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README.F2003
Design principles for this directory. 1. What is a sparse matrix? It is an object which does have some properties (number of rows, number of columns, whether it is a triangle, and in that case upper/lower, unit/nonunit), a state (null, build, assembled, update), a type (real/complex, single/double), and a storage format. Thus we have a three-level inheritance chain: i. The base object, defining the methods to set/query the various properties, and allocate and free. Some of the property getters/setters, allocate and free depend on the storage format, so at this level they will just throw an error. ii. The X_base_object, where X=s,d,c,z thus defining the type. At this level we define the computational interfaces to MV and SV, since they require the type of the vectors/scalars involved (should also add NRMI here!!!!), but again they will be empty shells. We also define the interface to CSPUT, required to build the object, and TO_COO,FROM_COO (see below). iii. The X_YYY_object where the real implementation of the MV/SV/NRMI/CSPUT/ALLOCATE/FREE/TO_COO/FROM_COO takes place. 2. What is a sparse matrix (take 2)? The above structure by itself does not allow a sparse matrix to switch among different storage formats during its life. To do this, we define all of the above to be INNER objects, encapsulated in an OUTER object which is what the rest of the library sees, as follows: type :: psbn_d_sparse_mat class(psbn_d_base_sparse_mat), allocatable :: a end type psbn_d_sparse_mat type(psbn_d_sparse_mat) :: a In this way we can have an outer object whose type is stable both statically (at compile time) and at runtime, while at runtime the type of the inner object switches from COO to CSR to whatever as needed. All of the methods are simply thrown onto the corresponding methods of the (allocatable, polymorphic) component A%A as needed (provided the component is allocated, that is). This is what is called a STATE design pattern (different from the internal state we discussed above). As an example, consider the allocate/build/assembly cycle: the outer code would do the following: 1. Allocate(psbn_d_coo_sparse_mat :: a%a) 2. During the build loop a call to A%CSINS() gets translated into CALL A%A%CSINS() 3. At assembly time the code would do the following subroutine psb_spasb(a,....) type(psbn_d_sparse_mat), intent(inout) :: a class(psbn_d_base_sparse_mat), allocatable :: temp select case (TYPE) case('CSR') allocate(psbn_d_csr_sparse_mat :: temp, stat=info) end select call temp%from_coo(a%a) call a%a%free() call move_alloc(temp,a%a) 4. Note in the above that to_coo, from_coo are defined so that every conceivable storage representation provides just 2 conversion routines, avoiding quadratic explosion. But since all have to provide them, the to_coo/from_coo is defined in d_base_mat_mod together with d_coo_sparse_mat, which enjoys the "crown prince" status with respect to all the other types derived from d_base_sparse_mat (its "siblings"). 5. How does a user add a new storage format? Very simple. After deriving the class and implementing all the necessary methods, the user declares in the program a dummy variable of the new inner type type(X_YYY_sparse_mat) :: reftype then calls call psb_spasb(a,....,mold=reftype) In psb_spasb we have class(psbn_d_base_sparse_mat), intent(in), optional :: mold if (present(mold)) then allocate(temp,source=mold,stat=info) end select call temp%from_coo(a%a) call a%a%free() call move_alloc(temp,a%a) AND IT'S DONE! Nothing else in the library requires the explicit knowledge of type of MOLD. 3. Data precisoin (aka KIND / aka byte size) Data precision is a bit of a thorny issue here, because it is used by the Fortran language to disambiguate generic interfaces. This means that we must be careful when choosing precision for data structures. On the other hand, we want to have some freedom of choice. The sticky point here is how to deal with integers, because real and complex are already standardized on S/D/C/Z. Integers are tricky because we do not want to use large integer sizes (read: 8 bytes) unless they are really necessary; moreover, the GPU code currently use 4 byte integers (and with good reason). However if we want to tackle large index spaces, we will need at some point 8-byte integers. So, here is the plan. A. We have two basic integer kinds, 4-byte PSB_MPK_ which takes its name from being the kind that is going to be passed to MPI for all arguments other than data buffers, and 8-byte PSB_EPK_, to be used as necessary; the PSB_SIZEOF functions which return data structure sizes (sometimes summed over all processes) are always 8-byte. B. At all levels where a function/subroutine is supposed to be interfaced with an array of integers, there should be two versions, distinguished by an M or an E in the specific name, all adding to a generic set. This applies to the internal utilities, such as sorting and reallocation. C. For computation we have I and L, as in psb_ipk_ and psb_lpk_. The idea is that I<=L, and I is used for almost everything, e.g. for the integer parts of the sparse matrix data structures. L is only used for a very small subset of data, and specifically for the indices in *GLOBAL* numbering mode, hence the I<=L constraint. D. The values for I and L can be remapped independently at configure time over M and E; thus, if a sparse matrix routine is reallocating integer data through the generic names of the utilities, the PSB_IPK_ is remapped at compile time onto PSB_MPK_ or PSB_EPK_ as needed. E. Because we must have I<=L, this means that supported configurations are (I=4,L=4), (I=4,L=8), (I=8,L=8). Default is (I=4,L=8), because it allows us to go to multi-billion linear systems while still keeping all local data structures on 4-byte integers. F. Thus, care must be taken in defining specific interfaces: to reiterate, if we are dealing with an interface which accepts an integer array, it should be defined with M and E (which are always distinct) and not I/L (which might be indistinguishable). Example in case: interface psb_realloc Subroutine psb_r_m_m_rk1(len,rrax,info,pad,lb) integer(psb_mpk_),Intent(in) :: len integer(psb_mpk_), allocatable, intent(inout) :: rrax(:) integer(psb_ipk_) :: info integer(psb_mpk_), optional, intent(in) :: pad integer(psb_mpk_), optional, intent(in) :: lb G. The INFO argument and others related to error handling should always be PSB_IPK_; H. Arguments related to MPI interfacing should always be PSB_MPK_ I. Encapsulated types such as psb_i_base_vect_mod can still be I and L, because if the name of the type is different, the types are interpreted as distinguishable even when the contents are identical. L. This means that most user-level interfaces will deal in I and L, not M and E, which are going to be used mostly in the internals. M. Actually, the user will probably never see M, but will (for sizeof & friends) see E.