diff --git a/.gitignore b/.gitignore
index 8b7a06b..8462796 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,3 +1,4 @@
 /target
 *.iml
-.idea
\ No newline at end of file
+.idea
+src/data/training.json
\ No newline at end of file
diff --git a/src/data/unittest.json b/src/data/unittest.json
new file mode 100644
index 0000000..da13f6f
--- /dev/null
+++ b/src/data/unittest.json
@@ -0,0 +1 @@
+{"x":[[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.001171875,0.00703125,0.00703125,0.00703125,0.04921875,0.053125,0.068359375,0.01015625,0.06484375,0.099609375,0.096484375,0.049609375,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.01171875,0.0140625,0.03671875,0.06015625,0.06640625,0.098828125,0.098828125,0.098828125,0.098828125,0.098828125,0.087890625,0.0671875,0.098828125,0.09453125,0.076171875,0.025,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.019140625,0.09296875,0.098828125,0.098828125,0.098828125,0.098828125,0.098828125,0.098828125,0.098828125,0.098828125,0.098046875,0.036328125,0.03203125,0.03203125,0.021875,0.015234375,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.00703125,0.085546875,0.098828125,0.098828125,0.098828125,0.098828125,0.098828125,0.07734375,0.07109375,0.096484375,0.094140625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.03125,0.0609375,0.041796875,0.098828125,0.098828125,0.080078125,0.004296875,0.0,0.016796875,0.06015625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.00546875,0.000390625,0.06015625,0.098828125,0.03515625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.054296875,0.098828125,0.07421875,0.00078125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.004296875,0.07421875,0.098828125,0.02734375,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.013671875,0.094140625,0.087890625,0.0625,0.0421875,0.000390625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.031640625,0.09375,0.098828125,0.098828125,0.046484375,0.009765625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.017578125,0.07265625,0.098828125,0.098828125,0.05859375,0.010546875,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.00625,0.036328125,0.0984375,0.098828125,0.073046875,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.097265625,0.098828125,0.097265625,0.025,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.01796875,0.05078125,0.071484375,0.098828125,0.098828125,0.080859375,0.00078125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.015234375,0.0578125,0.089453125,0.098828125,0.098828125,0.098828125,0.09765625,0.07109375,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.009375,0.04453125,0.086328125,0.098828125,0.098828125,0.098828125,0.098828125,0.078515625,0.03046875,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.008984375,0.02578125,0.083203125,0.098828125,0.098828125,0.098828125,0.098828125,0.07734375,0.031640625,0.00078125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.00703125,0.066796875,0.085546875,0.098828125,0.098828125,0.098828125,0.098828125,0.076171875,0.03125,0.003515625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.021484375,0.0671875,0.08828125,0.098828125,0.098828125,0.098828125,0.098828125,0.0953125,0.051953125,0.004296875,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.053125,0.098828125,0.098828125,0.098828125,0.0828125,0.052734375,0.0515625,0.00625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]], "y":[5]}
\ No newline at end of file
diff --git a/src/dataloader.rs b/src/dataloader.rs
index 7fae50b..a3ba0e5 100644
--- a/src/dataloader.rs
+++ b/src/dataloader.rs
@@ -1,19 +1,20 @@
 use std::iter::zip;
+use nalgebra::DMatrix;
 
 use rand::prelude::*;
 use serde::Deserialize;
 
-pub fn load_data() -> Data<f32, u8> {
-    /// the mnist data is structured as
-    /// x: [[[pixels]],[[pixels]], etc],
-    /// y: [label1, label2, etc]
-    /// this is transformed to:
-    /// Data : Vec<DataLine>
-    /// DataLine {inputs: Vec<pixels as f32>, label: f32}
+pub fn load_data() -> Data<f32, OneHotVector> {
+    // the mnist data is structured as
+    // x: [[[pixels]],[[pixels]], etc],
+    // y: [label1, label2, etc]
+    // this is transformed to:
+    // Data : Vec<DataLine>
+    // DataLine {inputs: Vec<pixels as f32>, label: f32}
     let raw_data: RawData = serde_json::from_slice(include_bytes!("data/unittest.json")).unwrap();
     let mut vec = Vec::new();
     for (x, y) in zip(raw_data.x, raw_data.y) {
-        vec.push(DataLine { inputs: x, label: y});
+        vec.push(DataLine { inputs: x, label: onehot(y) });
     }
 
