What does "only if" mean exactly? I learned the followings; 'if', 'only if', and 'if and only if'.
I understood like the followings;
'$A$ if $B$' means that 'That $B$ holds implies that $A$ holds'
'$A$ only if $B$' means that 'That $A$ holds implies that $B$ holds'
'$A$ if and only if $B$' means that 'That $B$ holds implies that $A$ holds. At the same 
time, that $A$ holds implies that $B$ holds'

However, in the textbook states 'DP can be applied numerically only if the dimensions of the spaces are relatively small.'
I do not understand why the author uses only if instead of if.
Is there any exception of these notations with respect to 'if' that I do not know?

"A if B".      When B is true then A must be true (sufficient).
"A only if B". When B is false then A must be false (necessary).
"A if and only if B". When B is true A must be true, When B is false A must be false. (necessary and sufficient)
"if" allows A to be any truth value when B is false.
"only if" allows A to be any truth value when B is true.
