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c -*- fortran -*-
c author: travis e. oliphant, 2004
c
c computational tools for sparse matrices in <_t>
c
c add two matrices in compressed sparse column format
c this assumes that the rowa indices are sorted for each column
c and indexes are 0-based
subroutine <_c>cscadd(n,a,rowa,ptra,nnzamax,b,rowb,ptrb,nnzbmax,
$ c,rowc,ptrc,nnzcmax,ierr)
<_t> a(0:nnzamax-1), b(0:nnzbmax-1)
<_t> c(0:nnzcmax-1), val
integer n, rowa(0:nnzamax-1), rowb(0:nnzbmax-1), rowc(0:nnzcmax-1)
integer ptra(0:n), ptrb(0:n), ptrc(0:n), nnzamax, nnzbmax
integer ia, ib, ra, rb, j, nnzcmax
integer ierr, nnzc
ierr=0
nnzc=0
ia=ptra(0)
ib=ptrb(0)
c is there a need to initialize the output arrays? assume no for now.
c do j = 0, n
c ptrc(j) = 0
c end do
c do j = 0, nnzcmax-1
c rowc(j) = 0
c c(j) = 0.0
c end do
do j = 0, n-1
iamax = ptra(j+1)
ibmax = ptrb(j+1)
do while ((ia.lt.iamax).and.(ib.lt.ibmax))
ra = rowa(ia)
rb = rowb(ib)
if (ra.eq.rb) then
c this is a common element
val = a(ia) + b(ib)
ia = ia + 1
ib = ib + 1
if (val.eq.0.0) goto 10
if (nnzc.ge.nnzcmax) goto 999
c(nnzc) = val
rowc(nnzc) = ra
else if (ra .lt. rb) then
c a has this but not b
val = a(ia)
ia = ia + 1
if (val.eq.0.0) goto 10
if (nnzc.ge.nnzcmax) goto 999
c(nnzc) = val
rowc(nnzc) = ra
else
c b has this but not a
val = b(ib)
ib = ib + 1
if (val.eq.0.0) goto 10
if (nnzc.ge.nnzcmax) goto 999
c(nnzc) = val
rowc(nnzc) = rb
end if
ptrc(j+1) = ptrc(j+1) + 1
nnzc = nnzc + 1
10 continue
end do
if (ia .eq. iamax) then
c all finished with a for this column just copy the rest from b
do while (ib .lt. ibmax)
val = b(ib)
rb = rowb(ib)
ib = ib+1
if (val.ne.0.0) then
if (nnzc.ge.nnzcmax) goto 999
c(nnzc) = val
rowc(nnzc) = rb
ptrc(j+1) = ptrc(j+1) + 1
nnzc = nnzc + 1
end if
end do
else if (ib .eq. ibmax) then
c all finished with b for this column just copy the rest from a
do while (ia .lt. iamax)
val = a(ia)
ra = rowa(ia)
ia = ia + 1
if (val.ne.0.0) then
if (nnzc.ge.nnzcmax) goto 999
c(nnzc) = val
rowc(nnzc) = ra
ptrc(j+1) = ptrc(j+1) + 1
nnzc = nnzc + 1
end if
end do
end if
end do
c successful completion (fix the ptr array)
cumsum = 0
do k = 1, n
cumsum = cumsum + ptrc(k)
ptrc(k) = cumsum
end do
return
999 continue
ierr = 1
return
end subroutine <_c>cscadd
c element-by-element multiplication
c can have at most the minimum of nnzamax and nnzbmax
subroutine <_c>cscmul(n,a,rowa,ptra,nnzamax,b,rowb,ptrb,nnzbmax,
$ c,rowc,ptrc,nnzcmax,ierr)
<_t> a(0:nnzamax-1), b(0:nnzbmax-1)
<_t> c(0:nnzcmax-1), val
