rad(theta)),0],
[0,0,1]])
return r
# Creating the rotation matrices
r_sensor0 = []
r_sensor1= []
r_sensor2= []
for i in range(len(sensor1)):
r_sensor1_z = np.matmul(Rot_Mat_X(sensor1[i][0]),GCS)
r_sensor1_zy = np.matmul(Rot_Mat_Y(sensor1[i][1]),r_sensor1_z)
r_R_Upperarm_medial_zyx = np.matmul(Rot_Mat_Z(sensor1[i][2]),r_sensor1_zy )
r_sensor1.append(r_R_Upperarm_medial_zyx )
r_sensor2_z = np.matmul(Rot_Mat_X(sensor2[i][0]),GCS)
r_sensor2_zy = np.matmul(Rot_Mat_Y(sensor2[i][1]),r_sensor2_z )
r_sensor2_zyx = np.matmul(Rot_Mat_Z(sensor2[i][2]),r_sensor2_zy )
r_sensor2.append(r_sensor2_zyx )
r_start_sensor1 = r_sensor1[0]
r_start_sensor2 = r_sensor2[0]
r_offset_sensor1 = []
r_offset_sensor2 = []
for i in range(len(sensor0)):
r_offset_sensor1.append(np.matmul(np.transpose(r_start_sensor1),r_sensor1[i]))
r_offset_sensor2.append(np.matmul(np.transpose(r_start_sensor2),r_sensor2[i]))
# result:
r_offset_sensor1[0] = [[1,0,0],[0,1,0],[0,0,1]]
r_offset_sensor1[1] = [[0.984,0.059,0.163],[0,0.939,-0.342],[-0.173,0.336,0.925]]
r_offset_sensor1[2] = [[0.748,0.466,0.471],[0.086,0.635,-0.767],[-0.657,0.615,0.434]]
r_offset_sensor2[0] = [[1,0,0],[0,1,0],[0,0,1]]
r_offset_sensor2[1] = [[0.984,0.086,0.150],[-0.03,0.938,-0.344],[-0.171,0.334,0.926]]
r_offset_sensor2[2] = [[0.748,0.541,0.383],[-0.028,0.603,-0.797],[-0.662,0.585,0.466]]
I expect the result of sensors 1 and 2 to be equal for all frames but it doesn't? And they should be:
frame[0] = [1,0,0],[0,1,0],[0,0,1]
frame[1] = [0.984,0,0.173],[0.059,0.939,-0.336],[-0.163,0.342,0.9254]
frame[2] = [0.750,-0.433,0.50],[0.625,0.216,-0.750],[0.216,0.875,0.433]

Deleting new lines once the price crosses it after the line was created

I have been creating new lines in pinescript that extend and want to delete them when the future price hits or crosses the line price. Any help will be appreciated.
// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
//#version=4
study("My RS", overlay=true)
float d = 1.0
t = time("60")
start = na(t[1]) or t > t[1]
ticker = syminfo.ticker
src=input(title="Source", type=input.source, defval=open)
float d_r = na
float d_s = na
if (start)
d_r := src + d
d_s := src - d
line lr = na
line ls = na
// drawing r/s lines every hour
if (start)
lr := line.new(x1 = bar_index, y1 = d_r, x2 = bar_index - 1, y2 = d_r, extend = extend.left, color = color.red, width = 2, style = line.style_dashed)
ls := line.new(x1 = bar_index, y1 = d_s, x2 = bar_index - 1, y2 = d_s, extend = extend.left, color = color.lime, width = 2, style = line.style_dashed)
// want to delete lines when the future price crosses the line, which is not working for me
for i = 0 to 100
if not na(lr[i]) and close < high[i]
line.delete(lr[i])
if not na(ls[i]) and close < low[i]
line.delete(ls[i])
you need to get the coordinate of the lines, so use inside a loop if line.get_y1(id[i]) < close if it true, line.delete(id[i]).
Is this what're you looking for?

Sequential sampling from conditional multivariate normal

I'm trying to sequentially sample from a Gaussian Process prior.
The problem is that the samples eventually converge to zero or diverge to infinity.
I'm using the basic conditionals described e.g. here
Note: the kernel(X,X) function returns the squared exponential kernel with isometric noise.
Here is my code:
n = 32
x_grid = np.linspace(-5,5,n)
x_all = []
y_all = []
for x in x_grid:
x_all = [x] + x_all
X = np.array(x_all).reshape(-1, 1)
# Mean and covariance of the prior
mu = np.zeros((X.shape), np.float)
cov = kernel(X, X)
if len(mu)==1: # first sample is not conditional
y = np.random.randn()*cov + mu
else:
# condition on all previous samples
u1 = mu[0]
u2 = mu[1:]
y2 = np.atleast_2d(np.array(y_all)).T
C11 = cov[:1,:1] # dependent sample
C12 = np.atleast_2d(cov[0,1:])
C21 = np.atleast_2d(cov[1:,0]).T
C22 = np.atleast_2d(cov[1:, 1:])
C22_ = la.inv(C22)
u = u1 + np.dot(C12, np.dot(C22_, (y2 - u2)))
C22_xC21 = np.dot(C22_, C21)
C_minus = np.dot(C12, C22_xC21) # this weirdly becomes larger than C!
C = C11 - C_minus
y = u + np.random.randn()*C
y_all = [y.flatten()[0]] + y_all
Here's an example with 32 samples, where it collapses:
enter image description here
Here's an example with 34 samples, where it explodes:
enter image description here
(for this particular kernel, 34 is the number of samples at which (or more) the samples start to diverge.