     Data(vec)
@@ -27,17 +28,38 @@ struct RawData {
 
 /// X is type of input
 /// Y is type of output
-pub struct DataLine<X,Y> {
+pub struct DataLine<X, Y> {
     pub inputs: Vec<X>,
     pub label: Y,
 }
 
-pub struct Data<X,Y>(pub Vec<DataLine<X,Y>>);
+pub struct Data<X, Y>(pub Vec<DataLine<X, Y>>);
+
+pub struct OneHotVector{
+    pub val: usize
+}
+
+impl OneHotVector{
+    fn new(val: usize) -> Self{
+        Self{
+            val
+        }
+    }
+
+    pub fn get(&self, index: usize) -> f32{
+        if self.val == index {
+            1.0
+        } else {
+            0.0
+        }
+    }
 
 
-impl<X,Y> Data<X,Y> {
+}
+
+impl<X, Y> Data<X, Y> {
     pub fn shuffle(&mut self) {
-        let mut rng = rand::thread_rng();
+        let mut rng = thread_rng();
         self.0.shuffle(&mut rng);
     }
 
@@ -45,7 +67,7 @@ impl<X,Y> Data<X,Y> {
         self.0.len()
     }
 
-    pub fn as_batches(&self, batch_size: usize) -> Vec<&[DataLine<X,Y>]> {
+    pub fn as_batches(&self, batch_size: usize) -> Vec<&[DataLine<X, Y>]> {
         let mut batches = Vec::with_capacity(self.0.len() / batch_size + 1);
         let mut offset = 0;
         for _ in 0..self.0.len() / batch_size {
@@ -55,6 +77,9 @@ impl<X,Y> Data<X,Y> {
         batches.push(&self.0[offset..self.0.len()]);
         batches
     }
-
-
 }
+
+/// returns a vector as matrix where y is one-hot encoded
+fn onehot(y: u8) -> OneHotVector {
+   OneHotVector::new(y as usize)
+}
\ No newline at end of file
diff --git a/src/lib.rs b/src/lib.rs
index f154dc1..ca821ee 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,2 +1,3 @@
 pub mod net;
-pub mod dataloader;
\ No newline at end of file
+pub mod dataloader;
+mod mat;
\ No newline at end of file
diff --git a/src/main.rs b/src/main.rs
index ebd727d..1f1a7f2 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -2,14 +2,15 @@ use mnist_rs::dataloader::load_data;
 
 fn main() {
     let mut net = mnist_rs::net::Network::from(vec![784, 30, 10]);
-    for w in net.weights.iter() {
-        println!("{}, {}", w.shape().0, w.shape().1);
-    }
-    println!();
-    for b in net.biases.iter() {
-        println!("{:?}", b.shape());
-    }
     let training_data = load_data();
 
