Blame view
fvn_sparse/UMFPACK/Demo/umf4hb64.f
11.9 KB
422234dc3
git-svn-id: https...
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 |
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
|