Probabilistic Record Linkage in Pandas

I have two dataframes (X & Y). I would like to link them together and to predict the probability that each potential match is correct.
X = pd.DataFrame({'A': ["One", "Two", "Three"]})
Y = pd.DataFrame({'A': ["One", "To", "Free"]})
Method A
I have not yet fully understood the theory but there is an approach presented in:
Sayers, A., Ben-Shlomo, Y., Blom, A.W. and Steele, F., 2015. Probabilistic record linkage. International journal of epidemiology, 45(3), pp.954-964.
Here is my attempt to implementat it in Pandas:
# Probability that Matches are True Matches
m = 0.95
# Probability that non-Matches are True non-Matches
u = min(len(X), len(Y)) / (len(X) * len(Y))
# Priors
M_Pr = u
U_Pr = 1 - M_Pr
O_Pr = M_Pr / U_Pr # Prior odds of a match
# Combine the dataframes
X['key'] = 1
Y['key'] = 1
Z = pd.merge(X, Y, on='key')
Z = Z.drop('key',axis=1)
X = X.drop('key',axis=1)
Y = Y.drop('key',axis=1)
# Levenshtein distance
def Levenshtein_distance(s1, s2):
if len(s1) > len(s2):
s1, s2 = s2, s1
distances = range(len(s1) + 1)
for i2, c2 in enumerate(s2):
distances_ = [i2+1]
for i1, c1 in enumerate(s1):
if c1 == c2:
distances_.append(distances[i1])
else:
distances_.append(1 + min((distances[i1], distances[i1 + 1], distances_[-1])))
distances = distances_
return distances[-1]
L_D = np.vectorize(Levenshtein_distance, otypes=[float])
Z["D"] = L_D(Z['A_x'], Z['A_y'])
# Max string length
def Max_string_length(X, Y):
return max(len(X), len(Y))
M_L = np.vectorize(Max_string_length, otypes=[float])
Z["L"] = M_L(Z['A_x'], Z['A_y'])
# Agreement weight
def Agreement_weight(D, L):
return 1 - ( D / L )
A_W = np.vectorize(Agreement_weight, otypes=[float])
Z["C"] = A_W(Z['D'], Z['L'])
# Likelihood ratio
def Likelihood_ratio(C):
return (m/u) - ((m/u) - ((1-m) / (1-u))) * (1-C)
L_R = np.vectorize(Likelihood_ratio, otypes=[float])
Z["G"] = L_R(Z['C'])
# Match weight
def Match_weight(G):
return math.log(G) * math.log(2)
M_W = np.vectorize(Match_weight, otypes=[float])
Z["R"] = M_W(Z['G'])
# Posterior odds
def Posterior_odds(R):
return math.exp( R / math.log(2)) * O_Pr
P_O = np.vectorize(Posterior_odds, otypes=[float])
Z["O"] = P_O(Z['R'])
# Probability
def Probability(O):
return O / (1 + O)
Pro = np.vectorize(Probability, otypes=[float])
Z["P"] = Pro(Z['O'])
I have verified that this gives the same results as in the paper. Here is a sensitivity check on m, showing that it doesn't make a lot of difference:
Method B
These assumptions won't apply to all applications but in some cases each row of X should match a row of Y. In that case:
The probabilities should sum to 1
If there are many credible candidates to match to then that should reduce the probability of getting the right one
then:
X["I"] = X.index
# Combine the dataframes
X['key'] = 1
Y['key'] = 1
Z = pd.merge(X, Y, on='key')
Z = Z.drop('key',axis=1)
X = X.drop('key',axis=1)
Y = Y.drop('key',axis=1)
# Levenshtein distance
def Levenshtein_distance(s1, s2):
if len(s1) > len(s2):
s1, s2 = s2, s1
distances = range(len(s1) + 1)
for i2, c2 in enumerate(s2):
distances_ = [i2+1]
for i1, c1 in enumerate(s1):
if c1 == c2:
distances_.append(distances[i1])
else:
distances_.append(1 + min((distances[i1], distances[i1 + 1], distances_[-1])))
distances = distances_
return distances[-1]
L_D = np.vectorize(Levenshtein_distance, otypes=[float])
Z["D"] = L_D(Z['A_x'], Z['A_y'])
# Max string length
def Max_string_length(X, Y):
return max(len(X), len(Y))
M_L = np.vectorize(Max_string_length, otypes=[float])
Z["L"] = M_L(Z['A_x'], Z['A_y'])
# Agreement weight
def Agreement_weight(D, L):
return 1 - ( D / L )
A_W = np.vectorize(Agreement_weight, otypes=[float])
Z["C"] = A_W(Z['D'], Z['L'])
# Normalised Agreement Weight
T = Z .groupby('I') .agg({'C' : sum})
D = pd.DataFrame(T)
D.columns = ['T']
J = Z.set_index('I').join(D)
J['P1'] = J['C'] / J['T']
Comparing it against Method A:
Method C
This combines method A with method B:
# Normalised Probability
U = Z .groupby('I') .agg({'P' : sum})
E = pd.DataFrame(U)
E.columns = ['U']
K = Z.set_index('I').join(E)
K['P1'] = J['P1']
K['P2'] = K['P'] / K['U']
We can see that method B (P1) doesn't take account of uncertainty whereas method C (P2) does.