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c----------------------------------------------------------------------c
subroutine amub (nrow,ncol,job,a,ja,ia,b,jb,ib,
* c,jc,ic,nzmax,iw,ierr)
double precision a(*), b(*), c(*)
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(*),ic(*),iw(ncol)
c-----------------------------------------------------------------------
c performs the matrix by matrix product C = A B
c-----------------------------------------------------------------------
c on entry:
c ---------
c nrow = integer. The row dimension of A = row dimension of C
c ncol = integer. The column dimension of B = column dimension of C
c job = integer. Job indicator. When job = 0, only the structure
c (i.e. the arrays jc, ic) is computed and the
c real values are ignored.
c
c a,
c ja,
c ia = Matrix A in compressed sparse row format.
c
c b,
c jb,
c ib = Matrix B in compressed sparse row format.
c
c nzmax = integer. The length of the arrays c and jc.
c amub will stop if the result matrix C has a number
c of elements that exceeds exceeds nzmax. See ierr.
c
c on return:
c----------
c c,
c jc,
c ic = resulting matrix C in compressed sparse row sparse format.
c
c ierr = integer. serving as error message.
c ierr = 0 means normal return,
c ierr .gt. 0 means that amub stopped while computing the
c i-th row of C with i=ierr, because the number
c of elements in C exceeds nzmax.
c
c work arrays:
c------------
c iw = integer work array of length equal to the number of
c columns in B.
c Note:
c-------
c The row dimension of B is not needed. However there is no checking
c on the condition that ncol(A) = nrow(B).
c
c-----------------------------------------------------------------------
double precision scal
logical values
values = (job .ne. 0)
len = 0
ic(1) = 1
ierr = 0
c initialize array iw.
do 1 j=1, ncol
iw(j) = 0
1 continue
c
do 500 ii=1, nrow
c row i
do 200 ka=ia(ii), ia(ii+1)-1
if (values) scal = a(ka)
jj = ja(ka)
do 100 kb=ib(jj),ib(jj+1)-1
jcol = jb(kb)
jpos = iw(jcol)
if (jpos .eq. 0) then
len = len+1
if (len .gt. nzmax) then
ierr = ii
return
endif
jc(len) = jcol
iw(jcol)= len
if (values) c(len) = scal*b(kb)
else
if (values) c(jpos) = c(jpos) + scal*b(kb)
endif
100 continue
200 continue
do 201 k=ic(ii), len
iw(jc(k)) = 0
201 continue
ic(ii+1) = len+1
500 continue
return
c-------------end-of-amub-----------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine amudia (nrow,job, a, ja, ia, diag, b, jb, ib)
double precision a(*), b(*), diag(*)
integer ja(*),jb(*), ia(nrow+1),ib(nrow+1)
c-----------------------------------------------------------------------
c performs the matrix by matrix product B = A * Diag (in place)
c-----------------------------------------------------------------------
c on entry:
c ---------
c nrow = integer. The row dimension of A
c
c job = integer. job indicator. Job=0 means get array b only
c job = 1 means get b, and the integer arrays ib, jb.
c
c a,
c ja,
c ia = Matrix A in compressed sparse row format.
c
c diag = diagonal matrix stored as a vector dig(1:n)
c
c on return:
c----------
c
c b,
c jb,
c ib = resulting matrix B in compressed sparse row sparse format.
c
c Notes:
c-------
c 1) The column dimension of A is not needed.
c 2) algorithm in place (B can take the place of A).
c-----------------------------------------------------------------
do 1 ii=1,nrow
c
c scale each element
c
k1 = ia(ii)
k2 = ia(ii+1)-1
do 2 k=k1, k2
b(k) = a(k)*diag(ja(k))
2 continue
1 continue
c
if (job .eq. 0) return
c
do 3 ii=1, nrow+1
ib(ii) = ia(ii)
3 continue
do 31 k=ia(1), ia(nrow+1) -1
jb(k) = ja(k)
31 continue
return
c-----------------------------------------------------------------------
c-----------end-of-amudiag----------------------------------------------
end
c----------------------------------------------------------------------c
subroutine amux (n, x, y, a,ja,ia)
double precision x(*), y(*), a(*)
integer n, ja(*), ia(*)
c-----------------------------------------------------------------------
c A times a vector
c-----------------------------------------------------------------------
c multiplies a matrix by a vector using the dot product form
c Matrix A is stored in compressed sparse row storage.
c
c on entry:
c----------
c n = row dimension of A
c x = real array of length equal to the column dimension of
c the A matrix.
c a, ja,
c ia = input matrix in compressed sparse row format.
c
c on return:
c-----------
c y = real array of length n, containing the product y=Ax
c
c-----------------------------------------------------------------------
c local variables
c
double precision t
integer i, k
c-----------------------------------------------------------------------
do 100 i = 1,n
c
c compute the inner product of row i with vector x
c
t = 0.0d0
do 99 k=ia(i), ia(i+1)-1
t = t + a(k)*x(ja(k))
99 continue
c
c store result in y(i)
c
y(i) = t
100 continue
c
return
end
c-----------------------------------------------------------------------
subroutine aplb (nrow,ncol,job,a,ja,ia,b,jb,ib,
* c,jc,ic,nzmax,iw,ierr)
double precision a(*), b(*), c(*)
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1),
* iw(ncol)
c-----------------------------------------------------------------------
c performs the matrix sum C = A+B.
c-----------------------------------------------------------------------
c on entry:
c ---------
c nrow = integer. The row dimension of A and B
c ncol = integer. The column dimension of A and B.
c job = integer. Job indicator. When job = 0, only the structure
c (i.e. the arrays jc, ic) is computed and the
c real values are ignored.
