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subroutine dinfo1(n,iout,a,ja,ia,valued,
* title,key,type,ao,jao,iao)
implicit real*8 (a-h,o-z)
real*8 a(*),ao(*)
integer ja(*),ia(n+1),jao(*),iao(n+1),nzdiag
character title*72,key*8,type*3
logical valued
c----------------------------------------------------------------------c
c SPARSKIT: ELEMENTARY INFORMATION ROUTINE. c
c----------------------------------------------------------------------c
c info1 obtains a number of statistics on a sparse matrix and writes c
c it into the output unit iout. The matrix is assumed c
c to be stored in the compressed sparse COLUMN format sparse a, ja, ia c
c----------------------------------------------------------------------c
c Modified Nov 1, 1989. 1) Assumes A is stored in column
c format. 2) Takes symmetry into account, i.e., handles Harwell-Boeing
c matrices correctly.
c *** (Because of the recent modification the words row and
c column may be mixed-up at occasions... to be checked...
c
c bug-fix July 25: 'upper' 'lower' mixed up in formats 108-107.
c
c On entry :
c-----------
c n = integer. column dimension of matrix
c iout = integer. unit number where the information it to be output.
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 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 title = a 72-character title describing the matrix
c NOTE: The first character in title is ignored (it is often
c a one).
c
c key = an 8-character key for the matrix
c type = a 3-character string to describe the type of the matrix.
c see harwell/Boeing documentation for more details on the
c above three parameters.
c
c on return
c----------
c 1) elementary statistics on the matrix is written on output unit
c iout. See below for detailed explanation of typical output.
c 2) the entries of a, ja, ia are sorted.
c
c----------
c
c ao = real*8 array of length nnz used as work array.
c jao = integer work array of length max(2*n+1,nnz)
c iao = integer work array of length n+1
c
c Note : title, key, type are the same paramaters as those
c used for Harwell-Bowing matrices.
c
c-----------------------------------------------------------------------
c Output description:
c--------------------
c *** The following info needs to be updated.
c
c + A header containing the Title, key, type of the matrix and, if values
c are not provided a message to that effect.
c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
c * SYMMETRIC STRUCTURE MEDIEVAL RUSSIAN TOWNS
c * Key = RUSSIANT , Type = SSA
c * No values provided - Information of pattern only
c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
c
c + dimension n, number of nonzero elements nnz, average number of
c nonzero elements per column, standard deviation for this average.
c + if the matrix is upper or lower triangular a message to that effect
c is printed. Also the number of nonzeros in the strict upper
c (lower) parts and the main diagonal are printed.
c + weight of longest column. This is the largest number of nonzero
c elements in a column encountered. Similarly for weight of
c largest/smallest row.
c + lower dandwidth as defined by
c ml = max ( i-j, / all a(i,j).ne. 0 )
c + upper bandwidth as defined by
c mu = max ( j-i, / all a(i,j).ne. 0 )
c NOTE that ml or mu can be negative. ml .lt. 0 would mean
c that A is confined to the strict upper part above the diagonal
c number -ml. Similarly for mu.
c
c + maximun bandwidth as defined by
c Max ( Max [ j ; a(i,j) .ne. 0 ] - Min [ j ; a(i,j) .ne. 0 ] )
c i
c + average bandwidth = average over all columns of the widths each column.
c
c + If there are zero columns /or rows a message is printed
c giving the number of such columns/rows.
c
c + matching elements in A and transp(A) :this counts the number of
c positions (i,j) such that if a(i,j) .ne. 0 then a(j,i) .ne. 0.
c if this number is equal to nnz then the matrix is symmetric.
c + Relative symmetry match : this is the ratio of the previous integer
c over nnz. If this ratio is equal to one then the matrix has a
c symmetric structure.
c
c + average distance of a given element from the diagonal, standard dev.
c the distance of a(i,j) is defined as iabs(j-i).
c
c + Frobenius norm of A
c Frobenius norm of 0.5*(A + transp(A))
c Frobenius norm of 0.5*(A - transp(A))
c these numbers provide information on the degree of symmetry
c of the matrix. If the norm of the nonsymmetric part is
c zero then the matrix is symmetric.
c
c + 90% of matrix is in the band of width k, means that
c by moving away and in a symmetric manner from the main
c diagonal you would have to include exactly k diagonals
c (k is always odd), in order to include 90% of the nonzero
c elements of A. The same thing is then for 80%.
c
c + The total number of nonvoid diagonals, i.e., among the
c 2n-1 diagonals of the matrix which have at least one nonxero
c element.
c
c + Most important diagonals. The code selects a number of k
c (k .le. 10) diagonals that are the most important ones, i.e.
c that have the largest number of nonzero elements. Any diagonal
c that has fewer than 1% of the nonzero elements of A is dropped.
c the numbers printed are the offsets with respect to the
c main diagonal, going from left tp right.
c Thus 0 means the main diagonal -1 means the subdiagonal, and
c +10 means the 10th upper diagonal.
