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|
c----------------------------------------------------------------------c
c S P A R S K I T c
c----------------------------------------------------------------------c
c INFORMATION ROUTINES. INFO MODULE c
c----------------------------------------------------------------------c
c bandwidth : Computes ml = lower_bandwidth(A) c
c mu = upper_bandwidth(A) c
c iband = max_bandwidth(A) c
c bndav = average_bandwidth(A) c
c nonz : Computes nzmaxc = max_column_length(A) c
c nzminc = min_column_length(A) c
c nzmaxr = max_row_length(A) c
c nzminr = min_row_length(A) c
c nzcol = zero_column_number(A) c
c nzrow = zero_row_number(A) c
c diag_domi : Computes ddomc = diag_domi_column_percentage(A) c
c ddomr = diag_domi_row_percentage(A) c
c frobnorm : Computes Fnorm = Frobenius_norm(A) c
c ansym : Computes fas = sym_part_Frobenius_norm(A) c
c fan = nonsym_part_Frobenius_norm(A) c
c imatch = matching_elements_number(A) c
c av = relative_sym_match(A) c
c distaij : Computes dist = average_dist_of_a(i,j)(A) c
c std = standard_deviation(A) c
c skyline : Computes nsky = nonzero_number_in_skyline(A) c
c distdiag : Computes dist = element_number_in_eachdiag(A) c
c bandpart : Computes band = bandwidth_width(A) c
c n_imp_diag: Computes ndiag = important_diag_number(A) c
c nonz_lud : Computes nlower = nonzero_number_of_lower_part(A) c
c nupper = nonzero_number_of_upper_part(A) c
c ndiag = nonzero_number_of_maindiag(A) c
c avnz_col : Computes av = average_nonzero_number_in_column(A) c
c st = standard_deviation(A) c
c vbrinfo : Print info on matrix in variable block row format c
c----------------------------------------------------------------------c
subroutine bandwidth(n,ja, ia, ml, mu, iband, bndav)
implicit none
integer n, ml, mu, iband
integer ja(*), ia(n+1)
real*8 bndav
c-----------------------------------------------------------------------
c this routine computes the lower, upper, maximum, and average
c bandwidths. revised -- July 12, 2001 -- bug fix -- YS.
c-----------------------------------------------------------------------
c On Entry:
c----------
c n = integer. column dimension of matrix
c a = real array containing the nonzero elements of the matrix
c the elements are stored by columns in order
c (i.e. column i comes before column i+1, but the elements
c within each column can be disordered).
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c
c on return
c----------
c ml = lower bandwidth as defined by
c ml = max(i-j | all a(i,j).ne. 0)
c mu = upper bandwidth as defined by
c mu = max ( j-i | all a(i,j).ne. 0 )
c iband = maximum bandwidth as defined by
c iband = Max ( Max [ j | a(i,j) .ne. 0 ] -
c Min [ j | a(i,j) .ne. 0 ] )
c bndav = Average Bandwidth
c-----------------------------------------------------------------------
c locals
integer max
integer j0, j1, jminc, jmaxc, i
c-----------------------------------------------------------------------
ml = -n
mu = -n
bndav = 0.0d0
iband = 0
do 10 i=1,n
j0 = ia(i)
j1 = ia(i+1) - 1
jminc = ja(j0)
jmaxc = ja(j1)
ml = max(ml,i-jminc)
mu = max(mu,jmaxc-i)
iband = max(iband,jmaxc-jminc+1)
bndav = bndav+real( jmaxc-jminc+1)
10 continue
bndav = bndav/real(n)
return
c-----end-of-bandwidth--------------------------------------------------
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine nonz(n,sym, ja, ia, iao, nzmaxc, nzminc,
* nzmaxr, nzminr, nzcol, nzrow)
implicit none
integer n , nzmaxc, nzminc, nzmaxr, nzminr, nzcol, nzrow
integer ja(*), ia(n+1), iao(n+1)
logical sym
c----------------------------------------------------------------------
c this routine computes maximum numbers of nonzero elements
c per column/row, minimum numbers of nonzero elements per column/row,
c and numbers of zero columns/rows.
c----------------------------------------------------------------------
c On Entry:
c----------
c n = integer column dimension of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c iao = similar array for the transpose of the matrix.
