Let A, B, C, and X be the dgematrix objects, and A, B, and C be the same size and initialized properly.

Calculation Procedures to Process "X=A*B+C;"
	CPPLapack	ordinary matrix libraries
operator*	calculate A*B, and put it to a local _dgematrix object P to return	calculate A*B, and put it to a local dgematrix object P to return
passing of returned object	make a temporary _dgematrix object Q as the shallow copy of P	make a temporary dgematrix object Q as the deep copy of P
destructor for local object	destruct local object P without deleting the array data	destruct local object P with deleting the array data
operator+	add C into Q, and return Q.	calculate C+Q and, put it to a local dgematrix object R to return.
passing of returned object	make a temporary _dgematrix object R as the shallow copy of Q	make a temporary dgematrix object S as the deep copy of R
destructor for local object	destruct local object Q without deleting the array data	destruct local object R with deleting the array data
operator=	set the array address of X to that of R	copy whole the data of S to X
implicit destructer (;)	destruct the temporary object R without deleting the array data	destruct the temporary objects Q and S with deleting the array data

CPPLapack does not consume any extra memory space using its original "Smart-Temporary" system. On the other hand, ordinary matrix libraries always generate useless temporary objects implicitly and consume a lot of extra memory space. CPPLapack is efficient not only in computing speed but also in saving memory space.

[NOTE] Recent advanced compilers automatically optimize the way of passing returned objects. The steps shown above is the case of the most primitive compiler. The performance of ordinary matrix libraries using advanced compilers becomes close to the performance of CPPLapack. However, CPPLapack still has some advantages in terms of the stepwise elimination, minimization of the number of temporary objects, and so on.