[DOCS] Transposition fix

docs/tutorials/matrix-transposition.rst

@@ -25,8 +25,8 @@ In Triton, however, kernels are single-threaded and the compiler automatically d
       int rm[TM] = pidm * TM + 0 ... TM; //(3)
       int rn[TN] = pidn * TN + 0 ... TN; //(4)
       // create 2D array of pointers
-      TYPE* px[TM, TN] = X + rm[:, newaxis] + rn[newaxis, :] * ldx; //(5)
+      TYPE* px[TM, TN] = X + rm[:, newaxis] * ldx + rn[newaxis, :]; //(5)
-      TYPE* py[TN, TM] = Y + rm[newaxis, :] * ldy + rn[:, newaxis]; //(6)
+      TYPE* py[TN, TM] = Y + rm[newaxis, :] + rn[:, newaxis] * ldy; //(6)
       // write back using the transposition operator '^'
       *py = ^(*px); //(7)
     }
@@ -73,6 +73,65 @@ which will be used in statements (5) and (6) to construct tiles of pointers
 - Statement (7) element-wise dereferences the above array of pointers `*px`, transposes it using the unary transposition operator `^`, and writes it back at the location specified by `py`.
 
 
+==================================
+A Note on Numpy-style Broadcasting
+==================================
+
+The construction statements (5) and (6) are a little subtle. To help understand them, consider the following numpy example.
+
+First, we create a row vector of numbers 0 to 11, which we reshape into a 4x3 matrix.
+
+.. code-block:: python
+
+  import numpy as np
+
+  vec = np.linspace(0,11,12)
+  mat = vec.reshape((4,3))
+
+Imagine that we would like to process this in two 2x3 tiles (i.e. tile 0 will consider the top half, and tile 1 will consider the bottom).
+
+::
+
+  [[ 0,  1,  2],
+   [ 3,  4,  5],
+   [ 6,  7,  8],
+   [ 9, 10, 11]]
+
+Given `pidm=0`, `pidn=0`, `TM=2`, `TN=3`, we would like for tile 0 to have the values:
+
+::
+
+    [ 0,  1,  2],
+    [ 3,  4,  5],
+
+We construct ranges `rm` and `rn` as:
+::
+
+    rm = [0, 1]
+    rn = [0, 1, 2]
+
+Using numpy-style broadcasting, we can add these together to create a matrix:
+
+::
+
+    rm[:, np.newaxis] + rn[np.newaxis, :]
+
+           rn -> [0, 1, 2]
+     rm -> [0., [[0, 1, 2],
+            1.]  [1, 2, 3]]
+
+The bottom row is incorrect. Notice that `rm` indexes the rows of the matrix; we need to offset it so that each element gives the index
+of the start of that row. For instance, to access row 1 column 0, we need to access location 3. To access row 2 column 0, we need
+to access location 6. To translate from row N, column 0, we need to multiply N by the number of columns in each row (the leading dimension).
+In this case this is 3, so what we really need is:
+
+::
+
+    ldx = 3
+    px  = rm[:, np.newaxis] * ldx + rn[np.newaxis,:]
+
+`newaxis` is built into Triton, and pointer arrays can be constructed in just the same way (as in this example).
+
 ==========================
 The __multipleof attribute
 ==========================
@@ -111,3 +170,5 @@ You might have noticed that the above code will fail when `M` and `N` are not mu
 
 
 Here, statements (7a) creates an array of booleans :code:`checkx[TM, TN]` such that :code:`checkx(i, j) = True` if and only if `px(i, j)` should be dereferenced. Statement (7b) does the same for `py`. Both `px` and `py` are then conditionally dereferenced using Triton-C's conditional dereferencing operator :code:`*?(predicate) pointer`.
+
+A runnable version of this kernel is available `here <https://github.com/ptillet/triton/tree/master/python/examples/tutorials/mat_transpose.py>`_.

python/examples/tutorials/mat_transpose.py

@@ -14,10 +14,15 @@ class _transpose(torch.autograd.Function):
           int rn[TN] = pidn * TN + 0 ... TN; //(4)
 
           // create 2D array of pointers
-          TYPE* px[TM, TN] = X + rm[:, newaxis] + rn[newaxis, :] * ldx; //(5)
+          TYPE* px[TM, TN] = X + rm[:, newaxis] * ldx + rn[newaxis, :]; //(5)
-          TYPE* py[TN, TM] = Y + rm[newaxis, :] * ldy + rn[:,newaxis]; //(6)
+          TYPE* py[TN, TM] = Y + rm[newaxis, :] + rn[:, newaxis] * ldy; //(6)
 
-          *py = ^*px;
+          // create bounds-checking mask
+          bool checkx[TM, TN] = (rm[:, newaxis] < M) && (rn[newaxis, :] < N); //(7a)
+          bool checky[TN, TM] = (rn[:, newaxis] < N) && (rm[newaxis, :] < M); //(7b)
+
+          // conditional write-back using the conditional dereferencing operatior '*?()'
+          *?(checky)py = ^(*?(checkx)px); //(7)
         }
     """
 
@@ -40,6 +45,7 @@ class _transpose(torch.autograd.Function):
            'TM'   : [32,64,128],
            'TN'   : [32,64,128],
        }
+
        grid = lambda opt: [triton.cdiv(M, opt.d('TM')), triton.cdiv(N, opt.d('TN'))]
 
        if _transpose.kernel is None:
@@ -53,7 +59,7 @@ transpose = _transpose.apply
 
 # test
 torch.manual_seed(0)
-x = torch.randn(128,200).cuda()
+x = torch.randn(1024,128).cuda()
 
 print(x)