c sym = logical variable indicating whether or not the matrix is
c stored in symmetric mode.
c on return
c----------
c nzmaxc = max length of columns
c nzminc = min length of columns
c nzmaxr = max length of rows
c nzminr = min length of rows
c nzcol = number of zero columns
c nzrow = number of zero rows
c-----------------------------------------------------------------------
integer i, j0, j0r, j1r, indiag, k, j1, lenc, lenr
c
nzmaxc = 0
nzminc = n
nzmaxr = 0
nzminr = n
nzcol = 0
nzrow = 0
c-----------------------------------------------------------------------
do 10 i = 1, n
j0 = ia(i)
j1 = ia(i+1)
j0r = iao(i)
j1r = iao(i+1)
indiag = 0
do 20 k=j0, j1-1
if (ja(k) .eq. i) indiag = 1
20 continue
c
lenc = j1-j0
lenr = j1r-j0r
c
if (sym) lenc = lenc + lenr - indiag
if (lenc .le. 0) nzcol = nzcol +1
nzmaxc = max0(nzmaxc,lenc)
nzminc = min0(nzminc,lenc)
if (lenr .le. 0) nzrow = nzrow+1
nzmaxr = max0(nzmaxr,lenr)
nzminr = min0(nzminr,lenr)
10 continue
return
end
c-----------------------------------------------------------------------
subroutine diag_domi(n,sym,valued,a, ja,ia,ao,jao, iao,
* ddomc, ddomr)
implicit none
real*8 a(*), ao(*), ddomc, ddomr
integer n, ja(*), ia(n+1), jao(*), iao(n+1)
logical sym, valued
c-----------------------------------------------------------------
c this routine computes the percentage of weakly diagonally
c dominant rows/columns
c-----------------------------------------------------------------
c on entry:
c ---------
c n = integer column dimension of matrix
c a = real array containing the nonzero elements of the matrix
c the elements are stored by columns in order
c (i.e. column i comes before column i+1, but the elements
c within each column can be disordered).
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c ao = real array containing the nonzero elements of the matrix
c the elements are stored by rows in order
c (i.e. row i comes before row i+1, but the elements
c within each row can be disordered).
c ao,jao, iao,
c structure for transpose of a
c sym = logical variable indicating whether or not the matrix is
c symmetric.
c valued= logical equal to .true. if values are provided and .false.
c if only the pattern of the matrix is provided. (in that
c case a(*) and ao(*) are dummy arrays.
c
c ON RETURN
c----------
c ddomc = percentage of weakly diagonally dominant columns
c ddomr = percentage of weakly diagonally dominant rows
c-------------------------------------------------------------------
c locals
integer i, j0, j1, k, j
real*8 aii, dsumr, dsumc
c number of diagonally dominant columns
c real arithmetic used to avoid problems.. YS. 03/27/01
ddomc = 0.0
c number of diagonally dominant rows
ddomr = 0.0
do 10 i = 1, n
j0 = ia(i)
j1 = ia(i+1) - 1
if (valued) then
aii = 0.0d0
dsumc = 0.0d0
do 20 k=j0,j1
j = ja(k)
if (j .eq. i) then
aii = abs(a(k))
else
dsumc = dsumc + abs(a(k))
endif
20 continue
dsumr = 0.0d0
if (.not. sym) then
do 30 k=iao(i), iao(i+1)-1
if (jao(k) .ne. i) dsumr = dsumr+abs(ao(k))
30 continue
else
dsumr = dsumc
endif
if (dsumc .le. aii) ddomc = ddomc + 1.0
if (dsumr .le. aii) ddomr = ddomr + 1.0
endif
10 continue
ddomr = ddomr / real(n)
ddomc = ddomc / real(n)
return
c-----------------------------------------------------------------------
c--------end-of-diag_moni-----------------------------------------------
end
c-----------------------------------------------------------------------
subroutine frobnorm(n,sym,a,ja,ia,Fnorm)
implicit none
integer n
real*8 a(*),Fnorm
integer ja(*),ia(n+1)
logical sym
c--------------------------------------------------------------------------
c this routine computes the Frobenius norm of A.
c--------------------------------------------------------------------------
c on entry:
c-----------
c n = integer colum dimension of matrix
c a = real array containing the nonzero elements of the matrix
c the elements are stored by columns in order
c (i.e. column i comes before column i+1, but the elements
c within each column can be disordered).
c ja = integer array containing the row indices of elements in a.