     net.sgd(training_data, 30, 10, 3.0, &None);
+
+
+    // let sizes = vec![5,3,2];
+    // let net = mnist_rs::net::Network::from(sizes);
+    // println!("biases {:?}", net.biases.iter().map(|b|b.shape()).collect::<Vec<(usize,usize)>>());
+    // println!("weights {:?}", net.weights.iter().map(|b|b.shape()).collect::<Vec<(usize,usize)>>());
+
+
 }
\ No newline at end of file
diff --git a/src/mat.rs b/src/mat.rs
new file mode 100644
index 0000000..4564cc1
--- /dev/null
+++ b/src/mat.rs
@@ -0,0 +1,205 @@
+use core::ops::Add;
+use std::fmt::Debug;
+use std::ops::AddAssign;
+use nalgebra::DMatrix;
+
+pub fn add<T>(v1: DMatrix<T>, v2: DMatrix<T>) -> Result<DMatrix<T>, String>
+    where T: PartialEq + Copy + Clone + Debug + Add + Add<Output=T> + AddAssign + 'static
+{
+    let (r1, c1) = v1.shape();
+    let (r2, c2) = v2.shape();
+
+    if r1 == r2 && c1 == c2 {
+        // same size, no broadcasting needed
+        Ok(v1 + v2)
+    } else if r1 == 1 && c2 == 1 {
+        Ok(DMatrix::from_fn(r2, c1, |r, c| *v1.get(c).unwrap() + *v2.get(r).unwrap()))
+    } else if c1 == 1 && r2 == 1 {
+        Ok(DMatrix::from_fn(r1, c2, |r, c| *v1.get(r).unwrap() + *v2.get(c).unwrap()))
+    } else if r1 == 1 && c1 == c2 {
+        Ok(DMatrix::from_fn(r2, c1, |r, c| *v1.get(c).unwrap() + *v2.get(c * r2 + r).unwrap()))
+    } else if r2 == 1 && c1 == c2 {
+        Ok(DMatrix::from_fn(r1, c2, |r, c| *v2.get(c).unwrap() + *v1.get(c * r1 + r).unwrap()))
+    } else if c1 == 1 && r1 == r2 {
+        Ok(DMatrix::from_fn(r1, c2, |r, c| *v1.get(r).unwrap() + *v2.get(c * r2 + r).unwrap()))
+    } else if c2 == 1 && r1 == r2 {
+        Ok(DMatrix::from_fn(r2, c1, |r, c| *v2.get(r).unwrap() + *v1.get(c * r2 + r).unwrap()))
+    } else {
+        Err(format!("ValueError: operands could not be broadcast together ({},{}), ({},{})", r1,c1, r2, c2))
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use nalgebra::dmatrix;
+    use super::*;
+
+    #[test]
+    fn stretch_row_column_to_square() {
+        let v1: DMatrix<u32> = dmatrix![1,2,3];
+        let v2: DMatrix<u32> = dmatrix![1;2;3];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (3, 3));
+        assert_eq!(sum, dmatrix![2,3,4;3,4,5;4,5,6]);
+    }
+
+    #[test]
+    fn stretch_row_column_to_rect() {
+        let v1: DMatrix<u32> = dmatrix![1,2,3];
+        let v2: DMatrix<u32> = dmatrix![1;2];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 3));
+        assert_eq!(sum, dmatrix![2,3,4;3,4,5]);
+    }
+
+    #[test]
+    fn stretch_column_row_to_square() {
+        let v1: DMatrix<u32> = dmatrix![1;2;3];
+        let v2: DMatrix<u32> = dmatrix![1,2,3];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (3, 3));
+        assert_eq!(sum, dmatrix![2,3,4;3,4,5;4,5,6]);
+    }
+
+    #[test]
+    fn stretch_column_row_to_rect() {
+        let v1: DMatrix<u32> = dmatrix![1;2;3];
+        let v2: DMatrix<u32> = dmatrix![1,2];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (3, 2));
+        assert_eq!(sum, dmatrix![2,3;3,4;4,5]);
+    }
+
+    #[test]
+    fn stretch_row() {
+        let v1: DMatrix<u32> = dmatrix![1,2,3];
+        let v2: DMatrix<u32> = dmatrix![1,2,3;4,5,6];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 3));
+        assert_eq!(sum, dmatrix![2,4,6;5,7,9]);
