Matrix free wave function optimization

[erikkjellgren]

For the wave functions WaveFunctionUPS and WaveFunctionSAUPS the memory requirements have been reduced from scaling as O(N^2) to O(N) with N being the number of determinants.
This is NOT the case for WaveFunctionUCC that still scales as O(N^2) in memory, this is due to the run-time increased a lot for WaveFunctionUCC when the O(N) algorithm was used.

A very rough estimate for the old and new memory requirements is,

Active-space	Old memory use (GB)	New memory use (GB)
(2, 2)	1.3e-7	3.2e-8
(4, 4)	1.0e-5	2.9e-7
(6, 6)	1.3e-3	3.2e-6
(8, 8)	1.9e-1	3.9e-5
(10, 10)	32	5.1e-4
(12, 12)	5800	6.8e-3
(14, 14)	-	9.4e-2
(16, 16)	-	1.3

The actual memory usage will ofc be some factor of the above, if an algorithm requires some copies of the state vector (memory bottleneck in the new implementation) then the memory requirement will be that factor times the table value (for the new implementation) approximately.

This is to say that memory usage is no longer a critical bottleneck for UPS and SAUPS.

The UPS wave function optimization is also faster now.
For chains of hydrogen atoms with 1-SA-fUpCCGSD the run times are the following,

Active-space	Old time per iteration (s)	New time per iteration (s)
(2, 2)	3.0e-3	2.8e-3
(4, 4)	4.3e-2	4.5e-2
(6, 6)	7.2e-1	6.1e-1
(8, 8)	32	15
(10, 10)	3900	400
(12, 12)	OOM	10000

A speed increase that increases with system size.

The speed is highly dependent on how dense the state vector of the system is, for O2 6-31G (12,12) an iteration is 800 s.

The WaveFunctionUCC run-time might be largely unaffected by this new structure of the code.
UCCSD H6 STO-3G had a timing of 2.1 s per iteration in the old implementation and now has 2.0 s per iteration.