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and
c ja. It is assumed that ia(*)= 1 and ia(n+1) = nnz +1.
c sym = logical variable indicating whether or not the matrix is
c symmetric.
c
c on return
c-----------
c Fnorm = Frobenius norm of A.
c--------------------------------------------------------------------------
real*8 Fdiag
integer i, k
Fdiag = 0.0
Fnorm = 0.0
do i =1,n
do k = ia(i), ia(i+1)-1
if (ja(k) .eq. i) then
Fdiag = Fdiag + a(k)**2
else
Fnorm = Fnorm + a(k)**2
endif
enddo
enddo
if (sym) then
Fnorm = 2*Fnorm +Fdiag
else
Fnorm = Fnorm + Fdiag
endif
Fnorm = sqrt(Fnorm)
return
end
c----------------------------------------------------------------------
subroutine ansym(n,sym,a,ja,ia,ao,jao,iao,imatch,
* av,fas,fan)
c---------------------------------------------------------------------
c this routine computes the Frobenius norm of the symmetric and
c non-symmetric parts of A, computes number of matching elements
c in symmetry and relative symmetry match.
c---------------------------------------------------------------------
c on entry:
c----------
c n = integer column dimension of matrix
c a = real array containing the nonzero elements of the matrix
c the elements are stored by columns in order
c (i.e. column i comes before column i+1, but the elements
c within each column can be disordered).
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c sym = logical variable indicating whether or not the matrix is
c symmetric.
c on return
c----------
c fas = Frobenius norm of symmetric part
c fan = Frobenius norm of non-symmetric part
c imatch = number of matching elements in symmetry
c av = relative symmetry match (symmetry = 1)
c ao,jao,iao = transpose of A just as a, ja, ia contains
c information of A.
c-----------------------------------------------------------------------
implicit real*8 (a-h, o-z)
real*8 a(*),ao(*),fas,fan,av, Fnorm, st
integer n, ja(*), ia(n+1), jao(*), iao(n+1),imatch
logical sym
c-----------------------------------------------------------------------
nnz = ia(n+1)-ia(1)
call csrcsc(n,1,1,a,ja,ia,ao,jao,iao)
if (sym) goto 7
st = 0.0d0
fas = 0.0d0
fan = 0.0d0
imatch = 0
do 6 i=1,n
k1 = ia(i)
k2 = iao(i)
k1max = ia(i+1) - 1
k2max = iao(i+1) - 1
c
5 if (k1 .gt. k1max .or. k2 .gt. k2max) goto 6
c
j1 = ja(k1)
j2 = jao(k2)
if (j1 .ne. j2 ) goto 51
fas = fas + (a(k1)+ao(k2))**2
fan = fan + (a(k1)-ao(k2))**2
st = st + a(k1)**2
imatch = imatch + 1
51 k1 = k1+1
k2 = k2+1
if (j1 .lt. j2) k2 = k2 - 1
if (j1 .gt. j2) k1 = k1 - 1
goto 5
6 continue
fas = 0.25D0 * fas
fan = 0.25D0 * fan
7 call frobnorm(n,sym,ao,jao,iao,Fnorm)
if (sym) then
imatch = nnz
fas = Fnorm
fan = 0.0d0
else
if (imatch.eq.nnz) then
st = 0.0D0
else
st = 0.5D0 * (Fnorm**2 - st)
if (st.lt.0.0D0) st = 0.0D0
endif
fas = sqrt(fas + st)
fan = sqrt(fan + st)
endif
av = real(imatch)/real(nnz)
return
end
c------end-of-ansym-----------------------------------------------------
c-----------------------------------------------------------------------
subroutine distaij(n,nnz,sym,ja,ia,dist, std)
implicit real*8 (a-h, o-z)
real*8 dist, std
integer ja(*), ia(n+1)
c-----------------------------------------------------------------------
c this routine computes the average distance of a(i,j) from diag and
c standard deviation for this average.
c-----------------------------------------------------------------------
c On entry :
c-----------
c n = integer. column dimension of matrix
c nnz = number of nonzero elements of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c sym = logical variable indicating whether or not the matrix is
c symmetric.
c on return
c----------
c dist = average distance of a(i,j) from diag.
