add first draft of scheduling docs

Author: Jessica Shi

documentation/docs/scheduling.md

@@ -0,0 +1,90 @@
+The scheduling language enables users to specify and compose transformations to further optimize the code generated by taco. 
+
+Consider the following SpMV computation and associated code, which we will transform below:
+```c++
+Format csr({Dense,Sparse});
+Tensor<double> A("A", {512, 64}, csr);
+Tensor<double> x("x", {64}, {Dense});
+Tensor<double> y("y", {512}, {Dense});
+
+IndexVar i, j; 
+y(i) = A(i, j) * x(j);
+IndexStmt stmt = y.getAssignment().concretize();
+```
+```c
+for (int32_t i = 0; i < A1_dimension; i++) {
+	double y_val = 0.0;
+	for (int32_t jA = A2_pos[i]; jA < A2_pos[(i + 1)]; jA++) {
+		int32_t j = A2_crd[jA];
+		y_val += A_vals[jA] * x_vals[j];
+	}
+	y_vals[i] = y_val;
+}
+```
+# Pos
+
+The `pos(i, ipos, access)` transformation takes in an index variable `i` that operates over the coordinate space of `access` and replaces it with a derived index variable `ipos` that operates over the same iteration range, but with respect to the the position space. 
+
+Since the `pos` transformation is not valid for dense level formats, for the SpMV example, the following would result in an error:
+```c++
+stmt = stmt.pos(i, IndexVar("ipos"), A);
+```
+
+We could instead have: 
+```c++
+stmt = stmt.pos(j, IndexVar("jpos"), A);
+```
+```c
+for (int32_t i = 0; i < A1_dimension; i++) {
+    for (int32_t jposA = A2_pos[i]; jposA < A2_pos[(i + 1)]; jposA++) {
+      	if (jposA < A2_pos[i] || jposA >= A2_pos[(i + 1)])
+        	continue;
+
+    	int32_t j = A2_crd[jposA];
+    	y_vals[i] = y_vals[i] + A_vals[jposA] * x_vals[j];
+    }
+} 
+```
+
+# Split 
+
+The `split(i, i0, i1, splitFactor)` transformation splits (strip-mines) an index variable `i` into two nested index variables `i0` and `i1`. The size of the inner index variable `i1` is then held constant at `splitFactor`, which must be a positive integer.
+
+For the SpMV example, we could have: 
+```c++
+stmt = stmt.split(j, IndexVar("i0"), IndexVar("i1"), 16);
+```
+```c
+for (int32_t i0 = 0; i0 < ((A1_dimension + 15) / 16); i0++) {
+    for (int32_t i1 = 0; i1 < 16; i1++) {
+      	int32_t i = i0 * 16 + i1;
+      	if (i >= A1_dimension)
+        	continue;
+
+    	for (int32_t jA = A2_pos[i]; jA < A2_pos[(i + 1)]; jA++) {
+        	int32_t j = A2_crd[jA];
+        	y_vals[i] = y_vals[i] + A_vals[jA] * x_vals[j];
+    	}
+    }
+}
+```
+
+# Reorder
+
+The `reorder(vars)` transformation takes in a new ordering for a set of index variables in the expression that are directly nested in the iteration order. 
+
+For the SpMV example, we could have: 
+```c++
+stmt = stmt.reorder({j, i});
+```
+```c
+for (int32_t jA = A2_pos[iA]; jA < A2_pos[(iA + 1)]; jA++) {
+    int32_t j = A2_crd[jA];
+    for (int32_t i = 0; i < A1_dimension; i++) {
+    	y_vals[i] = y_vals[i] + A_vals[jA] * x_vals[j];
+    }
+ }
+```
+
+
+

documentation/mkdocs.yml

@@ -15,6 +15,7 @@ pages:
     - C++ Library:
         - 'Defining Tensors': 'tensors.md'
         - 'Computing on Tensors': 'computations.md'
+        - 'Providing a Schedule': 'scheduling.md'
     - Python Library:
         - 'Tutorial': 'tutorial.md'
         - 'Defining Tensors': 'pytensors.md'