integer n, rowa(0:nnzamax-1), rowb(0:nnzbmax-1), rowc(0:nnzcmax-1)
integer ptra(0:n), ptrb(0:n), ptrc(0:n), nnzamax, nnzbmax
integer ia, ib, ra, rb, j, nnzcmax
integer ierr, k, cumsum
ierr=0
nnzc=0
ia=ptra(0)
ib=ptrb(0)
do j = 0, n-1
iamax = ptra(j+1)
ibmax = ptrb(j+1)
do while ((ia.lt.iamax).and.(ib.lt.ibmax))
ra = rowa(ia)
rb = rowb(ib)
if (ra.eq.rb) then
c this is a common element
val = a(ia)*b(ib)
ia = ia + 1
ib = ib + 1
if (val.eq.0.0) goto 10
if (nnzc.ge.nnzcmax) goto 999
c(nnzc) = val
rowc(nnzc) = ra
ptrc(j+1) = ptrc(j+1) + 1
nnzc = nnzc + 1
else if (ra .lt. rb) then
c a has this but not b
ia = ia + 1
else
c b has this but not a
ib = ib + 1
end if
10 continue
end do
end do
c successful completion (fix the ptr array)
cumsum = 0
do k = 1, n
cumsum = cumsum + ptrc(k)
ptrc(k) = cumsum
end do
return
999 continue
ierr = 1
return
end subroutine <_c>cscmul
c matrix-vector multiplication
subroutine <_c>cscmux(a,rowa,ptra,nnzamax,ncol,x,mrow,y)
<_t> a(0:nnzamax-1), x(0:ncol-1), y(0:mrow-1)
integer rowa(0:nnzamax-1), ptra(0:ncol)
integer nnzamax, mrow, ncol
integer i, j, ia, ra
do i = 0, mrow-1
y(i) = 0.0
end do
do j = 0, ncol-1
do ia = ptra(j), ptra(j+1)-1
ra = rowa(ia)
y(ra) = y(ra) + a(ia)*x(j)
end do
end do
return
end subroutine <_c>cscmux
subroutine <_c>csrmux(a,cola,ptra,nnzamax,ncol,x,mrow,y)
<_t> a(0:nnzamax-1),x(0:ncol-1),y(0:mrow-1)
integer cola(0:nnzamax-1), ptra(0:mrow)
integer nnzamax, mrow, ncol
integer i, ja, ca
do i = 0, mrow-1
y(i) = 0.0
do ja = ptra(i), ptra(i+1)-1
ca = cola(ja)
y(i) = y(i) + a(ja)*x(ca)
end do
end do
return
end subroutine <_c>csrmux
c matrix multiplication
c c = a * b
c
c where c is mxn csc matrix
c a is mxk csc matrix
c b is kxn csr matrix
c
c irow and kcol give position to start
c nnzc gives current last element in output array (initialize to 0)
c intended to recall so that calculation can continue
c if memory ran-out at last attempt
subroutine <_c>cscmucsr(m,k,n, a,rowa,ptra,nnzamax, b,colb,ptrb,
$ nnzbmax, c,rowc,ptrc,nnzcmax, irow,kcol,ierr)
<_t> a(0:nnzamax-1), b(0:nnzbmax-1), c(0:nnzcmax-1)
integer rowa(0:nnzamax-1), colb(0:nnzbmax-1), rowc(0:nnzcmax-1)
integer ptra(0:k), ptrb(0:k), ptrc(0:n)
integer nnzamax, nnzbmax, nnzcmax
integer m, k, n, irow, kcol, ierr, cumsum
integer kk, ii, jjb, jb, cb, ia, nnzc
<_t> val
nnzc = ierr
ierr = 0
do kk = kcol, n-1
do ii = irow, m-1
if (nnzc.ge.nnzcmax) goto 999
irow = 0
val = 0.0
c loop through the column array of b using the ptrb array
c so that we know which row we are on.