c std = standard deviation for above average.
c-----------------------------------------------------------------------
c
c distance of an element from diagonal.
c
dist = 0.0
std = 0.0
do 3 i=1,n
j0 = ia(i)
j1 = ia(i+1) - 1
do 31 k=j0, j1
j=ja(k)
dist = dist + real(iabs(j-i) )
31 continue
3 continue
dist = dist/real(nnz)
do 6 i = 1, n
do 61 k=ia(i), ia(i+1) - 1
std=std+(dist-real(iabs(ja(k)-i)))**2
61 continue
6 continue
std = sqrt(std/ real(nnz))
return
end
c-----------------------------------------------------------------------
subroutine skyline(n,sym,ja,ia,jao,iao,nsky)
implicit real*8 (a-h, o-z)
integer n, ja(*), ia(n+1), jao(*), iao(n+1)
integer nskyl, nskyu, nsky
logical sym
c-------------------------------------------------------------------
c this routine computes the number of nonzeros in the skyline storage.
c-------------------------------------------------------------------
c
c On entry :
c-----------
c n = integer. column dimension of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c iao = integer array containing of length n+1 containing the
c pointers to the beginning of the rows in arrays ao and jao.
c It is assumed that iao(*) = 1 and iao(n+1) = nzz+1.
c jao = integer array containing the column indices of elements in ao.
c sym = logical variable indicating whether or not the matrix is
c symmetric.
c on return
c----------
c nsky = number of nonzeros in skyline storage
c-------------------------------------------------------------------
c
c nskyu = skyline storage for upper part
nskyu = 0
c nskyl = skyline storage for lower part
nskyl = 0
do 10 i=1,n
j0 = ia(i)
j0r = iao(i)
jminc = ja(j0)
jminr = jao(j0r)
if (sym) jminc = jminr
nskyl = nskyl + i-jminr + 1
nskyu = nskyu + i-jminc + 1
10 continue
nsky = nskyl+nskyu-n
if (sym) nsky = nskyl
return
end
c-----------------------------------------------------------------------
subroutine distdiag(nrow,ncol,ja,ia,dist)
implicit real*8 (a-h, o-z)
integer nrow,ncol,ja(*), ia(nrow+1),dist(*)
c----------------------------------------------------------------------
c this routine computes the numbers of elements in each diagonal.
c----------------------------------------------------------------------
c On entry :
c-----------
c nrow = integer. row dimension of matrix
c ncol = integer. column dimension of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c on return
c----------
c dist = integer array containing the numbers of elements in each of
c the nrow+ncol-1 diagonals of A. dist(k) contains the
c number of elements in diagonal '-nrow+k'. k ranges from
c 1 to (nrow+ncol-1).
c----------------------------------------------------------------------
nnz = ia(nrow+1)-ia(1)
n2 = nrow+ncol-1
do 8 i=1, n2
dist(i) = 0
8 continue
do 9 i=1, nrow
k1 = ia(i)
k2 = ia(i+1) -1
do 91 k=k1, k2
j = ja(k)
dist(nrow+j-i) = dist(nrow+j-i) +1
91 continue
9 continue
return
end
c-----------------------------------------------------------------------
subroutine bandpart(n,ja,ia,dist,nper,band)
implicit real*8 (a-h, o-z)
integer n,ja(*), ia(n+1),dist(*)
integer nper,band
c-------------------------------------------------------------------------
c this routine computes the bandwidth of the banded matrix, which contains
c 'nper' percent of the original matrix.
c-------------------------------------------------------------------------
c On entry :
c-----------
c n = integer. column dimension of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c dist = integer array containing the numbers of elements in the
c matrix with different distance of row indices and column
c indices.
c nper = percentage of matrix within the bandwidth
c on return
c----------
c band = the width of the bandwidth
c----------------------------------------------------------------------
nnz = ia(n+1)-ia(1)
iacc = dist(n)
band = 0
j = 0
10 j = j+1
iacc = iacc + dist(n+j) +dist(n-j)
if (iacc*100 .le. nnz*nper) then
band = band +1
goto 10
endif
return
end
c-----------------------------------------------------------------------
subroutine n_imp_diag(n,nnz,dist, ipar1,ndiag,ioff,dcount)
implicit real*8 (a-h, o-z)
real*8 dcount(*)
integer n,nnz, dist(*), ndiag, ioff(*), ipar1
c-----------------------------------------------------------------------
c this routine computes the most important diagonals.
