def products():
result = {}
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x1 = umatrix.matrix([[0.71,-0.71,0.7],[0.71,0.71,0.5],[0,0,1]])
y_row = umatrix.matrix([[1,0,1]])
y_col = umatrix.matrix([1, 0, 1], cstride=1, rstride=1)
result['matrix * scaler'] = matrix_compare(x10*2, umatrix.matrix([[0, 2, 4, 6],[8, 10, 12, 14],[16, 18, 20, 22],[24, 26, 28, 30]]))
result['matrix * matrix elementwise'] = matrix_compare(x11*x11, umatrix.matrix([[0, 1, 4],[16, 25, 36],[64, 81, 100],[144, 169, 196]]))
result['row dot matrix 1x3 . 3x3'] = matrix_compare(ulinalg.dot(y_row,x1), umatrix.matrix([[ 0.71, -0.71, 1.7 ]]))
try:
result['matrix dot col 3x3 . 3x1'] = matrix_compare(ulinalg.dot(x1,y_col), umatrix.matrix([1.41, 1.21, 1.0], cstride=1, rstride=1), tol=eps)
except ValueError:
result['matrix dot col 3x3 . 3x1'] = False
x = umatrix.matrix([[ 3., -2., -2.]])
y = umatrix.matrix([[-1., 0., 5.]])
x1 = umatrix.matrix([[ 3., -2.]])
y1 = umatrix.matrix([[-1., 0.]])
result['cross product (x,y)'] = matrix_compare(ulinalg.cross(x,y), umatrix.matrix([[-10.0 , -13.0 , -2.0]]))
result['cross product (y,x)'] = matrix_compare(ulinalg.cross(y,x), umatrix.matrix([[10.0 , 13.0 , 2.0]]))
result['cross product 2 (x,y)'] = matrix_compare(ulinalg.cross(x1,y1), umatrix.matrix([[-2.0]]))
x = umatrix.matrix([[ 3., -2., -2.],[-1., 0., 5.]])
y = umatrix.matrix([[-1., 0., 5.]])
try:
result['cross product shape mismatch (x,y)'] = matrix_compare(ulinalg.cross(x,y), umatrix.matrix([[-10.0 , -13.0 , -2.0]]))
except ValueError:
result['cross product shape mismatch (x,y)'] = True
return result
def products():
result = {}
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x1 = umatrix.matrix([[0.71,-0.71,0.7],[0.71,0.71,0.5],[0,0,1]])
y_row = umatrix.matrix([[1,0,1]])
y_col = umatrix.matrix([1, 0, 1], cstride=1, rstride=1)
result['matrix * scaler'] = matrix_compare(x10*2, umatrix.matrix([[0, 2, 4, 6],[8, 10, 12, 14],[16, 18, 20, 22],[24, 26, 28, 30]]))
result['matrix * matrix elementwise'] = matrix_compare(x11*x11, umatrix.matrix([[0, 1, 4],[16, 25, 36],[64, 81, 100],[144, 169, 196]]))
result['row dot matrix 1x3 . 3x3'] = matrix_compare(ulinalg.dot(y_row,x1), umatrix.matrix([[ 0.71, -0.71, 1.7 ]]))
try:
result['matrix dot col 3x3 . 3x1'] = matrix_compare(ulinalg.dot(x1,y_col), umatrix.matrix([1.41, 1.21, 1.0], cstride=1, rstride=1))
except ValueError:
result['matrix dot col 3x3 . 3x1'] = False
x = umatrix.matrix([[ 3., -2., -2.]])
y = umatrix.matrix([[-1., 0., 5.]])
x1 = umatrix.matrix([[ 3., -2.]])
y1 = umatrix.matrix([[-1., 0.]])
result['cross product (x,y)'] = matrix_compare(ulinalg.cross(x,y), umatrix.matrix([[-10.0 , -13.0 , -2.0]]))
result['cross product (y,x)'] = matrix_compare(ulinalg.cross(y,x), umatrix.matrix([[10.0 , 13.0 , 2.0]]))
result['cross product 2 (x,y)'] = matrix_compare(ulinalg.cross(x1,y1), umatrix.matrix([[-2.0]]))
x = umatrix.matrix([[ 3., -2., -2.],[-1., 0., 5.]])
y = umatrix.matrix([[-1., 0., 5.]])
try:
result['cross product shape mismatch (x,y)'] = matrix_compare(ulinalg.cross(x,y), umatrix.matrix([[-10.0 , -13.0 , -2.0]]))
except ValueError:
result['cross product shape mismatch (x,y)'] = True
return result
def update_imu(self, gyroscope, accelerometer):
"""
Perform one update step with data from a IMU sensor array
:param gyroscope: A three-element array containing the gyroscope data in radians per second.
:param accelerometer: A three-element array containing the accelerometer data. Can be any unit since a normalized value is used.
