Actual source code: ex1f.F
1: ! "$Id: ex1f.F,v 1.56 2001/08/10 16:48:34 balay Exp $";
2: !
3: ! Description: This example solves a nonlinear system on 1 processor with SNES.
4: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
5: ! domain. The command line options include:
6: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
7: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
8: ! -mx <xg>, where <xg> = number of grid points in the x-direction
9: ! -my <yg>, where <yg> = number of grid points in the y-direction
10: !
11: !/*T
12: ! Concepts: SNES^sequential Bratu example
13: ! Processors: 1
14: !T*/
15: !
16: ! --------------------------------------------------------------------------
17: !
18: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
19: ! the partial differential equation
20: !
21: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
22: !
23: ! with boundary conditions
24: !
25: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
26: !
27: ! A finite difference approximation with the usual 5-point stencil
28: ! is used to discretize the boundary value problem to obtain a nonlinear
29: ! system of equations.
30: !
31: ! The parallel version of this code is snes/examples/tutorials/ex5f.F
32: !
33: ! --------------------------------------------------------------------------
35: program main
36: implicit none
38: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
39: ! Include files
40: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: !
42: ! The following include statements are generally used in SNES Fortran
43: ! programs:
44: ! petsc.h - base PETSc routines
45: ! petscvec.h - vectors
46: ! petscmat.h - matrices
47: ! petscksp.h - Krylov subspace methods
48: ! petscpc.h - preconditioners
49: ! petscsnes.h - SNES interface
50: ! In addition, we need the following for use of PETSc drawing routines
51: ! petscdraw.h - drawing routines
52: ! Other include statements may be needed if using additional PETSc
53: ! routines in a Fortran program, e.g.,
54: ! petscviewer.h - viewers
55: ! petscis.h - index sets
56: !
57: #include include/finclude/petsc.h
58: #include include/finclude/petscvec.h
59: #include include/finclude/petscis.h
60: #include include/finclude/petscdraw.h
61: #include include/finclude/petscmat.h
62: #include include/finclude/petscksp.h
63: #include include/finclude/petscpc.h
64: #include include/finclude/petscsnes.h
65: !
66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: ! Variable declarations
68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
69: !
70: ! Variables:
71: ! snes - nonlinear solver
72: ! x, r - solution, residual vectors
73: ! J - Jacobian matrix
74: ! its - iterations for convergence
75: ! matrix_free - flag - 1 indicates matrix-free version
76: ! lambda - nonlinearity parameter
77: ! draw - drawing context
78: !
79: SNES snes
80: Vec x,r
81: PetscDraw draw
82: Mat J
83: integer its,matrix_free,flg,N,ierr
84: integer mx,my,size,rank
85: integer fd_coloring
86: PetscReal lambda_max,lambda_min,lambda
87: MatFDColoring fdcoloring
88: ISColoring iscoloring
89: MatStructure str
90:
91: PetscScalar lx_v(0:1)
92: PetscOffset lx_i
94: ! Store parameters in common block
96: common /params/ lambda,mx,my
98: ! Note: Any user-defined Fortran routines (such as FormJacobian)
99: ! MUST be declared as external.
101: external FormFunction,FormInitialGuess,FormJacobian
103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: ! Initialize program
105: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
108: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
109: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
111: if (size .ne. 1) then
112: if (rank .eq. 0) then
113: write(6,*) 'This is a uniprocessor example only!'
114: endif
115: SETERRQ(1,' ',ierr)
116: endif
118: ! Initialize problem parameters
120: lambda_max = 6.81
121: lambda_min = 0.0
122: lambda = 6.0
123: mx = 4
124: my = 4
125: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr)
126: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-my',my,flg,ierr)
127: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',lambda, &
128: & flg,ierr)
129: if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
130: if (rank .eq. 0) write(6,*) 'Lambda is out of range'
131: SETERRQ(1,' ',ierr)
132: endif
133: N = mx*my
135: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: ! Create nonlinear solver context
137: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
141: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: ! Create vector data structures; set function evaluation routine
143: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: call VecCreate(PETSC_COMM_WORLD,x,ierr)
146: call VecSetSizes(x,PETSC_DECIDE,N,ierr)
147: call VecSetFromOptions(x,ierr)
148: call VecDuplicate(x,r,ierr)
150: ! Set function evaluation routine and vector. Whenever the nonlinear
151: ! solver needs to evaluate the nonlinear function, it will call this
152: ! routine.