c-----------------------------------------------------------------------
c
c On entry :
c-----------
c n = integer. column dimension of matrix
c nnz = number of nonzero elements of matrix
c dist = integer array containing the numbers of elements in the
c matrix with different distance of row indices and column
c indices. ipar1 = percentage of nonzero elements of A that
c a diagonal should have in order to be an important diagonal
c on return
c----------
c ndiag = number of the most important diagonals
c ioff = the offsets with respect to the main diagonal
c dcount= the accumulated percentages
c-----------------------------------------------------------------------
n2 = n+n-1
ndiag = 10
ndiag = min0(n2,ndiag)
itot = 0
ii = 0
idiag = 0
c sort diagonals by decreasing order of weights.
40 jmax = 0
i = 1
do 41 k=1, n2
j = dist(k)
if (j .lt. jmax) goto 41
i = k
jmax = j
41 continue
c permute ----
c save offsets and accumulated count if diagonal is acceptable
c (if it has at least ipar1*nnz/100 nonzero elements)
c quite if no more acceptable diagonals --
c
if (jmax*100 .lt. ipar1*nnz) goto 4
ii = ii+1
ioff(ii) = i-n
dist(i) = - jmax
itot = itot + jmax
dcount(ii) = real(100*itot)/real(nnz)
if (ii .lt. ndiag) goto 40
4 continue
ndiag = ii
return
c-----------------------------------------------------------------------
end
c-----------------------------------------------------------------------
subroutine nonz_lud(n,ja,ia,nlower, nupper, ndiag)
implicit real*8 (a-h, o-z)
integer n, ja(*), ia(n+1)
integer nlower, nupper, ndiag
c-----------------------------------------------------------------------
c this routine computes the number of nonzero elements in strict lower
c part, strict upper part, and main diagonal.
c-----------------------------------------------------------------------
c
c On entry :
c-----------
c n = integer. column dimension of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c on return
c----------
c nlower= number of nonzero elements in strict lower part
c nupper= number of nonzero elements in strict upper part
c ndiag = number of nonzero elements in main diagonal
c-------------------------------------------------------------------
c
c number of nonzero elements in upper part
c
nupper = 0
ndiag = 0
do 3 i=1,n
c indiag = nonzero diagonal element indicator
do 31 k=ia(i), ia(i+1)-1
j=ja(k)
if (j .lt. i) nupper = nupper+1
if (j .eq. i) ndiag = ndiag + 1
31 continue
3 continue
nlower = ia(n+1)-1-nupper-ndiag
return
end
c-----------------------------------------------------------------------
subroutine avnz_col(n,ja,ia,iao, ndiag, av, st)
implicit real*8 (a-h, o-z)
real*8 av, st
integer n, ja(*), ia(n+1), iao(n+1)
c---------------------------------------------------------------------
c this routine computes average number of nonzero elements/column and
c standard deviation for this average
c---------------------------------------------------------------------
c
c On entry :
c-----------
c n = integer. column dimension of matrix
c ja = integer array containing the row indices of elements in a
c ia = integer array containing of length n+1 containing the
c pointers to the beginning of the columns in arrays a and ja.
c It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
c ndiag = number of the most important diagonals
c On return
c----------
c av = average number of nonzero elements/column
c st = standard deviation for this average
c Notes
c---------
c standard deviation will not be correct for symmetric storage.
c----------------------------------------------------------------------
c standard deviatioan for the average
st = 0.0d0
c average and standard deviation
c
av = real(ia(n+1)-1)/real(n)
c
c will be corrected later.
c
do 3 i=1,n
j0 = ia(i)
j1 = ia(i+1) - 1
c indiag = nonzero diagonal element indicator
do 31 k=j0, j1
j=ja(k)
31 continue
lenc = j1+1-j0
st = st + (real(lenc) - av)**2
3 continue
c
st = sqrt( st / real(n) )
return
end
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
subroutine vbrinfo(nr, nc, kvstr, kvstc, ia, ja, ka, iwk, iout)
c-----------------------------------------------------------------------
integer nr, nc, kvstr(nr+1), kvstc(nc+1), ia(nr+1), ja(*), ka(*)
integer iwk(nr+nc+2+nr), iout
c-----------------------------------------------------------------------
c Print info on matrix in variable block row format.
