用fortran語言編寫數值程序時，如果要計算一個大型稀疏矩陣與一個向量的乘積，可以使用下面高效的方法
1. 首先使用CSR格式大型稀疏矩陣進行存儲
2. 調用mkl函數庫中的mkl_dcsrsymv計算
這樣做的目的不僅可以節約內存，而且計算速度也比較快
示例代碼如下：
program mkl_symv
implicit none
integer, parameter :: n = 5 !// depend on your equation
integer :: i, j, mm, tmp, fileid, first, num
real(kind=8) :: matrix(n,n), x(n), y(n)
real(kind=8), allocatable :: csra(:)
integer, allocatable :: ia(:), ja(:)
character(len=1) :: uplo = 'u'
type :: node
real(kind=8) :: s
integer :: k1, k2
type (node), pointer :: next
end type node
type (node), pointer :: head, tail, p, q
open ( newunit = fileid, file = 'SparseMatrix.txt' ) !// The sparse matrix data needs to be given by itself
do i = 1, n
read ( fileid,* ) matrix(i,:)
end do
read( fileid,* ) x
close ( fileid )
!// =========================store data by CSR format=======================
first = 1
if ( .not.associated(p) ) then
allocate( p )
q => p
nullify( p%next )
q%k2 = first
tmp = q%k2
end if
num = 0 !// calculate the number of no-zero
do i = 1, n
mm = 0 !// calculate the position of no-zero in every row
do j = i, n
If ( matrix(i,j) /= 0.0 ) then
if ( .not.associated(head) ) then
allocate( head )
tail => head
nullify( tail%next )
tail%s = matrix(i,j)
tail%k1 = j
num = num + 1
mm = mm + 1
else
allocate( tail%next )
tail => tail%next
tail%s = matrix(i,j)
tail%k1 = j
num = num + 1
mm = mm + 1
nullify( tail%next )
end if
End if
end do
if ( associated(p) ) then
allocate( q%next )
q => q%next
q%k2 = tmp + mm
tmp = q%k2
nullify( q%next )
end if
end do
allocate( csra(num), ja(num), ia(n+1) ) !// store the no-zero element
!// output a and ja
tail => head
j = 1
do
if ( .not.associated(tail) ) exit
csra(j) = tail%s
ja(j) = tail%k1
j = j + 1
tail => tail%next
end do
!// output ia
q => p
j = 1
do
if ( .not.associated(q) ) exit
ia(j) = q%k2
j = j + 1
q => q%next
end do
nullify( head, tail, p, q )
write ( *,'(a)' ) '>> Original data'
write ( *,'(5f7.2)' ) matrix
write ( *,'(a)' ) '>> CSR data'
write ( *,'(*(f7.2))' ) csra
write ( *,'(a)' ) '>> X data'
write ( *,'(*(f7.2))' ) x
write ( *,'(a)' ) '>> Colnum of CSR data'
write ( *,'(*(i4))' ) ja
write ( *,'(a)' ) '>> The position of CSR data'
write ( *,'(*(i4))' ) ia
write ( *,'(1x,a)' ) "The result of matmul function is..."
write ( *,'(*(f9.3))' ) matmul(matrix,x)
call mkl_dcsrsymv( uplo, n, csra, ia, ja, x, y )
print*
write ( *,'(1x,a)' ) "The result of mkl_dcsrsymv is..."
write ( *,'(*(f9.3))' ) y
end program mkl_symv
結果如下：
>> Original data
1.00 -1.00 0.00 -3.00 0.00
-1.00 5.00 0.00 0.00 0.00
0.00 0.00 4.00 6.00 4.00
-3.00 0.00 6.00 7.00 0.00
0.00 0.00 4.00 0.00 -5.00
>> CSR data
1.00 -1.00 -3.00 5.00 4.00 6.00 4.00 7.00 -5.00
>> X data
-13.00 9.00 56.00 43.00 -13.00
>> Colnum of CSR data
1 2 4 2 3 4 5 4 5
>> The position of CSR data
1 4 5 8 9 10
The result of matmul function is...
-151.000 58.000 430.000 676.000 289.000
The result of mkl_dcsrsymv is...
-151.000 58.000 430.000 676.000 289.000
從結果可以看出，計算正確
代碼中用到的示例數據存儲在SparseMatrix.txt中，如下所示：
1.00 -1.00 0.00 -3.00 0.00
-1.00 5.00 0.00 0.00 0.00
0.00 0.00 4.00 6.00 4.00
-3.00 0.00 6.00 7.00 0.00
0.00 0.00 4.00 0.00 -5.00
-13.00 9.00 56.00 43.00 -13.00
前五行爲矩陣m，最後一行爲向量v