153: ! - Note that the final routine argument is the user-defined
154: ! context that provides application-specific data for the
155: ! function evaluation routine.
157: call SNESSetFunction(snes,r,FormFunction,PETSC_NULL_OBJECT,ierr)
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Create matrix data structure; set Jacobian evaluation routine
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: ! Create matrix. Here we only approximately preallocate storage space
164: ! for the Jacobian. See the users manual for a discussion of better
165: ! techniques for preallocating matrix memory.
167: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
168: & matrix_free,ierr)
169: if (matrix_free .eq. 0) then
170: call MatCreateSeqAIJ(PETSC_COMM_WORLD,N,N,5,PETSC_NULL_INTEGER, &
171: & J,ierr)
172: endif
174: !
175: ! This option will cause the Jacobian to be computed via finite differences
176: ! efficiently using a coloring of the columns of the matrix.
177: !
178: fd_coloring = 0
179: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_fd_coloring', &
180: & fd_coloring,ierr)
181: if (fd_coloring .eq. 1) then
182:
183: !
184: ! This initializes the nonzero structure of the Jacobian. This is artificial
185: ! because clearly if we had a routine to compute the Jacobian we won't need
186: ! to use finite differences.
187: !
188: call FormJacobian(snes,x,J,J,str,0,ierr)
189: !
190: ! Color the matrix, i.e. determine groups of columns that share no common
191: ! rows. These columns in the Jacobian can all be computed simulataneously.
192: !
193: call MatGetColoring(J,MATCOLORING_NATURAL,iscoloring,ierr)
194:
195: !
196: ! Create the data structure that SNESDefaultComputeJacobianColor() uses
197: ! to compute the actual Jacobians via finite differences.
198: !
199: call MatFDColoringCreate(J,iscoloring,fdcoloring,ierr)
200: call MatFDColoringSetFunctionSNES(fdcoloring,FormFunction, &
201: & PETSC_NULL_OBJECT,ierr)
202: call MatFDColoringSetFromOptions(fdcoloring,ierr)
203: !
204: ! Tell SNES to use the routine SNESDefaultComputeJacobianColor()
205: ! to compute Jacobians.
206: !
207: call SNESSetJacobian(snes,J,J,SNESDefaultComputeJacobianColor, &
208: & fdcoloring,ierr)
209: call ISColoringDestroy(iscoloring,ierr)
211: else if (matrix_free .eq. 0) then
213: ! Set Jacobian matrix data structure and default Jacobian evaluation
214: ! routine. Whenever the nonlinear solver needs to compute the
215: ! Jacobian matrix, it will call this routine.
216: ! - Note that the final routine argument is the user-defined
217: ! context that provides application-specific data for the
218: ! Jacobian evaluation routine.
219: ! - The user can override with:
220: ! -snes_fd : default finite differencing approximation of Jacobian
221: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
222: ! (unless user explicitly sets preconditioner)
223: ! -snes_mf_operator : form preconditioning matrix as set by the user,
224: ! but use matrix-free approx for Jacobian-vector
225: ! products within Newton-Krylov method
226: !
227: call SNESSetJacobian(snes,J,J,FormJacobian,PETSC_NULL_OBJECT, &
228: & ierr)
229: endif
231: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
232: ! Customize nonlinear solver; set runtime options
233: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
235: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
237: call SNESSetFromOptions(snes,ierr)
239: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240: ! Evaluate initial guess; then solve nonlinear system.
241: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: ! Note: The user should initialize the vector, x, with the initial guess
244: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
245: ! to employ an initial guess of zero, the user should explicitly set
246: ! this vector to zero by calling VecSet().
248: call FormInitialGuess(x,ierr)
249: call SNESSolve(snes,x,ierr)
250: call SNESGetIterationNumber(snes,its,ierr);
251: if (rank .eq. 0) then
252: write(6,100) its
253: endif
254: 100 format('Number of Newton iterations = ',i1)
256: ! PetscDraw contour plot of solution
258: ! call PetscDrawOpenX(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,'Solution',
259: ! 300,0,300,300,draw,ierr)
260: call PetscDrawCreate(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER, &
261: & 'Solution',300,0,300,300,draw,ierr)
262: call PetscDrawSetType(draw,PETSC_DRAW_X,ierr)
264: call VecGetArray(x,lx_v,lx_i,ierr)
265: call PetscDrawTensorContour(draw,mx,my,PETSC_NULL_DOUBLE, &
266: & PETSC_NULL_DOUBLE,lx_v(lx_i+1),ierr)
267: call VecRestoreArray(x,lx_v,lx_i,ierr)
269: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
270: ! Free work space. All PETSc objects should be destroyed when they
271: ! are no longer needed.
