Moving to gemm and adding matmul backprop.

- Tentative `T` operator.

tests/grad_tests.rs

@@ -1,5 +1,5 @@
 use anyhow::{Context, Result};
-use candle::{Device, Tensor};
+use candle::{Device, Shape, Tensor};
 
 #[test]
 fn simple_grad() -> Result<()> {
@@ -14,3 +14,27 @@ fn simple_grad() -> Result<()> {
     assert_eq!(grad_x.to_vec1::<f32>()?, [11., 7., 13.]);
     Ok(())
 }
+
+#[test]
+fn matmul_grad() -> Result<()> {
+    let data: Vec<_> = (0..12).map(|i| i as f32).collect();
+    let x = Tensor::var_from_slice(&data, (2, 2, 3), &Device::Cpu)?;
+    let data: Vec<_> = (0..12).map(|i| i as f32).collect();
+    let y = Tensor::var_from_slice(&data, (2, 3, 2), &Device::Cpu)?;
+
+    let c = x.matmul(&y)?;
+    let grads = c.backward()?;
+    let grad_x = grads.get(&x).context("no grad for x")?;
+    let grad_y = grads.get(&y).context("no grad for y")?;
+    assert_eq!(grad_x.shape(), &Shape::from((2, 2, 3)));
+    assert_eq!(grad_y.shape(), &Shape::from((2, 3, 2)));
+    assert_eq!(
+        grad_x.as_slice::<f32>()?,
+        &[1., 5., 9., 1., 5., 9., 13., 17., 21., 13., 17., 21.]
+    );
+    assert_eq!(
+        grad_y.as_slice::<f32>()?,
+        &[3., 3., 5., 5., 7., 7., 15., 15., 17., 17., 19., 19.]
+    );
+    Ok(())
+}