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|
c $Id: blassm.f,v 1.1 2008-04-11 06:01:06 geuzaine Exp $
c----------------------------------------------------------------------c
c S P A R S K I T c
c----------------------------------------------------------------------c
c BASIC LINEAR ALGEBRA FOR SPARSE MATRICES. BLASSM MODULE c
c----------------------------------------------------------------------c
c amub : computes C = A*B c
c aplb : computes C = A+B c
c aplb1 : computes C = A+B [Sorted version: A, B, C sorted] c
c aplsb : computes C = A + s B c
c aplsb1 : computes C = A+sB [Sorted version: A, B, C sorted] c
c apmbt : Computes C = A +/- transp(B) c
c aplsbt : Computes C = A + s * transp(B) c
c diamua : Computes C = Diag * A c
c amudia : Computes C = A* Diag c
c aplsca : Computes A:= A + s I (s = scalar) c
c apldia : Computes C = A + Diag. c
c----------------------------------------------------------------------c
c Note: this module still incomplete. c
c----------------------------------------------------------------------c
subroutine amub (nrow,ncol,job,a,ja,ia,b,jb,ib,
* c,jc,ic,nzmax,iw,ierr)
real*8 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 A.
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-----------------------------------------------------------------------
real*8 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 aplb (nrow,ncol,job,a,ja,ia,b,jb,ib,
* c,jc,ic,nzmax,iw,ierr)
real*8 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
c-----------------------------------------------------------------------
subroutine aplb1(nrow,ncol,job,a,ja,ia,b,jb,ib,c,jc,ic,nzmax,ierr)
real*8 a(*), b(*), c(*)
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1)
c-----------------------------------------------------------------------
c performs the matrix sum C = A+B for matrices in sorted CSR format.
c the difference with aplb is that the resulting matrix is such that
c the elements of each row are sorted with increasing column indices in
c each row, provided the original matrices are sorted in the same way.
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 with entries sorted
c
c b,
c jb,
c ib = Matrix B in compressed sparse row format with entries sorted
c ascendly in each row
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 with entries sorted ascendly in each row.
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 Notes:
c-------
c this will not work if any of the two input matrices is not sorted
c-----------------------------------------------------------------------
logical values
values = (job .ne. 0)
ierr = 0
kc = 1
ic(1) = kc
c
do 6 i=1, nrow
ka = ia(i)
kb = ib(i)
kamax = ia(i+1)-1
kbmax = ib(i+1)-1
5 continue
if (ka .le. kamax) then
j1 = ja(ka)
else
j1 = ncol+1
endif
if (kb .le. kbmax) then
j2 = jb(kb)
else
j2 = ncol+1
endif
c
c three cases
c
if (j1 .eq. j2) then
if (values) c(kc) = a(ka)+b(kb)
jc(kc) = j1
ka = ka+1
kb = kb+1
kc = kc+1
else if (j1 .lt. j2) then
jc(kc) = j1
if (values) c(kc) = a(ka)
ka = ka+1
kc = kc+1
else if (j1 .gt. j2) then
jc(kc) = j2
if (values) c(kc) = b(kb)
kb = kb+1
kc = kc+1
endif
if (kc .gt. nzmax) goto 999
if (ka .le. kamax .or. kb .le. kbmax) goto 5
ic(i+1) = kc
6 continue
return
999 ierr = i
return
c------------end-of-aplb1-----------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine aplsb (nrow,ncol,a,ja,ia,s,b,jb,ib,c,jc,ic,
* nzmax,ierr)
real*8 a(*), b(*), c(*), s
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1)
c-----------------------------------------------------------------------
c performs the operation C = A+s B for matrices in sorted CSR format.
c the difference with aplsb is that the resulting matrix is such that
c the elements of each row are sorted with increasing column indices in
c each row, provided the original matrices are sorted in the same way.
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
c a,
c ja,
c ia = Matrix A in compressed sparse row format with entries sorted
c
c s = real. scalar factor for B.
c
c b,
c jb,
c ib = Matrix B in compressed sparse row format with entries sorted
c ascendly in each row
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 with entries sorted ascendly in each row.