do jjb = 0, k-1
do jb = ptrb(jjb), ptrb(jjb+1)-1
cb = colb(jb)
if (cb.eq.kk) then
c see if aij is nonzero and if so add to val
do ia = ptra(jjb), ptra(jjb+1)-1
if (rowa(ia).eq.ii) then
val = val + a(ia)*b(jb)
end if
end do
end if
end do
end do
if (val.ne.0.0) then
c there is a non-zero value for this value of i and k
c(nnzc) = val
rowc(nnzc) = ii
ptrc(kk+1) = ptrc(kk+1) + 1
nnzc = nnzc+1
end if
end do
end do
c successful completion (fix the ptr array)
cumsum = 0
do kk = 1, n
cumsum = cumsum + ptrc(kk)
ptrc(kk) = cumsum
end do
return
return
999 continue
kcol = kk
irow = ii
ierr = nnzc
return
end subroutine <_c>cscmucsr
c matrix multiplication
c c = a * b
c
c where c is mxn csc matrix
c a is mxk csr matrix
c b is kxn csc matrix
c
c irow and jcol give position to start
c bnum gives current size of output array
c intended to recall so that calculation can continue
c where it left off if memory runs-out during calculation
c
subroutine <_c>csrmucsc(m,n,a,cola,ptra,nnzamax,b,rowb,ptrb,
$ nnzbmax,c,rowc,ptrc,nnzcmax,irow,kcol,ierr)
<_t> a(0:nnzamax-1), b(0:nnzbmax-1), c(0:nnzcmax-1)
integer cola(0:nnzamax-1), rowb(0:nnzbmax-1), rowc(0:nnzcmax-1)
integer ptra(0:m), ptrb(0:n), ptrc(0:n)
integer nnzamax, nnzbmax, nnzcmax
integer m, n, irow, kcol, ierr, cumsum
integer kk, ii, nnzc
<_t> val
nnzc = ierr
ierr = 0
do kk = kcol, n-1
do ii = irow, m-1
if (nnzc.ge.nnzcmax) goto 999
irow = 0
val = 0.0
c loop through the non-zero rows of b
do ib = ptrb(kk), ptrb(kk+1)-1
rb = rowb(ib)
do ja = ptra(ii), ptra(ii+1)-1
if (cola(ja).eq.rb) then
val = val + a(ja)*b(ib)
end if
end do
end do
if (val.ne.0.0) then
c there is a non-zero value for this value of i and k
c(nnzc) = val
rowc(nnzc) = ii
ptrc(kk+1) = ptrc(kk+1) + 1
nnzc = nnzc+1
end if
end do
end do
c successful completion (fix the ptr array)
cumsum = 0
do kk = 1, n
cumsum = cumsum + ptrc(kk)
ptrc(kk) = cumsum
end do
return
return
999 continue
kcol = kk
irow = ii
ierr = nnzc
return
end subroutine <_c>csrmucsc
c matrix-matrix multiplication
c
c c = a * b where a, b, and c are
c compressed sparse column matrices
c
c or it computes
c
c c = b * a where b, a, and c are
c compressed sparse row matrices
c
c intentended for re-entry if nnzcmax is not big enough
subroutine <_c>cscmucsc(m,k,n,a,rowa,ptra,nnzamax,b,rowb,ptrb,
$ nnzbmax,c,rowc,ptrc,nnzcmax,irow,kcol,ierr)
<_t> a(0:nnzamax-1), b(0:nnzbmax-1), c(0:nnzcmax-1)
integer rowa(0:nnzamax-1), rowb(0:nnzbmax-1), rowc(0:nnzcmax-1)
integer ptra(0:k), ptrb(0:n), ptrc(0:n)
integer nnzamax, nnzbmax, nnzcmax
integer m, k, n, irow, kcol, ierr
integer kk, ii, jb, ia, ra, nnzc, cumsum
<_t> val
nnzc = ierr
ierr = 0
do kk = kcol, n-1
do ii = irow, m-1
if (nnzc.ge.nnzcmax) goto 999
c reset the irow to 0
irow = 0
val = 0.0
c loop through the row array of b for this column
do jb = ptrb(kk), ptrb(kk+1)-1
ra = rowb(jb)
do ia = ptra(ra), ptra(ra+1)-1
c see if aij is nonzero and if so add to val
if (rowa(ia).eq.ii) then
val = val + a(ia)*b(jb)
end if
end do
end do
if (val.ne.0.0) then
c there is a non-zero value for this value of i and k
c(nnzc) = val
rowc(nnzc) = ii
ptrc(kk+1) = ptrc(kk+1) + 1
nnzc = nnzc+1
end if
end do
end do
c successful completion (fix the ptr array)
cumsum = 0
do kk = 1, n
cumsum = cumsum + ptrc(kk)
ptrc(kk) = cumsum
end do
return
999 continue
kcol = kk
irow = ii
ierr = nnzc
return
end subroutine <_c>cscmucsc
|