+    }
+
+    #[test]
+    fn stretch_row_commute() {
+        let v1: DMatrix<u32> = dmatrix![1,2,3;4,5,6];
+        let v2: DMatrix<u32> = dmatrix![1,2,3];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 3));
+        assert_eq!(sum, dmatrix![2,4,6;5,7,9]);
+    }
+
+    #[test]
+    fn stretch_column() {
+        let v1: DMatrix<u32> = dmatrix![1;2];
+        let v2: DMatrix<u32> = dmatrix![1,2,3;4,5,6];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 3));
+        assert_eq!(sum, dmatrix![2,3,4;6,7,8]);
+    }
+
+    #[test]
+    fn stretch_column_commute() {
+        let v1: DMatrix<u32> = dmatrix![1,2,3;4,5,6];
+        let v2: DMatrix<u32> = dmatrix![1;2];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 3));
+        assert_eq!(sum, dmatrix![2,3,4;6,7,8]);
+    }
+
+    #[test]
+    fn test_broadcast_2dims() {
+        let v1: DMatrix<u32> = dmatrix![1,2,3];
+        let v2: DMatrix<u32> = dmatrix![1;2;3];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (3, 3));
+        assert_eq!(sum, dmatrix![2,3,4;3,4,5;4,5,6]);
+    }
+
+    #[test]
+    fn test_add_commutative() {
+        let v1 = dmatrix![1,2,3];
+        let v2 = dmatrix![1;2;3];
+
+        let sum = add(v2, v1).unwrap();
+        assert_eq!(sum.shape(), (3, 3));
+        assert_eq!(sum, dmatrix![2,3,4;3,4,5;4,5,6]);
+    }
+
+    #[test]
+    fn test_add_same_size() {
+        let v1 = dmatrix![1,2;3,4];
+        let v2 = dmatrix![3,4;5,6];
+
+        let sum = add(v2, v1).unwrap();
+        assert_eq!(sum.shape(), (2, 2));
+        assert_eq!(sum, dmatrix![4,6;8,10]);
+    }
+
+    #[test]
+    fn test_add_row_broadcast() {//
+        let v1 = dmatrix![1,2;3,4];
+        let v2 = dmatrix![3,4];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum, dmatrix![4,6;6,8]);
+    }
+
+    #[test]
+    fn test_add_row_broadcast2() {
+        let v1 = dmatrix![1,1];
+        let v2 = dmatrix![1,2;3,4];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 2));
+        assert_eq!(sum, dmatrix![2,3;4,5]);
+    }
+
+    #[test]
+    fn test_column_broadcast() {
+        let v1 = dmatrix![1;1];
+        let v2 = dmatrix![1,2;3,4];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 2));
+        assert_eq!(sum, dmatrix![2,3;4,5]);
+    }
+
+    #[test]
+    fn test_column_broadcast2() {
+        let v1 = dmatrix![1,2;3,4];
+        let v2 = dmatrix![1;1];
+
+        let sum = add(v1, v2).unwrap();
+        assert_eq!(sum.shape(), (2, 2));
+        assert_eq!(sum, dmatrix![2,3;4,5]);
+    }
+
+    #[test]
+    fn column_too_long() {
+        let v1 = dmatrix![1;1;1];
+        let v2 = dmatrix![1,2;3,4];
+
+        let result = add(v1, v2);
+        assert_eq!(result, Err("ValueError: operands could not be broadcast together".to_owned()));
+    }
+
+    #[test]
+    fn row_too_long() {
+        let v1 = dmatrix![1,1,1];
+        let v2 = dmatrix![1,2;3,4];
+
+        let result = add(v1, v2);
+        assert_eq!(result, Err("ValueError: operands could not be broadcast together".to_owned()));
+    }
+
+
+}
\ No newline at end of file
diff --git a/src/net.rs b/src/net.rs
index 49504ef..0b68ce6 100644
--- a/src/net.rs
+++ b/src/net.rs
@@ -1,17 +1,18 @@
-use std::convert::identity;
 use std::iter::zip;
-use std::ops::{Add, Sub};
+use std::ops::Add;
 