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 Notes:
c-------
c this will not work if any of the two input matrices is not sorted
c-----------------------------------------------------------------------
ierr = 0
kc = 1
ic(1) = kc
c
c the following loop does a merge of two sparse rows + adds them.
c
do 6 i=1, nrow
ka = ia(i)
kb = ib(i)
kamax = ia(i+1)-1
kbmax = ib(i+1)-1
5 continue
c
c this is a while -- do loop --
c
if (ka .le. kamax .or. kb .le. kbmax) then
c
if (ka .le. kamax) then
j1 = ja(ka)
else
c take j1 large enough that always j2 .lt. j1
j1 = ncol+1
endif
if (kb .le. kbmax) then
j2 = jb(kb)
else
c similarly take j2 large enough that always j1 .lt. j2
j2 = ncol+1
endif
c
c three cases
c
if (j1 .eq. j2) then
c(kc) = a(ka)+s*b(kb)
jc(kc) = j1
ka = ka+1
kb = kb+1
kc = kc+1
else if (j1 .lt. j2) then
jc(kc) = j1
c(kc) = a(ka)
ka = ka+1
kc = kc+1
else if (j1 .gt. j2) then
jc(kc) = j2
c(kc) = s*b(kb)
kb = kb+1
kc = kc+1
endif
if (kc .gt. nzmax) goto 999
goto 5
c
c end while loop
c
endif
ic(i+1) = kc
6 continue
return
999 ierr = i
return
c------------end-of-aplsb ---------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine aplsb1 (nrow,ncol,a,ja,ia,s,b,jb,ib,c,jc,ic,
* nzmax,ierr)
real*8 a(*), b(*), c(*), s
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1)
c-----------------------------------------------------------------------
c performs the operation C = A+s B for matrices in sorted CSR format.
c the difference with aplsb is that the resulting matrix is such that
c the elements of each row are sorted with increasing column indices in
c each row, provided the original matrices are sorted in the same way.
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
c a,
c ja,
c ia = Matrix A in compressed sparse row format with entries sorted
c
c s = real. scalar factor for B.
c
c b,
c jb,
c ib = Matrix B in compressed sparse row format with entries sorted
c ascendly in each row
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 with entries sorted ascendly in each row.
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 Notes:
c-------
c this will not work if any of the two input matrices is not sorted
c-----------------------------------------------------------------------
ierr = 0
kc = 1
ic(1) = kc
c
c the following loop does a merge of two sparse rows + adds them.
c
do 6 i=1, nrow
ka = ia(i)
kb = ib(i)
kamax = ia(i+1)-1
kbmax = ib(i+1)-1
5 continue
c
c this is a while -- do loop --
c
if (ka .le. kamax .or. kb .le. kbmax) then
c
if (ka .le. kamax) then
j1 = ja(ka)
else
c take j1 large enough that always j2 .lt. j1
j1 = ncol+1
endif
if (kb .le. kbmax) then
j2 = jb(kb)
else
c similarly take j2 large enough that always j1 .lt. j2
j2 = ncol+1
endif
c
c three cases
c
if (j1 .eq. j2) then
c(kc) = a(ka)+s*b(kb)
jc(kc) = j1
ka = ka+1
kb = kb+1
kc = kc+1
else if (j1 .lt. j2) then
jc(kc) = j1
c(kc) = a(ka)
ka = ka+1
kc = kc+1
else if (j1 .gt. j2) then
jc(kc) = j2
c(kc) = s*b(kb)
kb = kb+1
kc = kc+1
endif
if (kc .gt. nzmax) goto 999
goto 5
c
c end while loop
c
endif
ic(i+1) = kc
6 continue
return
999 ierr = i
return
c------------end-of-aplsb1 ---------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine apmbt (nrow,ncol,job,a,ja,ia,b,jb,ib,
* c,jc,ic,nzmax,iw,ierr)
real*8 a(*), b(*), c(*)
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(ncol+1),ic(*),iw(*)
c-----------------------------------------------------------------------
c performs the matrix sum C = A + transp(B) or C = A - transp(B)
c-----------------------------------------------------------------------
c on entry:
c ---------
c nrow = integer. The row dimension of A and transp(B)
c ncol = integer. The column dimension of A. Also the row
c dimension of B.
c
c job = integer. if job = -1, apmbt will compute C= A - transp(B)
c (structure + values)
c if (job .eq. 1) it will compute C=A+transp(A)
c (structure+ values)
c if (job .eq. 0) it will compute the structure of
c C= A+/-transp(B) only (ignoring all real values).
c any other value of job will be treated as job=1
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, jc, and ic.
