(docs) several docs improvements across nimplex and stitching

nimplex.nim

@@ -186,6 +186,29 @@ proc simplex_graph*(
     ## neighbors for each node. The current implementation utilizes GC-allocated `seq` for neighbors to reduce memory footprint in cases where `ndiv` is close to `dim` and not 
     ## all nodes have the complete set of `dim(dim-1)` neighbors. This is a tradeoff between memory and performance, which can be adjusted by switching to a (N_S(dim, ndiv), 
     ## dim(dim-1)) `Tensor[int]` with `-1` padding for missing neighbors, just like done in `outFunction_graph`_ for NumPy output generation.
+
+    runnableExamples:
+        import arraymancer/Tensor
+        let (nodes, neighbors) = simplex_graph(3, 4)
+        let nodeSequence = nodes.toSeq2D()
+        for i in 0..<nodeSequence.len:
+            echo i, ":  ", nodeSequence[i], " -> ", neighbors[i]
+        # 0:  @[0, 0, 4] -> @[1, 5]
+        # 1:  @[0, 1, 3] -> @[0, 2, 5, 6]
+        # 2:  @[0, 2, 2] -> @[1, 3, 6, 7]
+        # 3:  @[0, 3, 1] -> @[2, 4, 7, 8]
+        # 4:  @[0, 4, 0] -> @[3, 8]
+        # 5:  @[1, 0, 3] -> @[1, 0, 6, 9]
+        # 6:  @[1, 1, 2] -> @[2, 1, 5, 7, 9, 10]
+        # 7:  @[1, 2, 1] -> @[3, 2, 6, 8, 10, 11]
+        # 8:  @[1, 3, 0] -> @[4, 3, 7, 11]
+        # 9:  @[2, 0, 2] -> @[6, 5, 10, 12]
+        # 10:  @[2, 1, 1] -> @[7, 6, 9, 11, 12, 13]
+        # 11:  @[2, 2, 0] -> @[8, 7, 10, 13]
+        # 12:  @[3, 0, 1] -> @[10, 9, 13, 14]
+        # 13:  @[3, 1, 0] -> @[11, 10, 12, 14]
+        # 14:  @[4, 0, 0] -> @[13, 12]
+
     let L: int = binom(ndiv+dim-1, dim-1)
     var nodes = newTensor[int]([L, dim])
     var neighbors = newSeq[seq[int]](L)
@@ -253,6 +276,23 @@ proc attainable2elemental*(simplexPoints: Tensor[SomeNumber],
         let grid = simplex_grid_fractional(3, 4)
         let elementalGrid = grid.attainable2elemental(components)
         echo elementalGrid
+        # Tensor[system.float] of shape "[15, 3]" on backend "Cpu"
+        # |0.2            0       0.8|
+        # |0.3375    0.0625       0.6|
+        # |0.475      0.125       0.4|
+        # |0.6125    0.1875       0.2|
+        # |0.75        0.25         0|
+        # |0.385     0.0125    0.6025|
+        # |0.5225     0.075    0.4025|
+        # |0.66      0.1375    0.2025|
+        # |0.7975       0.2    0.0025|
+        # |0.57       0.025     0.405|
+        # |0.7075    0.0875     0.205|
+        # |0.845       0.15     0.005|
+        # |0.755     0.0375    0.2075|
+        # |0.8925       0.1    0.0075|
+        # |0.94        0.05      0.01|
+
     # Tensor of components which can be "integer" ([2,2,1]) or "fractional" ([0.4,0.4,0.2]) compositions
     var cmpTensor: Tensor[float] = components.mapIt(it.mapIt(it.float)).toTensor()
     # Normalize components to sum to 1
@@ -263,15 +303,23 @@ proc attainable2elemental*(simplexPoints: Tensor[SomeNumber],
 
 func pure_component_indexes*(dim: int, ndiv: int): seq[int] =
     ## This helper function returns a `seq[int]` of indexes of pure components in a simplex grid of `dim` dimensions and `ndiv` divisions per dimension (e.g., from `simplex_grid`_).
+    runnableExamples:
+        echo "A B C pure components at indices: ", pure_component_indexes(3, 12)
+        # A B C pure components at indices: @[90, 12, 0]
     for d in 1..dim:
         result.add(binom(ndiv+d-1, ndiv)-1)
     # Reverse the order as the last pure component is the first in the grid
     result.reverse()
 
 func pure_component_indexes_internal*(dim: int, ndiv: int): seq[int] =
-    ## This helper function returns a `seq[int]` of indexes of pure components in an **internal** simplex grid of `dim` dimensions and `ndiv` divisions per dimension (e.g., from `simplex_internal_grid`_).
+    ## This helper function returns a `seq[int]` of indexes of pure components in an **internal** simplex grid of `dim` dimensions and `ndiv` divisions per dimension 
+    ## (e.g., from `simplex_internal_grid`_). In this context, by pure components we mean corners of the simplex, corresponding to the points where one component is
+    ## at its maximum and all others are at exactly one quanta (e.g., 1/ndiv).
+    runnableExamples:
+        echo "A+B1C1 B+A1C1 C+A1B1 pure components at indices: ", pure_component_indexes_internal(3, 12)
+        # A+B1C1 B+A1C1 C+A1B1 pure components at indices: @[54, 10, 0]
     for d in 1..dim:
-        result.add(binom(ndiv-1, dim-1)-1)
+        result.add(binom(ndiv-1, d-1)-1)
     # Reverse the order as the last pure component is the first in the grid
     result.reverse()
 

utils/stitching.nim

@@ -141,10 +141,14 @@ proc findStitchingPoints*(
     ## 
     runnableExamples:
         import std/tables
-        let stitch1Table = findStitchingPoints(3, 12, components = @["TiAlloy", "CrV", "VNi"])
-        let stitch2Table = findStitchingPoints(5, 12, components = @["AlCr", "VNi", "Hf90Zr10", "Ti5Zr95", "TiAlloy"])
+        let stitch1Table = findStitchingPoints(
+            3, 12, components = @["TiAlloy", "CrV", "VNi"])
+        let stitch2Table = findStitchingPoints(
+            5, 12, components = @["AlCr", "VNi", "Hf90Zr10", "Ti5Zr95", "TiAlloy"])
         echo "Subspace 1: ", stitch1Table["TiAlloy-VNi"]
+            # Subspace 1: @[90, 88, 85, 81, 76, 70, 63, 55, 46, 36, 25, 13, 0]
         echo "Subspace 2: ", stitch2Table["TiAlloy-VNi"]
+            # Subspace 2: @[0, 91, 169, 235, 290, 335, 371, 399, 420, 435, 445, 451, 454]
 
     let L: int = binom(ndiv+dim-1, dim-1)
     var