diff --git a/pyproject.toml b/pyproject.toml
index 804de13..dc38b9e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -25,4 +25,4 @@ doc = [
 ]
 
 [tool.poetry.scripts]
-wmin = "wmin.app:main"
+wmin = "wmin.app:main"
\ No newline at end of file
diff --git a/wmin/app.py b/wmin/app.py
index cf679f1..ffbfb29 100644
--- a/wmin/app.py
+++ b/wmin/app.py
@@ -11,6 +11,7 @@
     "wmin.model",
     "wmin.utils",
     "wmin.basis",
+    "wmin.completeness",
 ]
 
 
diff --git a/wmin/completeness.py b/wmin/completeness.py
new file mode 100644
index 0000000..b10bb4f
--- /dev/null
+++ b/wmin/completeness.py
@@ -0,0 +1,200 @@
+"""
+wmin.completeness.py
+
+This module contains the functions for checking the completeness of a weight-minimisation
+basis. It includes plotting tools.
+"""
+
+from validphys.core import PDF
+from reportengine.figure import figure, figuregen
+
+import matplotlib.pyplot as plt
+
+import numpy as np
+
+
+def basis_to_target_distances(
+    target_pdfs,
+    wmin_basis_pdfs,
+    nweights,
+    pdf_aliases,
+    dist_type=0,
+    Q=1.65,
+    x_grid=np.logspace(-5, 0, 50),
+    flavours=[1, -1, 2, -2, 3, -3, 4, 21],
+):
+    """Computes the distances from the target PDFs to the wmin_basis_pdfs."""
+
+    target_pdf_sets = []
+    for target_pdf in target_pdfs:
+        name = pdf_aliases.get(target_pdf, target_pdf)
+        target_pdf_sets.append(
+            {"name": name, "members": PDF(target_pdf).load().members[1:]}
+        )
+
+    wmin_bases = []
+    for pdf_basis in wmin_basis_pdfs:
+        name = pdf_aliases.get(pdf_basis, pdf_basis)
+        loaded_pdf = PDF(pdf_basis).load()
+        wmin_bases.append(
+            {
+                "name": name,
+                "central": pdf_grid_allflav(
+                    loaded_pdf.central_member, flavours, x_grid, Q
+                ),
+                "members": loaded_pdf.members[1 : nweights + 1],
+            }
+        )
+
+    distances = {}
+    for basis in wmin_bases:
+        distances[basis["name"]] = []
+        for pdf in target_pdf_sets:
+            distance = []
+            for member in pdf["members"]:
+                original, reco, w, d = wmin_distance(
+                    member,
+                    basis["central"],
+                    basis["members"],
+                    flavours,
+                    x_grid,
+                    Q,
+                    dist_type=dist_type,
+                )
+                distance.append(d)
+            distances[basis["name"]].append(
+                {"name": pdf["name"], "distances": distance}
+            )
+
+    return distances
+
+
+@figuregen
+def histogram_individual_target_sets(basis_to_target_distances):
+    """Produces plots showing the error in the approximation when the
+    wmin_basis_pdf is used to approximate the target_pdfs.
+    """
+
+    for basis, targets in basis_to_target_distances.items():
+        fig, ax = plt.subplots(figsize=(7, 5))
+        overflow_threshold = 0.05
+        bins = np.linspace(0, overflow_threshold, 30)
+
+        for index, target in enumerate(targets):
+            d = np.array(target["distances"])
+            d[d > overflow_threshold] = overflow_threshold + 0.001
+            targets[index] = {"name": target["name"], "distances": d}
+
+        ax.hist(
+            [target["distances"] for target in targets],
+            label=[target["name"] for target in targets],
+            # alpha=0.6,
+            bins=np.append(bins, 0.052),
+            # edgecolor="black",
+            linewidth=2,
+            histtype="step",
+            density=False,
+            stacked=True,
+        )
+        ax.set_title("Distances of PDF sets from %s " % basis)
+        ax.set_xlabel("Score", fontsize=16)
+        ax.set_ylabel("Count", fontsize=16)
+        ax.legend(frameon=False, fontsize=14)
+        # set xticks to specific values
+        ax.set_xticks([0, 0.01, 0.02, 0.03, 0.04])
+        # add a tick after 0.05, overflow, with label > 0.5
+        ax.set_xticks([0.051], minor=True)
+        ax.set_xticklabels(["$>$0.05"], minor=True)
+
+        yield fig
+
+
+@figure
+def histogram_complete_target_set(basis_to_target_distances):
+    """Produces a plot showing the error in the approximation when
+    the wmin_basis_pdf is used to approximate the target_pdfs.