"""
q = self.quaternion
# Normalise accelerometer measurement
if ulinalg.norm(accelerometer) is 0:
print("accelerometer is zero")
return
accelerometer = accelerometer / ulinalg.norm(accelerometer)
# Gradient descent algorithm corrective step
f = umatrix.matrix([
2 * (q[1] * q[3] - q[0] * q[2]) - accelerometer[0, 0], 2 *
(q[0] * q[1] + q[2] * q[3]) - accelerometer[0, 1], 2 *
(0.5 - q[1]**2 - q[2]**2) - accelerometer[0, 2]
],
cstride=1,
rstride=1,
dtype=float)
j = umatrix.matrix([
-2 * q[2], 2 * q[3], -2 * q[0], 2 * q[1], 2 * q[1], 2 * q[0],
2 * q[3], 2 * q[2], 0, -4 * q[1], -4 * q[2], 0
],
cstride=1,
rstride=4,
dtype=float)
step = ulinalg.dot(j.transpose(), f)
step = step / ulinalg.norm(step) # normalise step magnitude
# Compute rate of change of quaternion
qdot = (q * Quaternion(0, gyroscope[0, 0], gyroscope[0, 1],
gyroscope[0, 2])) * 0.5 - Quaternion(
step.T * self.beta)
# Integrate to yield quaternion
q = q + qdot * (self.samplePeriod)
self.quaternion = q * (1 / ulinalg.norm(q._q)) # normalise quaternion
y = int(round(rd * math.sin(math.radians(azm_i[index] - 90)), 0))
xm = xc + x
ym = yc + y
graphics.fill_circle(xm, ym, 2, 1)
# show current location if visible
if visible_i[index] == 'Yes':
rd = int(round(rad * math.cos(math.radians(alc_i[index])), 0))
x = int(round(rd * math.cos(math.radians(azc_i[index] - 90)), 0))
y = int(round(rd * math.sin(math.radians(azc_i[index] - 90)), 0))
xcu = xc + x
ycu = yc + y
graphics.circle(xcu, ycu, 2, 1)
# find path of transit
A = matrix.matrix([[xr**2, xr, 1], [xm**2, xm, 1], [xs**2, xs, 1]])
B = matrix.matrix([[yr], [ym], [ys]])
d_i = linalg.det_inv(A)
invA = d_i[1]
X = linalg.dot(invA, B)
for i in range(xr - xs):
x = xs + i
oled.pixel(x, yc - int((X[0] * x**2)) + int(
(X[1] * x)) + int(X[2]), 1)
oled.show()
utime.sleep(10)
# collect garbage just in case that is causing the crashes
gc.collect()
def skyChart(name):
# display stuff
oled.text(name, 0, 0)
oled.text("Visible:", 0, 10)
oled.text(visible_i[names.index(name)], 80, 10)
oled.show()
# sky chart
xc = 94
yc = 31
rad = 29
graphics.circle(xc, yc, rad, 1)
# show planet rise azimuth
x = int(
round(rad * math.cos(math.radians(azr_i[names.index(name)] - 90)), 0))
y = int(
round(rad * math.sin(math.radians(azr_i[names.index(name)] - 90)), 0))
xr = xc + x
yr = yc + y
graphics.fill_circle(xr, yr, 2, 1)
# show planet set azimuth
x = int(
round(rad * math.cos(math.radians(azs_i[names.index(name)] - 90)), 0))
y = int(
round(rad * math.sin(math.radians(azs_i[names.index(name)] - 90)), 0))
xs = xc + x
ys = yc + y
graphics.fill_circle(xs, ys, 2, 1)
# show location at maximum altitude
rd = int(round(rad * math.cos(math.radians(alm_i[names.index(name)])), 0))
x = int(
round(rd * math.cos(math.radians(azm_i[names.index(name)] - 90)), 0))
y = int(
round(rd * math.sin(math.radians(azm_i[names.index(name)] - 90)), 0))
xm = xc + x
ym = yc + y
graphics.fill_circle(xm, ym, 2, 1)
# show current location if visible
if visible_i[index] == 'Yes':
rd = int(
round(rad * math.cos(math.radians(alc_i[names.index(name)])), 0))
x = int(
round(rd * math.cos(math.radians(azc_i[names.index(name)] - 90)),
0))
y = int(
round(rd * math.sin(math.radians(azc_i[names.index(name)] - 90)),
0))
xcu = xc + x
ycu = yc + y
graphics.circle(xcu, ycu, 2, 1)
# find path of transit
A = matrix.matrix([[xr**2, xr, 1], [xm**2, xm, 1], [xs**2, xs, 1]])
B = matrix.matrix([[yr], [ym], [ys]])
d_i = linalg.det_inv(A)
invA = d_i[1]
X = linalg.dot(invA, B)
for i in range(xr - xs):
x = xs + i
oled.pixel(x, yc - int((X[0] * x**2)) + int((X[1] * x)) + int(X[2]), 1)
oled.show()
# collect garbage just in case that is causing the crashes
gc.collect()