5.8 Memory Management and Two-Dimensional Partitioning
221
The proton 2p-2h part of ˆ
H writes evidently the same. The proton-neutron 2p-2h
part of ˆ
H is very similar, except that there is no intermediate Slater determinant:
SD f | ˆ
H |SD i = =α p β n | ˆ
V |γ p δ n
× ×SD p (f) |a
†
α p |SD p (int) SD p (int) |a γ p |SD p (i)
× ×SD n(f) |a
†
β n
|SD n(int) SD n(int) |a δ n |SD n(i) ,
(5.70)
where p and n refer to proton and neutron state, respectively. Otherwise, the
computational method is the same as with the neutron 2p-2h part of the ˆ
H matrix.
m-reversal symmetry is also taken into account for even-even nuclei, because
[ ˆ
H , ˆ
T ] = 0 if m = 0, so that it allows to calculate only half of the output Gamow
shell model vector when one multiplies ˆ
H by an input Gamow shell model vector.
At this point, ˆ
H has been stored in N squares. There are no message passing
interface communications because the phases needed in one node are already stored
therein. For the ˆ
H times vector operation, one uses row and column communicators,
as in Ref. [34], which connect each n d nodes, so that message passing interface
communications involve n d nodes within the 2D partitioning scheme. A simple
example of matrix and vector distribution in the 2D scheme is depicted in Fig. 5.3.
Let us now describe the algorithm of matrix times vector when one applies ˆ
H on
a Gamow shell model vector within the 2D partitioning scheme, of dimension d:
• All occupied squares (see Fig. 5.3) are considered simultaneously.
• If one is on a diagonal square, whose associated node, i.e., the node where this
square is stored, is the master node of the row and column communicators, one
distributes its input Gamow shell model vector part to all the nodes of the row
and column via the row and column communicators. For example, on Fig. 5.3,
the nodes 2, 4, and 15 form a row communicator on the second row, whose master
node is node 4, while the nodes 4, 5, and 6 form a column communicator. The
Fig. 5.3 Example of the 2D
partitioning scheme for the
Hamiltonian matrix.
Occupied squares are denoted
by numbers and unoccupied
squares by dashed lines (from
Ref. [28])
221
The proton 2p-2h part of ˆ
H writes evidently the same. The proton-neutron 2p-2h
part of ˆ
H is very similar, except that there is no intermediate Slater determinant:
SD f | ˆ
H |SD i = =α p β n | ˆ
V |γ p δ n
× ×SD p (f) |a
†
α p |SD p (int) SD p (int) |a γ p |SD p (i)
× ×SD n(f) |a
†
β n
|SD n(int) SD n(int) |a δ n |SD n(i) ,
(5.70)
where p and n refer to proton and neutron state, respectively. Otherwise, the
computational method is the same as with the neutron 2p-2h part of the ˆ
H matrix.
m-reversal symmetry is also taken into account for even-even nuclei, because
[ ˆ
H , ˆ
T ] = 0 if m = 0, so that it allows to calculate only half of the output Gamow
shell model vector when one multiplies ˆ
H by an input Gamow shell model vector.
At this point, ˆ
H has been stored in N squares. There are no message passing
interface communications because the phases needed in one node are already stored
therein. For the ˆ
H times vector operation, one uses row and column communicators,
as in Ref. [34], which connect each n d nodes, so that message passing interface
communications involve n d nodes within the 2D partitioning scheme. A simple
example of matrix and vector distribution in the 2D scheme is depicted in Fig. 5.3.
Let us now describe the algorithm of matrix times vector when one applies ˆ
H on
a Gamow shell model vector within the 2D partitioning scheme, of dimension d:
• All occupied squares (see Fig. 5.3) are considered simultaneously.
• If one is on a diagonal square, whose associated node, i.e., the node where this
square is stored, is the master node of the row and column communicators, one
distributes its input Gamow shell model vector part to all the nodes of the row
and column via the row and column communicators. For example, on Fig. 5.3,
the nodes 2, 4, and 15 form a row communicator on the second row, whose master
node is node 4, while the nodes 4, 5, and 6 form a column communicator. The
Fig. 5.3 Example of the 2D
partitioning scheme for the
Hamiltonian matrix.
Occupied squares are denoted
by numbers and unoccupied
squares by dashed lines (from
Ref. [28])