c-----------------------------------------------------------------------
c On entry:
c--------------
c nr,nc = matrix block row and block column dimension
c kvstr = first row number for each block row
c kvstc = first column number for each block column
c ia,ja,ka,a = input matrix in VBR format
c iout = unit number for printed output
c
c On return:
c---------------
c Printed output to unit number specified in iout. If a non-square
c matrix is provided, the analysis will be performed on the block
c rows, otherwise a row/column conformal partitioning will be used.
c
c Work space:
c----------------
c iwk(1:nb+1) = conformal block partitioning
c (nb is unknown at start but is no more than nr+nc)
c iwk(nb+2:nb+2+nr) = frequency of each blocksize
c The workspace is not assumed to be initialized to zero, nor is it
c left that way.
c
c-----------------------------------------------------------------------
c-----local variables
integer n, nb, nnz, nnzb, i, j, neq, max, num
character*101 tmpst
integer bsiz(10), freq(10)
c-----------------------------------------------------------------------
n = kvstr(nr+1)-1
nnz = ka(ia(nr+1)) - ka(1)
nnzb = ia(nr+1) - ia(1)
write (iout, 96)
write (iout, 100) n, nnz, real(nnz)/real(n)
write (iout, 101) nr, nnzb, real(nnzb)/real(nr)
c-----if non-square matrix, do analysis on block rows,
c else do analysis on conformal partitioning
if (kvstr(nr+1) .ne. kvstc(nc+1)) then
write (iout, 103)
do i = 1, nr+1
iwk(i) = kvstr(i)
enddo
nb = nr
else
call kvstmerge(nr, kvstr, nc, kvstc, nb, iwk)
if ((nr .ne. nc) .or. (nc .ne. nb)) write (iout, 104) nb
endif
c-----accumulate frequencies of each blocksize
max = 1
iwk(1+nb+2) = 0
do i = 1, nb
neq = iwk(i+1) - iwk(i)
if (neq .gt. max) then
do j = max+1, neq
iwk(j+nb+2) = 0
enddo
max = neq
endif
iwk(neq+nb+2) = iwk(neq+nb+2) + 1
enddo
c-----store largest 10 of these blocksizes
num = 0
do i = max, 1, -1
if ((iwk(i+nb+2) .ne. 0) .and. (num .lt. 10)) then
num = num + 1
bsiz(num) = i
freq(num) = iwk(i+nb+2)
endif
enddo
c-----print information about blocksizes
write (iout, 109) num
write (tmpst,'(10i6)') (bsiz(j),j=1,num)
write (iout,110) num,tmpst
write (tmpst,'(10i6)') (freq(j),j=1,num)
write (iout,111) tmpst
write (iout, 96)
c-----------------------------------------------------------------------
99 format (2x,38(2h *))
96 format (6x,' *',65(1h-),'*')
100 format(
* 6x,' * Number of rows = ',
* i10,' *'/
* 6x,' * Number of nonzero elements = ',
* i10,' *'/
* 6x,' * Average number of nonzero elements/Row = ',
* f10.4,' *')
101 format(
* 6x,' * Number of block rows = ',
* i10,' *'/
* 6x,' * Number of nonzero blocks = ',
* i10,' *'/
* 6x,' * Average number of nonzero blocks/Block row = ',
* f10.4,' *')
103 format(
* 6x,' * Non-square matrix. ',
* ' *'/
* 6x,' * Performing analysis on block rows. ',
* ' *')
104 format(
* 6x,' * Non row-column conformal partitioning supplied. ',
* ' *'/
* 6x,' * Using conformal partitioning. Number of bl rows = ',
* i10,' *')
109 format(
* 6x,' * Number of different blocksizes = ',
* i10,' *')
110 format(6x,' * The ', i2, ' largest dimension nodes',
* ' have dimension : ',10x,' *',/,
* 6x,' *',a61,3x,' *')
111 format(6x,' * The frequency of nodes these ',
* 'dimensions are : ',10x,' *',/,
* 6x,' *',a61,3x,' *')
c---------------------------------
return
end
c-----------------------------------------------------------------------
c-----------------------end-of-vbrinfo----------------------------------
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