Add a file containing the function to calculate the voltage corrections

src/bimorph_mirror_analysis/maths.py

@@ -0,0 +1,38 @@
+def find_voltages(data: np.ndarray, v: float, baseline_voltage_scan: str = 'first' ) -> np.ndarray:
+    '''
+    given a matrix of beamline centroid data, with columns of beamline scans at different actuator voltages and rows of slit positions, calculate the necessary voltages corrections to achive the target centroid position.
+
+    Parameters:
+    data: np.ndarray
+        matrix of beamline centroid data, with rows of different slit positions and columns of pencil beam scans at different actuator voltages
+    v: float
+        The voltage increment applied to the actuators between pencil beam scans
+    baseline_voltage_scan: str
+        The pencil beam scan to use as the baseline for the centroid calculation. Options are 'first' and 'last'. 
+        'first' uses the first pencil beam scan, where no incremental voltage has been applied to the actuators. 
+        'last' uses the last pencil beam scan, where the incremental voltage has been applied to every actuator.
+
+    Returns:
+    np.ndarray
+        array of voltage corrections required to move the centroid of each pencil beam scan to the target position
+    '''
+    responses = np.diff(data, axis=1) # calculate the response of each actuator by subtracting previous pencil beam 
+
+    H = responses / v #response per unit charge
+    H = np.hstack((np.ones((H.shape[0],1)),H)) #add columns of 1's to the left of H
+    H_inv = np.linalg.pinv(H) # calculate the Moore-Penrose pseudo inverse of H
+
+
+    if baseline_voltage_scan == 'first':
+        baseline_voltage_beamline_positions = data[:,0]
+    elif baseline_voltage_scan == 'last':
+        baseline_voltage_beamline_positions = data[:,-1]
+    else:
+        raise ValueError('baseline_voltage_scan must be either "first" or "last"')
+
+    target = np.mean(baseline_voltage_beamline_positions)
+    Y = target - baseline_voltage_beamline_positions
+
+    voltage_corrections = np.matmul(H_inv,Y) #calculate the voltage required to move the centroid to the target position
+
+    return voltage_corrections[1:] #return the voltages required to move the centroid of each pencil beam scan to the target position