Creating a heat map by fetching and balancing from a three-dimensional array

Question

I have some experimental data that exist like this:

x = array([1, 1.12, 1.109, 2.1, 3, 4.104, 3.1, ...])
y = array([-9, -0.1, -9.2, -8.7, -5, -4, -8.75, ...])
z = array([10, 4, 1, 4, 5, 0, 1, ...])

If this is convenient, we can assume that the data exists as a 3D array or even pandas DataFrame:

df = pd.DataFrame({'x': x, 'y': y, 'z': z})

The interpretation, which is for each position x[i], y[i], the value of some variable z[i]. These are not uniformly sampled , so there will be some parts that are “tightly selected” (for example, between 1 and 1.2 in x) and others that are very sparse (for example, between 2 and 3 in x). Because of this, I cannot just insert them in pcolormeshor contourf.

Instead, I would like to make a resample xand yevenly at some fixed interval, and then aggregate the values z. For my needs, zyou can summarize or average to get meaningful values, so this is not a problem. My naive attempt was this:

X = np.arange(min(x), max(x), 0.1)  
Y = np.arange(min(y), max(y), 0.1)
x_g, y_g = np.meshgrid(X, Y)
nx, ny = x_g.shape
z_g = np.full(x_g.shape, np.nan)

for ix in range(nx - 1):
    for jx in range(ny - 1):
        x_min = x_g[ix, jx]
        x_max = x_g[ix + 1, jx + 1]
        y_min = y_g[ix, jx]
        y_max = y_g[ix + 1, jx + 1]
        vals = df[(df.x >= x_min) & (df.x < x_max) & 
                  (df.y >= y_min) & (df.y < y_max)].z.values
        if vals.any():
            z_g[ix, jx] = sum(vals)

It works, and I get the desired result with help plt.contourf(x_g, y_g, z_g), but it is SLOW! I have ~ 20k samples, which then I select into ~ 800 samples in x and ~ 500 by y, that is, the for loop is 400k.

Is there a way to vectorize / optimize this? Even better if there is some function that already does this!

(Also marking this as MATLAB, because the syntax between numpy / MATLAB is very similar, and I have access to both programs.)

Answer 1

Python NumPy broadcasting matrix multiplication np.dot -

x_mask = ((x >= X[:-1,None]) & (x < X[1:,None]))
y_mask = ((y >= Y[:-1,None]) & (y < Y[1:,None]))

z_g_out = np.dot(y_mask*z[None].astype(np.float32), x_mask.T)

# If needed to fill invalid places with NaNs
z_g_out[y_mask.dot(x_mask.T.astype(np.float32))==0] = np.nan

, meshgrid. , , , meshgrid, , , .

# Original app
def org_app(x,y,z):    
    X = np.arange(min(x), max(x), 0.1)  
    Y = np.arange(min(y), max(y), 0.1)
    x_g, y_g = np.meshgrid(X, Y)
    nx, ny = x_g.shape
    z_g = np.full(np.asarray(x_g.shape)-1, np.nan)

    for ix in range(nx - 1):
        for jx in range(ny - 1):
            x_min = x_g[ix, jx]
            x_max = x_g[ix + 1, jx + 1]
            y_min = y_g[ix, jx]
            y_max = y_g[ix + 1, jx + 1]
            vals = z[(x >= x_min) & (x < x_max) & 
                      (y >= y_min) & (y < y_max)]
            if vals.any():
                z_g[ix, jx] = sum(vals)
    return z_g

# Proposed app
def app1(x,y,z):
    X = np.arange(min(x), max(x), 0.1)  
    Y = np.arange(min(y), max(y), 0.1)
    x_mask = ((x >= X[:-1,None]) & (x < X[1:,None]))
    y_mask = ((y >= Y[:-1,None]) & (y < Y[1:,None]))

    z_g_out = np.dot(y_mask*z[None].astype(np.float32), x_mask.T)

    # If needed to fill invalid places with NaNs
    z_g_out[y_mask.dot(x_mask.T.astype(np.float32))==0] = np.nan
    return z_g_out

, , .

-

In [143]: x = np.array([1, 1.12, 1.109, 2.1, 3, 4.104, 3.1])
     ...: y = np.array([-9, -0.1, -9.2, -8.7, -5, -4, -8.75])
     ...: z = np.array([10, 4, 1, 4, 5, 0, 1])
     ...: 

# Verify outputs
In [150]: np.nansum(np.abs(org_app(x,y,z) - app1(x,y,z)))
Out[150]: 0.0

In [145]: %timeit org_app(x,y,z)
10 loops, best of 3: 19.9 ms per loop

In [146]: %timeit app1(x,y,z)
10000 loops, best of 3: 39.1 µs per loop

In [147]: 19900/39.1  # Speedup figure
Out[147]: 508.95140664961633

Answer 2

MATLAB:

X = min(x)-1 :.1:max(x)+1; % the grid needs to be expanded slightly beyond the min and max
Y = min(y)-1 :.1:max(y)+1;
x_o = interp1(X, 1:numel(X), x, 'nearest');
y_o = interp1(Y, 1:numel(Y), y, 'nearest');
z_g = accumarray([x_o(:) y_o(:)], z(:),[numel(X) numel(Y)]);