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 format.
c
c ierr = integer. serving as error message.
c ierr = 0 means normal return.
c ierr = -1 means that nzmax was .lt. either the number of
c nonzero elements of A or the number of nonzero elements in B.
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 at least max(ncol,nrow)
c
c Notes:
c------- It is important to note that here all of three arrays c, ic,
c and jc are assumed to be of length nnz(c). This is because
c the matrix is internally converted in coordinate format.
c
c-----------------------------------------------------------------------
logical values
values = (job .ne. 0)
c
ierr = 0
do 1 j=1, ncol
iw(j) = 0
1 continue
c
nnza = ia(nrow+1)-1
nnzb = ib(ncol+1)-1
len = nnzb
if (nzmax .lt. nnzb .or. nzmax .lt. nnza) then
ierr = -1
return
endif
c
c trasnpose matrix b into c
c
ljob = 0
if (values) ljob = 1
ipos = 1
call csrcsc (ncol,ljob,ipos,b,jb,ib,c,jc,ic)
c-----------------------------------------------------------------------
if (job .eq. -1) then
do 2 k=1,len
c(k) = -c(k)
2 continue
endif
c
c--------------- main loop --------------------------------------------
c
do 500 ii=1, nrow
do 200 k = ic(ii),ic(ii+1)-1
iw(jc(k)) = k
200 continue
c-----------------------------------------------------------------------
do 300 ka = ia(ii), ia(ii+1)-1
jcol = ja(ka)
jpos = iw(jcol)
if (jpos .eq. 0) then
c
c if fill-in append in coordinate format to matrix.
c
len = len+1
if (len .gt. nzmax) goto 999
jc(len) = jcol
ic(len) = ii
if (values) c(len) = a(ka)
else
c else do addition.
if (values) c(jpos) = c(jpos) + a(ka)
endif
300 continue
do 301 k=ic(ii), ic(ii+1)-1
iw(jc(k)) = 0
301 continue
500 continue
c
c convert first part of matrix (without fill-ins) into coo format
c
ljob = 2
if (values) ljob = 3
do 501 i=1, nrow+1
iw(i) = ic(i)
501 continue
call csrcoo (nrow,ljob,nnzb,c,jc,iw,nnzb,c,ic,jc,ierr)
c
c convert the whole thing back to csr format.
c
ljob = 0
if (values) ljob = 1
call coicsr (nrow,len,ljob,c,jc,ic,iw)
return
999 ierr = ii
return
c--------end-of-apmbt---------------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine aplsbt(nrow,ncol,a,ja,ia,s,b,jb,ib,
* c,jc,ic,nzmax,iw,ierr)
real*8 a(*), b(*), c(*), s
integer ja(*),jb(*),jc(*),ia(nrow+1),ib(ncol+1),ic(*),iw(*)
c-----------------------------------------------------------------------
c performs the matrix sum C = A + transp(B).
c-----------------------------------------------------------------------
c on entry:
c ---------
c nrow = integer. The row dimension of A and transp(B)
c ncol = integer. The column dimension of A. Also the row
c dimension of B.
c
c a,
c ja,
c ia = Matrix A in compressed sparse row format.
c
c s = real. scalar factor for B.
c
c
c b,
c jb,
c ib = Matrix B in compressed sparse row format.
c
c nzmax = integer. The length of the arrays c, jc, and ic.
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 format.
c
c ierr = integer. serving as error message.
c ierr = 0 means normal return.
c ierr = -1 means that nzmax was .lt. either the number of
c nonzero elements of A or the number of nonzero elements in B.
