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v0.2.0
v0.3.0
252 changes: 252 additions & 0 deletions v0.3.0/_downloads/0cd804d4bb1b789ed7d110b2910079bf/jacobian.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "ed2827e5",
"metadata": {
"execution": {
"iopub.execute_input": "2024-10-08T19:49:32.363199Z",
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"shell.execute_reply": "2024-10-08T19:49:32.576805Z"
}
},
"outputs": [],
"source": [
"import numba\n",
"import numpy as np\n",
"from choclo.prism import gravity_u\n",
"\n",
"@numba.jit(nopython=True, parallel=True)\n",
"def build_jacobian(coordinates, prisms):\n",
" \"\"\"\n",
" Build a sensitivity matrix for gravity_u of a prism\n",
" \"\"\"\n",
" # Unpack coordinates of the observation points\n",
" easting, northing, upward = coordinates[:]\n",
" # Initialize an empty 2d array for the sensitivity matrix\n",
" n_coords = easting.size\n",
" n_prisms = prisms.shape[0]\n",
" jacobian = np.empty((n_coords, n_prisms), dtype=np.float64)\n",
" # Compute the gravity_u field that each prism generate on every observation\n",
" # point, considering that they have a unit density\n",
" for i in numba.prange(len(easting)):\n",
" for j in range(prisms.shape[0]):\n",
" jacobian[i, j] = gravity_u(\n",
" easting[i],\n",
" northing[i],\n",
" upward[i],\n",
" prisms[j, 0],\n",
" prisms[j, 1],\n",
" prisms[j, 2],\n",
" prisms[j, 3],\n",
" prisms[j, 4],\n",
" prisms[j, 5],\n",
" 1.0,\n",
" )\n",
" return jacobian"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "ba4ab9d7",
"metadata": {
"execution": {
"iopub.execute_input": "2024-10-08T19:49:32.579385Z",
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}
},
"outputs": [],
"source": [
"easting = np.linspace(-5.0, 5.0, 21)\n",
"northing = np.linspace(-4.0, 4.0, 21)\n",
"easting, northing = np.meshgrid(easting, northing)\n",
"upward = 10 * np.ones_like(easting)\n",
"\n",
"coordinates = (easting.ravel(), northing.ravel(), upward.ravel())"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1fce33a7",
"metadata": {
"execution": {
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"shell.execute_reply": "2024-10-08T19:49:32.586985Z"
}
},
"outputs": [],
"source": [
"prisms = np.array(\n",
" [\n",
" [-10.0, 0.0, -7.0, 0.0, -15.0, -10.0],\n",
" [-10.0, 0.0, 0.0, 7.0, -25.0, -15.0],\n",
" [0.0, 10.0, -7.0, 0.0, -20.0, -13.0],\n",
" [0.0, 10.0, 0.0, 7.0, -12.0, -8.0],\n",
" ]\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "65c544bc",
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"execution": {
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"shell.execute_reply": "2024-10-08T19:49:34.244918Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-4.49966911e-11, -4.76014375e-11, -3.80054986e-11,\n",
" -2.83231448e-11],\n",
" [-4.49659418e-11, -4.75828152e-11, -3.86898648e-11,\n",
" -2.90433576e-11],\n",
" [-4.48738920e-11, -4.75270202e-11, -3.93578743e-11,\n",
" -2.97540033e-11],\n",
" ...,\n",
" [-3.19387365e-11, -4.58884222e-11, -4.10526880e-11,\n",
" -4.48751701e-11],\n",
" [-3.12924999e-11, -4.52460654e-11, -4.11114162e-11,\n",
" -4.49880072e-11],\n",
" [-3.06338007e-11, -4.45849449e-11, -4.11310225e-11,\n",
" -4.50257165e-11]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"jacobian = build_jacobian(coordinates, prisms)\n",
"jacobian"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "a3e1efe4",
"metadata": {
"execution": {
"iopub.execute_input": "2024-10-08T19:49:34.248257Z",
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"shell.execute_reply": "2024-10-08T19:49:34.250874Z"
}
},
"outputs": [],
"source": [
"# Define densities for the prisms\n",
"densities = np.array([200.0, 300.0, -100.0, 400.0])\n",
"\n",
"# Compute result\n",
"g_u = jacobian @ densities"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "cb6da38a",
"metadata": {
"execution": {
"iopub.execute_input": "2024-10-08T19:49:34.252971Z",
"iopub.status.busy": "2024-10-08T19:49:34.252796Z",
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"shell.execute_reply": "2024-10-08T19:49:34.256492Z"
}
},
"outputs": [],
"source": [
"@numba.jit(nopython=True, parallel=True)\n",
"def gravity_upward_parallel(coordinates, prisms, densities):\n",
" \"\"\"\n",
" Compute the upward component of the acceleration of a set of prisms\n",
" \"\"\"\n",
" # Unpack coordinates of the observation points\n",
" easting, northing, upward = coordinates[:]\n",
" # Initialize a result array full of zeros\n",
" result = np.zeros_like(easting, dtype=np.float64)\n",
" # Compute the upward component that every prism generate on each\n",
" # observation point\n",
" for i in numba.prange(len(easting)):\n",
" for j in range(prisms.shape[0]):\n",
" result[i] += gravity_u(\n",
" easting[i],\n",
" northing[i],\n",
" upward[i],\n",
" prisms[j, 0],\n",
" prisms[j, 1],\n",
" prisms[j, 2],\n",
" prisms[j, 3],\n",
" prisms[j, 4],\n",
" prisms[j, 5],\n",
" densities[j],\n",
" )\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f54e8c06",
"metadata": {
"execution": {
"iopub.execute_input": "2024-10-08T19:49:34.258473Z",
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"shell.execute_reply": "2024-10-08T19:49:34.909611Z"
}
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"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expected = gravity_upward_parallel(coordinates, prisms, densities)\n",
"np.allclose(g_u, expected)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
118 changes: 118 additions & 0 deletions v0.3.0/_downloads/21b045eb65658e7f0dbd75b01bedc72a/jacobian.py
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#!/usr/bin/env python
# coding: utf-8

