How to utilize GPUs to accelerate my code?

Hi, I have a function `render_texture` that implements the z-buffer algorithm to render texture, but it’s very slow. I need to backpropagate through this function. How can I accelerate it by utilizing GPU’s parallelization?

``````def render_texture(vertices, colors, triangles, h, w, c=3, device="cpu"):
"""render mesh by z buffer. vertices,colors, and triangles are tensors
Args:
shape of vertices: 3 x n vertices
shape of colors: 3 x n vertices
shape of triangles: 3 x n triangles
h: height
w: width
"""
# initial
image = torch.zeros((h, w, c)).to(device)

depth_buffer = torch.zeros([h, w]) - 999999.0
# triangle depth: approximate the depth to the average value of z in each
# vertex(v0, v1, v2), since the vertices are closed to each other
tri_depth = (
vertices[2, triangles[0, :]]
+ vertices[2, triangles[1, :]]
+ vertices[2, triangles[2, :]]
) / 3.0
tri_tex = (
colors[:, triangles[0, :]]
+ colors[:, triangles[1, :]]
+ colors[:, triangles[2, :]]
) / 3.0

for i in range(triangles.shape[1]):
tri = triangles[:, i]  # 3 vertex indices

# the inner bounding box
umin = max(int(torch.ceil(torch.min(vertices[0, tri]))), 0)
umax = min(int(torch.floor(torch.max(vertices[0, tri]))), w - 1)

vmin = max(int(torch.ceil(torch.min(vertices[1, tri]))), 0)
vmax = min(int(torch.floor(torch.max(vertices[1, tri]))), h - 1)

if umax < umin or vmax < vmin:
continue

for u in range(umin, umax + 1):
for v in range(vmin, vmax + 1):
if tri_depth[i] > depth_buffer[v, u] and isPointInTriangle(
[u, v], vertices[:2, tri].cpu().numpy()
):
depth_buffer[v, u] = tri_depth[i]
image[v, u, :] = tri_tex[:, i]
return image

def isPointInTriangle(point, tri_points):
"""Judge whether the point is in the triangle
Method:
http://blackpawn.com/texts/pointinpoly/
Args:
point: [u, v] or [x, y]
tri_points: three vertices(2d points) of a triangle. 2 coords x 3 vertices
Returns:
bool: true for in triangle
"""
tp = tri_points

# vectors
v0 = tp[:, 2] - tp[:, 0]
v1 = tp[:, 1] - tp[:, 0]
v2 = point - tp[:, 0]

# dot products
dot00 = np.matmul(v0.T, v0)
dot01 = np.matmul(v0.T, v1)
dot02 = np.matmul(v0.T, v2)
dot11 = np.matmul(v1.T, v1)
dot12 = np.matmul(v1.T, v2)

# barycentric coordinates
if dot00 * dot11 - dot01 * dot01 == 0:
inverDeno = 0
else:
inverDeno = 1 / (dot00 * dot11 - dot01 * dot01)

u = (dot11 * dot02 - dot01 * dot12) * inverDeno
v = (dot00 * dot12 - dot01 * dot02) * inverDeno

# check if point in triangle
return (u >= 0) & (v >= 0) & (u + v < 1)
``````