c
c a,
c ja,
c ia = Matrix A in compressed sparse row format.
c
c b,
c jb,
c ib = Matrix B in compressed sparse row format.
c
c nzmax = integer. The length of the arrays c and jc.
c amub will stop if the result matrix C has a number
c of elements that exceeds exceeds nzmax. See ierr.
c
c on return:
c----------
c c,
c jc,
c ic = resulting matrix C in compressed sparse row sparse format.
c
c ierr = integer. serving as error message.
c ierr = 0 means normal return,
c ierr .gt. 0 means that amub stopped while computing the
c i-th row of C with i=ierr, because the number
c of elements in C exceeds nzmax.
c
c work arrays:
c------------
c iw = integer work array of length equal to the number of
c columns in A.
c
c-----------------------------------------------------------------------
logical values
values = (job .ne. 0)
ierr = 0
len = 0
ic(1) = 1
do 1 j=1, ncol
iw(j) = 0
1 continue
c
do 500 ii=1, nrow
c row i
do 200 ka=ia(ii), ia(ii+1)-1
len = len+1
jcol = ja(ka)
if (len .gt. nzmax) goto 999
jc(len) = jcol
if (values) c(len) = a(ka)
iw(jcol)= len
200 continue
c
do 300 kb=ib(ii),ib(ii+1)-1
jcol = jb(kb)
jpos = iw(jcol)
if (jpos .eq. 0) then
len = len+1
if (len .gt. nzmax) goto 999
jc(len) = jcol
if (values) c(len) = b(kb)
iw(jcol)= len
else
if (values) c(jpos) = c(jpos) + b(kb)
endif
300 continue
do 301 k=ic(ii), len
iw(jc(k)) = 0
301 continue
ic(ii+1) = len+1
500 continue
return
999 ierr = ii
return
c------------end of aplb -----------------------------------------------
c-----------------------------------------------------------------------
end
subroutine csrmsr (n,a,ja,ia,ao,jao,wk,iwk,nnzao,ierr)
double precision a(*),ao(*),wk(n)
integer ia(n+1),ja(*),jao(*),iwk(n+1),nnzao,ierr
c-----------------------------------------------------------------------
c Compressed Sparse Row to Modified - Sparse Row
c Sparse row with separate main diagonal
c-----------------------------------------------------------------------
c converts a general sparse matrix a, ja, ia into
c a compressed matrix using a separated diagonal (referred to as
c the bell-labs format as it is used by bell labs semi conductor
c group. We refer to it here as the modified sparse row format.
c Note: this has been coded in such a way that one can overwrite
c the output matrix onto the input matrix if desired by a call of
c the form
c
c call csrmsr (n, a, ja, ia, a, ja, wk,iwk)
c
c In case ao, jao, are different from a, ja, then one can
c use ao, jao as the work arrays in the calling sequence:
c
c call csrmsr (n, a, ja, ia, ao, jao, ao,jao)
c
c-----------------------------------------------------------------------
c
c on entry :
c---------
c a, ja, ia = matrix in csr format. note that the
c algorithm is in place: ao, jao can be the same
c as a, ja, in which case it will be overwritten on it
c upon return.
c nnzao = the number of non-zero entries in ao, jao
c
c on return :
c-----------
c
c ao, jao = sparse matrix in modified sparse row storage format:
c + ao(1:n) contains the diagonal of the matrix.
c + ao(n+2:nnz) contains the nondiagonal elements of the
c matrix, stored rowwise.
c + jao(n+2:nnz) : their column indices
c + jao(1:n+1) contains the pointer array for the nondiagonal
c elements in ao(n+2:nnz) and jao(n+2:nnz).
c i.e., for i .le. n+1 jao(i) points to beginning of row i
c in arrays ao, jao.
c here nnz = number of nonzero elements+1
c ierr:
c = -1 : length of ao, jao < itpr
c
c work arrays:
c------------
c wk = real work array of length n
c iwk = integer work array of length n+1
c
c notes:
c-------
c Algorithm is in place. i.e. both:
c
c call csrmsr (n, a, ja, ia, ao, jao, ao,jao)
c (in which ao, jao, are different from a, ja)
c and
c call csrmsr (n, a, ja, ia, a, ja, wk,iwk)
c (in which wk, jwk, are different from a, ja)
c are OK.
c--------
c coded by Y. Saad Sep. 1989. Rechecked Feb 27, 1990.
c Modified by Pin Ng on June 11, 2002 to provide warning when
c iptr > nnzao+1
c-----------------------------------------------------------------------
icount = 0
c
c store away diagonal elements and count nonzero diagonal elements.
c
do 1 i=1,n
wk(i) = 0.0d0
iwk(i+1) = ia(i+1)-ia(i)
do 2 k=ia(i),ia(i+1)-1
if (ja(k) .eq. i) then
wk(i) = a(k)
icount = icount + 1
iwk(i+1) = iwk(i+1)-1
endif
2 continue
1 continue
c
c compute total length
c
iptr = n + ia(n+1) - icount
if (iptr .gt. nnzao+1) then
ierr = -1
return
endif
c
c copy backwards (to avoid collisions)
c
do 500 ii=n,1,-1
do 100 k=ia(ii+1)-1,ia(ii),-1
j = ja(k)
if (j .ne. ii) then
ao(iptr) = a(k)
jao(iptr) = j
iptr = iptr-1
endif
100 continue
500 continue
c
c compute pointer values and copy wk(*)
c
jao(1) = n+2
do 600 i=1,n
ao(i) = wk(i)
jao(i+1) = jao(i)+iwk(i+1)
600 continue
return
c------------ end of subroutine csrmsr ---------------------------------
c-----------------------------------------------------------------------
end
|
