Matrix Arithmetic

The basic arithmetic operators in camlFloat are +$, -$ and *$. The trailing dollar sign serves the same purpose as the period in the equivalent floating point operators.

Some simple manipulations might look like

# let x = eye 4 4 in
  x +$ x ;;
   2       0       0       0
   0       2       0       0
   0       0       2       0
   0       0       0       2
- : Nla.DBlop.matrix = 

# ones 3 3 *$ ones 3 3 *$ ones 3 3;;
   9       9       9
   9       9       9
   9       9       9
- : Nla.DBlop.matrix = 

Multiplying transposes

Instead of calculating matrix transposes explicitly, we can use efficient algorithms to calculate a product involving a transpose. To do this we use the operators *~$ and *$~ . It is worth taking a moment to get used to this notation, as it establishes the convention used for the other operators.

The * must come first, as it is the leading symbol which establishes precedence. Then we view the $ as a divider, with the tilde going on the side where the transposition is happening. Thus a *$~ b multiplies a by the transpose of b, whereas a *~$ b multiplies the transpose of a by b. We demonstrate below by taking the inner and outer product of two vectors.

# let a = ones 3 1
  and b = consts 4.0 3 1 in
  a *~$ b ;;
  12
- : Nla.DBlop.matrix = 

# let a = ones 3 1
  and b = consts 4.0 3 1 in
  a *$~ b ;;
   4       4       4
   4       4       4
   4       4       4
- : Nla.DBlop.matrix =