feat: enhance linear algebra operations (#2972)

- Add `dot()` for vector/matrix products
- Implement the `Frobenius` norm
- Add `mv()` for matrix-vector multiply

candle-core/tests/matmul_tests.rs

@@ -82,6 +82,26 @@ fn broadcast_matmul(device: &Device) -> Result<()> {
     Ok(())
 }
 
+#[test]
+fn tensor_dot() -> Result<()> {
+    let lhs = Tensor::new(&[1., 2., 3.], &Device::Cpu)?;
+    let rhs = Tensor::new(&[4., 5., 6.], &Device::Cpu)?;
+    let expected = Tensor::new(32., &Device::Cpu)?;
+    let dot_ret = lhs.dot(&rhs)?;
+    candle_core::test_utils::assert_tensor_eq(&dot_ret, &expected)?;
+    Ok(())
+}
+
+#[test]
+fn tensor_mv() -> Result<()> {
+    let mat = Tensor::new(&[[1., 2., 3.], [4., 5., 6.]], &Device::Cpu)?;
+    let vec = Tensor::new(&[1., 1., 1.], &Device::Cpu)?;
+    let expected = Tensor::new(&[6., 15.], &Device::Cpu)?;
+    let mv_ret = mat.mv(&vec)?;
+    candle_core::test_utils::assert_tensor_eq(&mv_ret, &expected)?;
+    Ok(())
+}
+
 // https://github.com/huggingface/candle/issues/1948
 fn squeeze_mm(device: &Device) -> Result<()> {
     let seq_len = 8_usize;

candle-core/tests/tensor_tests.rs

@@ -1880,3 +1880,11 @@ fn tensor_new() -> Result<()> {
     );
     Ok(())
 }
+
+#[test]
+fn tensor_norm() -> Result<()> {
+    let t = Tensor::new(&[[3., 4.], [0., 0.]], &Device::Cpu)?;
+    let norm = t.norm()?;
+    assert_eq!(norm.to_scalar::<f64>()?, 5.);
+    Ok(())
+}