c + The accumulated percentages in the next line represent the
c percentage of the nonzero elements represented by the diagonals
c up the current one put together.
c Thus:
c * The 10 most important diagonals are (offsets) : *
c * 0 1 2 24 21 4 23 22 20 19 *
c * The accumulated percentages they represent are : *
c * 40.4 68.1 77.7 80.9 84.0 86.2 87.2 88.3 89.4 90.4 *
c *-----------------------------------------------------------------*
c shows the offsets of the most important diagonals and
c 40.4 represent ratio of the number of nonzero elements in the
c diagonal zero (main diagonal) over the total number of nonzero
c elements. the second number indicates that the diagonal 0 and the
c diagonal 1 together hold 68.1% of the matrix, etc..
c
c + Block structure:
c if the matrix has a block structure then the block size is found
c and printed. Otherwise the info1 will say that the matrix
c does not have a block structure. Note that block struture has
c a very specific meaning here. the matrix has a block structure
c if it consists of square blocks that are dense. even if there
c are zero elements in the blocks they should be represented
c otherwise it would be possible to determine the block size.
c
c-----------------------------------------------------------------------
real*8 dcount(20),amx
integer ioff(20)
character*61 tmpst
logical sym
c-----------------------------------------------------------------------
data ipar1 /1/
write (iout,99)
write (iout,97) title(2:72), key, type
97 format(2x,' * ',a71,' *'/,
* 2x,' *',20x,'Key = ',a8,' , Type = ',a3,25x,' *')
if (.not. valued) write (iout,98)
98 format(2x,' * No values provided - Information on pattern only',
* 23x,' *')
c---------------------------------------------------------------------
nnz = ia(n+1)-ia(1)
sym = ((type(2:2) .eq. 'S') .or. (type(2:2) .eq. 'Z')
* .or. (type(2:2) .eq. 's') .or. (type(2:2) .eq. 'z'))
c
write (iout, 99)
write(iout, 100) n, nnz
job = 0
if (valued) job = 1
ipos = 1
call csrcsc(n, job, ipos, a, ja, ia, ao, jao, iao)
call csrcsc(n, job, ipos, ao, jao, iao, a, ja, ia)
c-------------------------------------------------------------------
c computing max bandwith, max number of nonzero elements per column
c min nonzero elements per column/row, row/column diagonal dominance
c occurences, average distance of an element from diagonal, number of
c elemnts in lower and upper parts, ...
c------------------------------------------------------------------
c jao will be modified later, so we call skyline here
call skyline(n,sym,ja,ia,jao,iao,nsky)
call nonz_lud(n,ja,ia,nlower, nupper, ndiag)
call avnz_col(n,ja,ia,iao, ndiag, av, st)
c------ write out info ----------------------------------------------
if (sym) nupper = nlower
write(iout, 101) av, st
if (nlower .eq. 0 ) write(iout, 105)
1 if (nupper .eq. 0) write(iout, 106)
write(iout, 107) nlower
write(iout, 108) nupper
write(iout, 109) ndiag
c
call nonz(n,sym, ja, ia, iao, nzmaxc, nzminc,
* nzmaxr, nzminr, nzcol, nzrow)
write(iout, 1020) nzmaxc, nzminc
c
if (.not. sym) write(iout, 1021) nzmaxr, nzminr
c
if (nzcol .ne. 0) write(iout,116) nzcol
if (nzrow .ne. 0) write(iout,115) nzrow
c
call diag_domi(n,sym,valued,a, ja,ia,ao, jao, iao,
* ddomc, ddomr)
c-----------------------------------------------------------------------
c symmetry and near symmetry - Frobenius norms
c-----------------------------------------------------------------------
call frobnorm(n,sym,a,ja,ia,Fnorm)
call ansym(n,sym,a,ja,ia,ao,jao,iao,imatch,av,fas,fan)
call distaij(n,nnz,sym,ja,ia,dist, std)
amx = 0.0d0
do 40 k=1, nnz
amx = max(amx, abs(a(k)) )
40 continue
write (iout,103) imatch, av, dist, std
write(iout,96)
if (valued) then
write(iout,104) Fnorm, fas, fan, amx, ddomr, ddomc
write (iout,96)
endif
c-----------------------------------------------------------------------
c--------------------bandedness- main diagonals ----------------------- -
c-----------------------------------------------------------------------
n2 = n+n-1
do 8 i=1, n2
jao(i) = 0
8 continue
do 9 i=1, n
k1 = ia(i)
k2 = ia(i+1) -1
do 91 k=k1, k2
j = ja(k)
jao(n+i-j) = jao(n+i-j) +1
91 continue
9 continue
c
call bandwidth(n,ja, ia, ml, mu, iband, bndav)
c
c write bandwidth information .