-use nalgebra::{DMatrix, Matrix, OMatrix};
+use nalgebra::DMatrix;
 use rand::prelude::*;
 use rand_distr::Normal;
 
-use crate::dataloader::{Data, DataLine};
+use crate::dataloader::{Data, DataLine, OneHotVector};
+use crate::mat;
+use crate::mat::add;
 
 #[derive(Debug)]
 pub struct Network {
     _sizes: Vec<usize>,
-    _num_layers: usize,
+    num_layers: usize,
     pub biases: Vec<DMatrix<f32>>,
     pub weights: Vec<DMatrix<f32>>,
 }
@@ -30,7 +31,7 @@ impl Network {
     pub fn from(sizes: Vec<usize>) -> Self {
         Self {
             _sizes: sizes.clone(),
-            _num_layers: sizes.len(),
+            num_layers: sizes.len(),
             biases: biases(sizes[1..].to_vec()),
             weights: weights(zip(sizes[..sizes.len() - 1].to_vec(), sizes[1..].to_vec()).collect()),
         }
@@ -39,13 +40,13 @@ impl Network {
     fn feed_forward(&self, input: Vec<f32>) -> Vec<f32> {
         let mut a = DMatrix::from_vec(input.len(), 1, input);
         for (b, w) in zip(&self.biases, &self.weights) {
-            a = b.add_scalar(w.dot(&a));
+            a = add(b.clone(), w * a).unwrap();
             a.apply(sigmoid_inplace);
         }
         a.column(1).iter().map(|v| *v).collect()
     }
 
-    pub fn sgd(&mut self, mut training_data: Data<f32, u8>, epochs: usize, minibatch_size: usize, eta: f32, test_data: &Option<Data<f32, u8>>) {
+    pub fn sgd(&mut self, mut training_data: Data<f32, OneHotVector>, epochs: usize, minibatch_size: usize, eta: f32, test_data: &Option<Data<f32, OneHotVector>>) {
         for j in 0..epochs {
             training_data.shuffle();
             let mini_batches = training_data.as_batches(minibatch_size);
@@ -65,7 +66,7 @@ impl Network {
     /// gradient descent using backpropagation to a single mini batch.
     /// The ``mini_batch`` is a list of tuples ``(x, y)``, and ``eta``
     /// is the learning rate.
-    fn update_mini_batch(&mut self, mini_batch: &[DataLine<f32, u8>], eta: f32) {
+    fn update_mini_batch(&mut self, mini_batch: &[DataLine<f32, OneHotVector>], eta: f32) {
         let mut nabla_b: Vec<DMatrix<f32>> = self.biases.iter()
             .map(|b| b.shape())
             .map(|s| DMatrix::zeros(s.0, s.1))
@@ -75,34 +76,34 @@ impl Network {
             .map(|s| DMatrix::zeros(s.0, s.1))
             .collect();
         for line in mini_batch.iter() {
-            let (delta_nabla_b, delta_nabla_w) = self.backprop(line.inputs.to_vec(), line.label);
+            let (delta_nabla_b, delta_nabla_w) = self.backprop(line.inputs.to_vec(), &line.label);
 
             nabla_b = zip(&nabla_b, &delta_nabla_b).map(|(nb, dnb)| nb.add(dnb)).collect();
             nabla_w = zip(&nabla_w, &delta_nabla_w).map(|(nw, dnw)| nw.add(dnw)).collect();
         }
 
         self.weights = zip(&self.weights, &nabla_w)
-            .map(|(w, nw)| w.add_scalar(-eta / mini_batch.len() as f32)).collect();
+            .map(|(w, nw)| (w.add_scalar(-eta / mini_batch.len() as f32)).component_mul(nw)).collect();
         self.biases = zip(&self.biases, &nabla_b)
-            .map(|(b, nb)| b.add_scalar(-eta / mini_batch.len() as f32)).collect();
+            .map(|(b, nb)| (b.add_scalar(-eta / mini_batch.len() as f32)).component_mul(nb)).collect();
     }
 
     /// Return the number of test inputs for which the neural
     /// network outputs the correct result. Note that the neural
     /// network's output is assumed to be the index of whichever
     /// neuron in the final layer has the highest activation.
-    fn evaluate(&self, test_data: &Data<f32, u8>) -> usize {
-        let test_results: Vec<(usize, u8)> = test_data.0.iter()
-            .map(|line| (argmax(self.feed_forward(line.inputs.clone())), line.label))
+    fn evaluate(&self, test_data: &Data<f32, OneHotVector>) -> usize {
+        let test_results: Vec<(usize, usize)> = test_data.0.iter()
+            .map(|line| (argmax(self.feed_forward(line.inputs.clone())), line.label.val))
             .collect();
-        test_results.into_iter().filter(|(x, y)| *x == *y as usize).count()
+        test_results.into_iter().filter(|(x, y)| x == y).count()
     }
 
