c======================================================================= c== umf4hb ============================================================= c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c umf4hb64: c read a sparse matrix in the Harwell/Boeing format, factorizes c it, and solves Ax=b. Also saves and loads the factors to/from a c file. Saving to a file is not required, it's just here to c demonstrate how to use this feature of UMFPACK. This program c only works on square RUA-type matrices. c c This is HIGHLY non-portable. It may not work with your C and c FORTRAN compilers. See umf4_f77wrapper.c for more details. c c usage (for example): c c in a Unix shell: c umf4hb64 < HB/arc130.rua integer*8 $ nzmax, nmax parameter (nzmax = 5000000, nmax = 160000) integer*8 $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel, $ numeric, symbolic, status, sys, filenum character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 double precision Ax (nzmax), x (nmax), b (nmax), aij, xj, $ r (nmax), control (20), info (90) character rhstyp*3 c ---------------------------------------------------------------- c read the Harwell/Boeing matrix c ---------------------------------------------------------------- read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp, nrhs, nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) print *, 'Matrix key: ', key n = nrow if (type .ne. 'RUA' .or. nrow .ne. ncol) then print *, 'Error: can only handle square RUA matrices' stop endif if (n .ge. nmax .or. nz .gt. nzmax) then print *, ' Matrix too big!' stop endif c read the matrix (1-based) read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Ai (p), p = 1, nz) read (5, valfmt, err = 998) (Ax (p), p = 1, nz) c ---------------------------------------------------------------- c create the right-hand-side, assume x (i) = 1 + i/n c ---------------------------------------------------------------- do 30 i = 1,n b (i) = 0 30 continue c b = A*x do 50 j = 1,n xj = j xj = 1 + xj / n do 40 p = Ap (j), Ap (j+1)-1 i = Ai (p) aij = Ax (p) b (i) = b (i) + aij * xj 40 continue 50 continue c ---------------------------------------------------------------- c convert from 1-based to 0-based c ---------------------------------------------------------------- do 60 j = 1, n+1 Ap (j) = Ap (j) - 1 60 continue do 70 p = 1, nz Ai (p) = Ai (p) - 1 70 continue c ---------------------------------------------------------------- c factor the matrix and save to a file c ---------------------------------------------------------------- c set default parameters call umf4def (control) c print control parameters. set control (1) to 1 to print c error messages only control (1) = 2 call umf4pcon (control) c pre-order and symbolic analysis call umf4sym (n, n, Ap, Ai, Ax, symbolic, control, info) c print statistics computed so far c call umf4pinf (control, info) could also be done. print 80, info (1), info (16), $ (info (21) * info (4)) / 2**20, $ (info (22) * info (4)) / 2**20, $ info (23), info (24), info (25) 80 format ('symbolic analysis:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, ' (sec)'/, $ ' estimates (upper bound) for numeric LU:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4sym error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4sym: ', info (1) stop endif c numeric factorization call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) c print statistics for the numeric factorization c call umf4pinf (control, info) could also be done. print 90, info (1), info (66), $ (info (41) * info (4)) / 2**20, $ (info (42) * info (4)) / 2**20, $ info (43), info (44), info (45) 90 format ('numeric factorization:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, /, $ ' actual numeric LU statistics:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4num error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4num: ', info (1) stop endif c save the symbolic analysis to the file s0.umf c note that this is not needed until another matrix is c factorized, below. filenum = 0 call umf4ssym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4ssym: ', status stop endif c save the LU factors to the file n0.umf call umf4snum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4snum: ', status stop endif c free the symbolic analysis call umf4fsym (symbolic) c free the numeric factorization call umf4fnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c ---------------------------------------------------------------- c load the LU factors back in, and solve the system c ---------------------------------------------------------------- c At this point the program could terminate and load the LU C factors (numeric) from the n0.umf file, and solve the c system (see below). Note that the symbolic object is not c required. c load the numeric factorization back in (filename: n0.umf) call umf4lnum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4lnum: ', status stop endif c solve Ax=b, without iterative refinement sys = 0 call umf4sol (sys, x, b, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c free the numeric factorization call umf4fnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c print final statistics call umf4pinf (control, info) c print the residual. x (i) should be 1 + i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) c ---------------------------------------------------------------- c load the symbolic analysis back in, and factorize a new matrix c ---------------------------------------------------------------- c Again, the program could terminate here, recreate the matrix, c and refactorize. Note that umf4sym is not called. c load the symbolic factorization back in (filename: s0.umf) call umf4lsym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4lsym: ', status stop endif c arbitrarily change the values of the matrix but not the pattern do 100 p = 1, nz Ax (p) = Ax (p) + 3.14159 / 100.0 100 continue c numeric factorization of the modified matrix call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4num: ', info (1) stop endif c free the symbolic analysis call umf4fsym (symbolic) c create a new right-hand-side, assume x (i) = 7 - i/n do 110 i = 1,n b (i) = 0 110 continue c b = A*x, with the modified matrix A (note that A is now 0-based) do 130 j = 1,n xj = j xj = 7 - xj / n do 120 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = Ax (p) b (i) = b (i) + aij * xj 120 continue 130 continue c ---------------------------------------------------------------- c solve Ax=b, with iterative refinement c ---------------------------------------------------------------- sys = 0 call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4solr: ', info (1) stop endif c print the residual. x (i) should be 7 - i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) c ---------------------------------------------------------------- c solve Ax=b, without iterative refinement, broken into steps c ---------------------------------------------------------------- c the factorization is PAQ=LU, PRAQ=LU, or P(R\A)Q=LU. c x = R*b (or x=R\b, or x=b, as appropriate) call umf4scal (x, b, numeric, status) if (status .lt. 0) then print *, 'Error occurred in umf4scal: ', status stop endif c solve P'Lr=x for r (using r as workspace) sys = 3 call umf4sol (sys, r, x, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c solve UQ'x=r for x sys = 9 call umf4sol (sys, x, r, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c free the numeric factorization call umf4fnum (numeric) c print the residual. x (i) should be 7 - i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) stop 998 print *, 'Read error: Harwell/Boeing matrix' stop end c======================================================================= c== resid ============================================================== c======================================================================= c Compute the residual, r = Ax-b, its max-norm, and print the max-norm C Note that A is zero-based. subroutine resid (n, nz, Ap, Ai, Ax, x, b, r) integer*8 $ n, nz, Ap (n+1), Ai (n), j, i, p double precision Ax (nz), x (n), b (n), r (n), rmax, aij do 10 i = 1, n r (i) = -b (i) 10 continue do 30 j = 1,n do 20 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = Ax (p) r (i) = r (i) + aij * x (j) 20 continue 30 continue rmax = 0 do 40 i = 1, n rmax = max (rmax, r (i)) 40 continue print *, 'norm (A*x-b): ', rmax return end