# In[1]:


import numba
import numpy as np
from choclo.prism import gravity_u

@numba.jit(nopython=True, parallel=True)
def build_jacobian(coordinates, prisms):
"""
Build a sensitivity matrix for gravity_u of a prism
"""
# Unpack coordinates of the observation points
easting, northing, upward = coordinates[:]
# Initialize an empty 2d array for the sensitivity matrix
n_coords = easting.size
n_prisms = prisms.shape[0]
jacobian = np.empty((n_coords, n_prisms), dtype=np.float64)
# Compute the gravity_u field that each prism generate on every observation
# point, considering that they have a unit density
for i in numba.prange(len(easting)):
for j in range(prisms.shape[0]):
jacobian[i, j] = gravity_u(
easting[i],
northing[i],
upward[i],
prisms[j, 0],
prisms[j, 1],
prisms[j, 2],
prisms[j, 3],
prisms[j, 4],
prisms[j, 5],
1.0,
)
return jacobian


# In[2]:


easting = np.linspace(-5.0, 5.0, 21)
northing = np.linspace(-4.0, 4.0, 21)
easting, northing = np.meshgrid(easting, northing)
upward = 10 * np.ones_like(easting)

coordinates = (easting.ravel(), northing.ravel(), upward.ravel())


# In[3]:


prisms = np.array(
[
[-10.0, 0.0, -7.0, 0.0, -15.0, -10.0],
[-10.0, 0.0, 0.0, 7.0, -25.0, -15.0],
[0.0, 10.0, -7.0, 0.0, -20.0, -13.0],
[0.0, 10.0, 0.0, 7.0, -12.0, -8.0],
]
)


# In[4]:


jacobian = build_jacobian(coordinates, prisms)
jacobian


# In[5]:


# Define densities for the prisms
densities = np.array([200.0, 300.0, -100.0, 400.0])

# Compute result
g_u = jacobian @ densities


# In[6]:


@numba.jit(nopython=True, parallel=True)
def gravity_upward_parallel(coordinates, prisms, densities):
"""
Compute the upward component of the acceleration of a set of prisms
"""
# Unpack coordinates of the observation points
easting, northing, upward = coordinates[:]
# Initialize a result array full of zeros
result = np.zeros_like(easting, dtype=np.float64)
# Compute the upward component that every prism generate on each
# observation point
for i in numba.prange(len(easting)):
for j in range(prisms.shape[0]):
result[i] += gravity_u(
easting[i],
northing[i],
upward[i],
prisms[j, 0],
prisms[j, 1],
prisms[j, 2],
prisms[j, 3],
prisms[j, 4],
prisms[j, 5],
densities[j],
)
return result


# In[7]:


expected = gravity_upward_parallel(coordinates, prisms, densities)
np.allclose(g_u, expected)

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