     /// Return a tuple `(nabla_b, nabla_w)` representing the
     /// gradient for the cost function C_x.  `nabla_b` and
     /// `nabla_w` are layer-by-layer lists of matrices, similar
     /// to `self.biases` and `self.weights`.
-    fn backprop(&self, x: Vec<f32>, y: u8) -> (Vec<DMatrix<f32>>, Vec<DMatrix<f32>>) {
+    fn backprop(&self, x: Vec<f32>, y: &OneHotVector) -> (Vec<DMatrix<f32>>, Vec<DMatrix<f32>>) {
         // zero_grad ie. set gradient to zero
         let mut nabla_b: Vec<DMatrix<f32>> = self.biases.iter()
             .map(|b| b.shape())
@@ -119,38 +120,40 @@ impl Network {
         let mut zs = vec![];
 
         for (b, w) in zip(&self.biases, &self.weights) {
-            // println!("{:?}", w.shape());
-            // println!("{:?}", activation.shape());
-            // println!("{:?}", b.shape());
-
-            let mut z: DMatrix<f32> = w * &activation + b;
+            let z = add(w * &activation, b.clone()).unwrap();
             zs.push(z.clone());
             activation = z.map(sigmoid);
             activations.push(activation.clone());
         }
-
         // backward pass
-        let delta: DMatrix<f32> = self.cost_derivative(
-            &activations[activations.len() - 1],
-            y as f32);
-        println!("delta {:?}", delta.shape());
-        println!("z {:?}", &zs[zs.len() - 1].transpose().shape());
-        let delta = delta * (&zs[zs.len() - 1].transpose().map(sigmoid_prime));
-        println!("delta {:?}", delta.shape());
+        // delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1])
+        let delta: DMatrix<f32> = self.cost_derivative(&activations[activations.len() - 1], y).component_mul((&zs[zs.len() - 1].map(sigmoid_prime)));
         let index = nabla_b.len() - 1;
         nabla_b[index] = delta.clone();
 
-        println!("delta {:?}", delta.shape());
-        println!("activation {:?}", activations[activations.len() - 2].shape());
         let index = nabla_w.len() - 1;
-        nabla_w[index] = delta * &activations[activations.len() - 2];
-
+        let ac = &activations[activations.len() - 2].transpose();
+        nabla_w[index] = &delta * ac;
+        let lens_zs = zs.len();
+        for l in 2..self.num_layers {
+            let z = &zs[lens_zs - l];
+            let sp = z.map(sigmoid_prime);
+            let weight = self.weights[self.weights.len() - l + 1].transpose();
+            let delta2 = (weight * &delta).component_mul(&sp);
+            let len_nb = nabla_b.len();
+            nabla_b[len_nb - l] = delta2.clone();
+            let len_nw = nabla_w.len();
+            nabla_w[len_nw - l] = delta2 * activations[activations.len() - l - 1].transpose();
+        }
 
         (nabla_b, nabla_w)
     }
 
-    fn cost_derivative(&self, output_activations: &DMatrix<f32>, y: f32) -> DMatrix<f32> {
-        output_activations.add_scalar(-y)
+    fn cost_derivative(&self, output_activations: &DMatrix<f32>, y: &OneHotVector) -> DMatrix<f32> {
+        // output_activations - y
+        let shape = output_activations.shape();
+        DMatrix::from_iterator(shape.0, shape.1, output_activations.iter().enumerate()
+            .map(|(index, a)| a - y.get(index)))
     }
 }
 
@@ -171,7 +174,6 @@ fn biases(sizes: Vec<usize>) -> Vec<DMatrix<f32>> {
 }
 
 fn weights(sizes: Vec<(usize, usize)>) -> Vec<DMatrix<f32>> {
-    println!("{:?}", sizes);
     sizes.iter().map(|size| random_matrix(size.1, size.0)).collect()
 }