c
write(iout,117) ml, mu, iband, bndav
c
write(iout,1175) nsky
c
c call percentage_matrix(n,nnz,ja,ia,jao,90,jb2)
c call percentage_matrix(n,nnz,ja,ia,jao,80,jb1)
nrow = n
ncol = n
call distdiag(nrow,ncol,ja,ia,jao)
call bandpart(n,ja,ia,jao,90,jb2)
call bandpart(n,ja,ia,jao,80,jb1)
write (iout,112) 2*jb2+1, 2*jb1+1
c-----------------------------------------------------------------
nzdiag = 0
n2 = n+n-1
do 42 i=1, n2
if (jao(i) .ne. 0) nzdiag=nzdiag+1
42 continue
call n_imp_diag(n,nnz,jao,ipar1, ndiag,ioff,dcount)
write (iout,118) nzdiag
write (tmpst,'(10i6)') (ioff(j),j=1,ndiag)
write (iout,110) ndiag,tmpst
write (tmpst,'(10f6.1)')(dcount(j), j=1,ndiag)
write (iout,111) tmpst
write (iout, 96)
c jump to next page -- optional //
c write (iout,'(1h1)')
c-----------------------------------------------------------------------
c determine block size if matrix is a block matrix..
c-----------------------------------------------------------------------
call blkfnd(n, ja, ia, nblk)
if (nblk .le. 1) then
write(iout,113)
else
write(iout,114) nblk
endif
write (iout,96)
c
c---------- done. Next define all the formats --------------------------
c
99 format (2x,38(2h *))
96 format (6x,' *',65(1h-),'*')
c-----------------------------------------------------------------------
100 format(
* 6x,' * Dimension N = ',
* i10,' *'/
* 6x,' * Number of nonzero elements = ',
* i10,' *')
101 format(
* 6x,' * Average number of nonzero elements/Column = ',
* f10.4,' *'/
* 6x,' * Standard deviation for above average = ',
* f10.4,' *')
c-----------------------------------------------------------------------
1020 format(
* 6x,' * Weight of longest column = ',
* i10,' *'/
* 6x,' * Weight of shortest column = ',
* i10,' *')
1021 format(
* 6x,' * Weight of longest row = ',
* i10,' *'/
* 6x,' * Weight of shortest row = ',
* i10,' *')
117 format(
* 6x,' * Lower bandwidth (max: i-j, a(i,j) .ne. 0) = ',
* i10,' *'/
* 6x,' * Upper bandwidth (max: j-i, a(i,j) .ne. 0) = ',
* i10,' *'/
* 6x,' * Maximum Bandwidth = ',
* i10,' *'/
* 6x,' * Average Bandwidth = ',
* e10.3,' *')
1175 format(
* 6x,' * Number of nonzeros in skyline storage = ',
* i10,' *')
103 format(
* 6x,' * Matching elements in symmetry = ',
* i10,' *'/
* 6x,' * Relative Symmetry Match (symmetry=1) = ',
* f10.4,' *'/
* 6x,' * Average distance of a(i,j) from diag. = ',
* e10.3,' *'/
* 6x,' * Standard deviation for above average = ',
* e10.3,' *')
104 format(
* 6x,' * Frobenius norm of A = ',
* e10.3,' *'/
* 6x,' * Frobenius norm of symmetric part = ',
* e10.3,' *'/
* 6x,' * Frobenius norm of nonsymmetric part = ',
* e10.3,' *'/
* 6x,' * Maximum element in A = ',
* e10.3,' *'/
* 6x,' * Percentage of weakly diagonally dominant rows = ',
* e10.3,' *'/
* 6x,' * Percentage of weakly diagonally dominant columns = ',
* e10.3,' *')
105 format(
* 6x,' * The matrix is lower triangular ... ',21x,' *')
106 format(
* 6x,' * The matrix is upper triangular ... ',21x,' *')
107 format(
* 6x,' * Nonzero elements in strict lower part = ',
* i10,' *')
108 format(
* 6x,' * Nonzero elements in strict upper part = ',
* i10,' *')
109 format(
* 6x,' * Nonzero elements in main diagonal = ',
* i10,' *')
110 format(6x,' * The ', i2, ' most important',
* ' diagonals are (offsets) : ',10x,' *',/,
* 6x,' *',a61,3x,' *')
111 format(6x,' * The accumulated percentages they represent are ',
* ' : ', 10x,' *',/,
* 6x,' *',a61,3x,' *')
c 111 format(
c * 6x,' * They constitute the following % of A = ',
c * f8.1,' % *')
112 format(
* 6x,' * 90% of matrix is in the band of width = ',
* i10,' *',/,
* 6x,' * 80% of matrix is in the band of width = ',
* i10,' *')
113 format(
* 6x,' * The matrix does not have a block structure ',19x,
* ' *')
114 format(
* 6x,' * Block structure found with block size = ',
* i10,' *')
115 format(
* 6x,' * There are zero rows. Number of such rows = ',
* i10,' *')
116 format(
* 6x,' * There are zero columns. Number of such columns = ',
* i10,' *')
118 format(
* 6x,' * The total number of nonvoid diagonals is = ',
* i10,' *')
c-------------------------- end of dinfo --------------------------
return
end
|