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 at least max(nrow,ncol)
c
c Notes:
c------- It is important to note that here all of three arrays c, ic,
c and jc are assumed to be of length nnz(c). This is because
c the matrix is internally converted in coordinate format.
c
c-----------------------------------------------------------------------
ierr = 0
do 1 j=1, ncol
iw(j) = 0
1 continue
c
nnza = ia(nrow+1)-1
nnzb = ib(ncol+1)-1
len = nnzb
if (nzmax .lt. nnzb .or. nzmax .lt. nnza) then
ierr = -1
return
endif
c
c transpose matrix b into c
c
ljob = 1
ipos = 1
call csrcsc (ncol,ljob,ipos,b,jb,ib,c,jc,ic)
do 2 k=1,len
2 c(k) = c(k)*s
c
c main loop. add rows from ii = 1 to nrow.
c
do 500 ii=1, nrow
c iw is used as a system to recognize whether there
c was a nonzero element in c.
do 200 k = ic(ii),ic(ii+1)-1
iw(jc(k)) = k
200 continue
c
do 300 ka = ia(ii), ia(ii+1)-1
jcol = ja(ka)
jpos = iw(jcol)
if (jpos .eq. 0) then
c
c if fill-in append in coordinate format to matrix.
c
len = len+1
if (len .gt. nzmax) goto 999
jc(len) = jcol
ic(len) = ii
c(len) = a(ka)
else
c else do addition.
c(jpos) = c(jpos) + a(ka)
endif
300 continue
do 301 k=ic(ii), ic(ii+1)-1
iw(jc(k)) = 0
301 continue
500 continue
c
c convert first part of matrix (without fill-ins) into coo format
c
ljob = 3
do 501 i=1, nrow+1
iw(i) = ic(i)
501 continue
call csrcoo (nrow,ljob,nnzb,c,jc,iw,nnzb,c,ic,jc,ierr)
c
c convert the whole thing back to csr format.
c
ljob = 1
call coicsr (nrow,len,ljob,c,jc,ic,iw)
return
999 ierr = ii
return
c--------end-of-aplsbt--------------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine diamua (nrow,job, a, ja, ia, diag, b, jb, ib)
real*8 a(*), b(*), diag(nrow), scal
integer ja(*),jb(*), ia(nrow+1),ib(nrow+1)
c-----------------------------------------------------------------------
c performs the matrix by matrix product B = Diag * A (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 in this case use job=0.
c-----------------------------------------------------------------
do 1 ii=1,nrow
c
c normalize each row
c
k1 = ia(ii)
k2 = ia(ii+1)-1
scal = diag(ii)
do 2 k=k1, k2
b(k) = a(k)*scal
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----------end-of-diamua------------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine amudia (nrow,job, a, ja, ia, diag, b, jb, ib)
real*8 a(*), b(*), diag(nrow)
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-----------------------------------------------------------------------
subroutine aplsca (nrow, a, ja, ia, scal,iw)
real*8 a(*), scal
integer ja(*), ia(nrow+1),iw(*)
c-----------------------------------------------------------------------
c Adds a scalar to the diagonal entries of a sparse matrix A :=A + s I
c-----------------------------------------------------------------------
c on entry:
c ---------
c nrow = integer. The row dimension of A
c
c a,
c ja,
c ia = Matrix A in compressed sparse row format.
c
c scal = real. scalar to add to the diagonal entries.
c
c on return:
c----------
c
c a,
c ja,
c ia = matrix A with diagonal elements shifted (or created).
c
c iw = integer work array of length n. On return iw will
c contain the positions of the diagonal entries in the
c output matrix. (i.e., a(iw(k)), ja(iw(k)), k=1,...n,
c are the values/column indices of the diagonal elements
c of the output matrix. ).
c
c Notes:
c-------
c The column dimension of A is not needed.
c important: the matrix a may be expanded slightly to allow for
c additions of nonzero elements to previously nonexisting diagonals.
c The is no checking as to whether there is enough space appended
c to the arrays a and ja. if not sure allow for n additional
c elemnts.
c coded by Y. Saad. Latest version July, 19, 1990
c-----------------------------------------------------------------------
logical test
c
call diapos (nrow,ja,ia,iw)
icount = 0
do 1 j=1, nrow
if (iw(j) .eq. 0) then
icount = icount+1
else
a(iw(j)) = a(iw(j)) + scal
endif
1 continue
c
c if no diagonal elements to insert in data structure return.