+    """
+
+    fig, ax = plt.subplots(figsize=(7, 5))
+    overflow_threshold = 0.05
+    bins = np.linspace(0, overflow_threshold, 30)
+    for basis, targets in basis_to_target_distances.items():
+        all_distances = []
+        for target in targets:
+            all_distances.extend(target["distances"])
+        d = np.array(all_distances)
+        d[d > overflow_threshold] = overflow_threshold + 0.001
+        ax.hist(
+            d,
+            label="Basis: %s" % basis,
+            # alpha=0.6,
+            bins=np.append(bins, 0.052),
+            # edgecolor="black",
+            linewidth=2,
+            histtype="step",
+            density=False,
+        )
+    ax.set_title("Distances of weight-minimisation bases to target set")
+    ax.set_xlabel("Score", fontsize=16)
+    ax.set_ylabel("Count", fontsize=16)
+    ax.legend(frameon=False, fontsize=14)
+    # set xticks to specific values
+    ax.set_xticks([0, 0.01, 0.02, 0.03, 0.04])
+    # add a tick after 0.05, overflow, with label > 0.5
+    ax.set_xticks([0.051], minor=True)
+    ax.set_xticklabels(["$>$0.05"], minor=True)
+
+    return fig
+
+
+def pdf_grid(pdf, pid, x_grid, Q):
+    out = []
+    for x in x_grid:
+        out.append(pdf.xfxQ(pid, x, Q))
+    return np.array(out)
+
+
+def pdf_grid_allflav(pdf, flavours, x_grid, Q):
+    out = np.array([])
+    for pid in flavours:
+        out = np.append(out, pdf_grid(pdf, pid, x_grid, Q))
+    return out
+
+
+def wmin_distance(
+    pdf_target, center_pdf_grid, wmin_basis, flavours, x_grid, Q, dist_type=0
+):
+    Y = pdf_grid_allflav(pdf_target, flavours, x_grid, Q) - center_pdf_grid
+    X = np.array(
+        [
+            pdf_grid_allflav(replica, flavours, x_grid, Q) - center_pdf_grid
+            for replica in wmin_basis
+        ]
+    ).T
+
+    if dist_type == 0:
+        Sigma = np.identity(len(Y))
+
+    elif dist_type == 1:
+        Sigma = np.diag(np.abs(1 / (Y + center_pdf_grid)))
+
+    elif dist_type == 2:
+        Sigma = np.diag(np.abs(1 / (Y + center_pdf_grid) ** 2))
+
+    elif dist_type == 3:
+        X_grid = np.tile(x_grid, len(flavours))
+        Sigma = np.diag(np.abs(X_grid / (Y + center_pdf_grid)))
+
+    elif dist_type == 4:
+        X_grid = np.tile(x_grid, len(flavours))
+        Sigma = np.diag(np.abs(X_grid))
+
+    w = np.linalg.inv(X.T @ Sigma @ X) @ X.T @ Sigma @ Y
+    distance = (Y - X @ w) @ Sigma @ (Y - X @ w)
+
+    original = pdf_grid_allflav(pdf_target, flavours, x_grid, Q).reshape(
+        len(flavours), len(x_grid)
+    )
+    reco = (center_pdf_grid + X @ w).reshape(len(flavours), len(x_grid))
+
+    return original, reco, w, distance
diff --git a/wmin/runcards/basis_completeness_plots.yaml b/wmin/runcards/basis_completeness_plots.yaml
new file mode 100644
index 0000000..8a0eb05
--- /dev/null
+++ b/wmin/runcards/basis_completeness_plots.yaml
@@ -0,0 +1,39 @@
+meta:
+  author: James Moore
+  title: Plotting
+  keywords: [wmin basis]
+
+pdf_aliases:
+  NNPDF23_nnlo_as_0118: NNPDF2.3
+  240918_mnc_wmin_nnpdf40_basis_disonly_pca: NNPDF40dis_pca
+  240919_mnc_pdf4lhc_basis_pca: PDF4LHC_pca
+  240919_mnc_mixed_pdf4lhc_nnpdf40_basis_pca: PDF4LHC_NNPDF40_pca
+
+target_pdfs:
+  - NNPDF23_nnlo_as_0118
+  - JAM19PDF_proton_nlo
+  - NNPDF40_nlo_as_01180
+  - NNPDF40_lo_as_01180
+
+wmin_basis_pdfs: 
+  - 240918_mnc_wmin_nnpdf40_basis_disonly_pca
+  - 240919_mnc_pdf4lhc_basis_pca
+  - 240919_mnc_mixed_pdf4lhc_nnpdf40_basis_pca 
+
+dist_types:
+  - dist_type: 0
+  - dist_type: 1
+
+nweights: 60
+
+template_text: |
+  {@with dist_types@}
+  # Distances with distance type {@dist_type@}
+  ## Distances to complete target set
+  {@histogram_complete_target_set@}
+  ## Distances from bases to each target set
+  {@histogram_individual_target_sets@}
+  {@endwith@}
+
+actions_:
+  - report(main=True)