c
if (icount .eq. 0) return
c
c shift the nonzero elements if needed, to allow for created
c diagonal elements.
c
ko = ia(nrow+1)+icount
c
c copy rows backward
c
do 5 ii=nrow, 1, -1
c
c go through row ii
c
k1 = ia(ii)
k2 = ia(ii+1)-1
ia(ii+1) = ko
test = (iw(ii) .eq. 0)
do 4 k = k2,k1,-1
j = ja(k)
if (test .and. (j .lt. ii)) then
test = .false.
ko = ko - 1
a(ko) = scal
ja(ko) = ii
iw(ii) = ko
endif
ko = ko-1
a(ko) = a(k)
ja(ko) = j
4 continue
c diagonal element has not been added yet.
if (test) then
ko = ko-1
a(ko) = scal
ja(ko) = ii
iw(ii) = ko
endif
5 continue
ia(1) = ko
return
c-----------------------------------------------------------------------
c----------end-of-aplsca------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine apldia (nrow, job, a, ja, ia, diag, b, jb, ib, iw)
real*8 a(*), b(*), diag(nrow)
integer ja(*),jb(*), ia(nrow+1),ib(nrow+1), iw(*)
c-----------------------------------------------------------------------
c Adds a diagonal matrix to a general sparse matrix: B = A + Diag
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 (i.e. assume that a has already been copied into array b,
c or that algorithm is used in place. ) For all practical
c purposes enter job=0 for an in-place call and job=1 otherwise
c
c Note: in case there are missing diagonal elements in A,
c then the option job =0 will be ignored, since the algorithm
c must modify the data structure (i.e. jb, ib) in this
c situation.
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
c iw = integer work array of length n. On return iw will
c contain the positions of the diagonal entries in the
c output matrix. (i.e., a(iw(k)), ja(iw(k)), k=1,...n,
c are the values/column indices of the diagonal elements
c of the output matrix. ).
c
c Notes:
c-------
c 1) The column dimension of A is not needed.
c 2) algorithm in place (b, jb, ib, can be the same as
c a, ja, ia, on entry). See comments for parameter job.
c
c coded by Y. Saad. Latest version July, 19, 1990
c-----------------------------------------------------------------
logical test
c
c copy integer arrays into b's data structure if required
c
if (job .ne. 0) then
nnz = ia(nrow+1)-1
do 2 k=1, nnz
jb(k) = ja(k)
b(k) = a(k)
2 continue
do 3 k=1, nrow+1
ib(k) = ia(k)
3 continue
endif
c
c get positions of diagonal elements in data structure.
c
call diapos (nrow,ja,ia,iw)
c
c count number of holes in diagonal and add diag(*) elements to
c valid diagonal entries.
c
icount = 0
do 1 j=1, nrow
if (iw(j) .eq. 0) then
icount = icount+1
else
b(iw(j)) = a(iw(j)) + diag(j)
endif
1 continue
c
c if no diagonal elements to insert return
c
if (icount .eq. 0) return
c
c shift the nonzero elements if needed, to allow for created
c diagonal elements.
c
ko = ib(nrow+1)+icount
c
c copy rows backward
c
do 5 ii=nrow, 1, -1
c
c go through row ii
c
k1 = ib(ii)
k2 = ib(ii+1)-1
ib(ii+1) = ko
test = (iw(ii) .eq. 0)
do 4 k = k2,k1,-1
j = jb(k)
if (test .and. (j .lt. ii)) then
test = .false.
ko = ko - 1
b(ko) = diag(ii)
jb(ko) = ii
iw(ii) = ko
endif
ko = ko-1
b(ko) = a(k)
jb(ko) = j
4 continue
c diagonal element has not been added yet.
if (test) then
ko = ko-1
b(ko) = diag(ii)
jb(ko) = ii
iw(ii) = ko
endif
5 continue
ib(1) = ko
return
c-----------------------------------------------------------------------
c------------end-of-apldiag---------------------------------------------
end
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