272: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
274: if (matrix_free .eq. 0) call MatDestroy(J,ierr)
275: if (fd_coloring .ne. 0) call MatFDColoringDestroy(fdcoloring,ierr)
277: call VecDestroy(x,ierr)
278: call VecDestroy(r,ierr)
279: call SNESDestroy(snes,ierr)
280: call PetscDrawDestroy(draw,ierr)
281: call PetscFinalize(ierr)
282: end
284: ! ---------------------------------------------------------------------
285: !
286: ! FormInitialGuess - Forms initial approximation.
287: !
288: ! Input Parameter:
289: ! X - vector
290: !
291: ! Output Parameters:
292: ! X - vector
293: ! ierr - error code
294: !
295: ! Notes:
296: ! This routine serves as a wrapper for the lower-level routine
297: ! "ApplicationInitialGuess", where the actual computations are
298: ! done using the standard Fortran style of treating the local
299: ! vector data as a multidimensional array over the local mesh.
300: ! This routine merely accesses the local vector data via
301: ! VecGetArray() and VecRestoreArray().
302: !
303: subroutine FormInitialGuess(X,ierr)
304: implicit none
306: #include include/finclude/petsc.h
307: #include include/finclude/petscvec.h
308: #include include/finclude/petscmat.h
309: #include include/finclude/petscsnes.h
311: ! Input/output variables:
312: Vec X
313: integer ierr
315: ! Declarations for use with local arrays:
316: PetscScalar lx_v(0:1)
317: PetscOffset lx_i
319: 0
321: ! Get a pointer to vector data.
322: ! - For default PETSc vectors, VecGetArray() returns a pointer to
323: ! the data array. Otherwise, the routine is implementation dependent.
324: ! - You MUST call VecRestoreArray() when you no longer need access to
325: ! the array.
326: ! - Note that the Fortran interface to VecGetArray() differs from the
327: ! C version. See the users manual for details.
329: call VecGetArray(X,lx_v,lx_i,ierr)
331: ! Compute initial guess
333: call ApplicationInitialGuess(lx_v(lx_i),ierr)
335: ! Restore vector
337: call VecRestoreArray(X,lx_v,lx_i,ierr)
339: return
340: end
342: ! ---------------------------------------------------------------------
343: !
344: ! ApplicationInitialGuess - Computes initial approximation, called by
345: ! the higher level routine FormInitialGuess().
346: !
347: ! Input Parameter:
348: ! x - local vector data
349: !
350: ! Output Parameters:
351: ! f - local vector data, f(x)
352: ! ierr - error code
353: !
354: ! Notes:
355: ! This routine uses standard Fortran-style computations over a 2-dim array.
356: !
357: subroutine ApplicationInitialGuess(x,ierr)
359: implicit none
361: ! Common blocks:
362: PetscReal lambda
363: integer mx,my
364: common /params/ lambda,mx,my
366: ! Input/output variables:
367: PetscScalar x(mx,my)
368: integer ierr
370: ! Local variables:
371: integer i,j,hxdhy,hydhx
372: PetscScalar temp1,temp,hx,hy,sc,one
374: ! Set parameters
376: 0
377: one = 1.0
378: hx = one/(dble(mx-1))
379: hy = one/(dble(my-1))
380: sc = hx*hy*lambda
381: hxdhy = hx/hy
382: hydhx = hy/hx
383: temp1 = lambda/(lambda + one)
385: do 20 j=1,my
386: temp = dble(min(j-1,my-j))*hy
387: do 10 i=1,mx
388: if (i .eq. 1 .or. j .eq. 1 &
389: & .or. i .eq. mx .or. j .eq. my) then
390: x(i,j) = 0.0
391: else
392: x(i,j) = temp1 * &
393: & sqrt(min(dble(min(i-1,mx-i)*hx),dble(temp)))
394: endif
395: 10 continue
396: 20 continue
398: return
399: end
401: ! ---------------------------------------------------------------------
402: !
403: ! FormFunction - Evaluates nonlinear function, F(x).
404: !
405: ! Input Parameters:
406: ! snes - the SNES context
407: ! X - input vector
408: ! dummy - optional user-defined context, as set by SNESSetFunction()
409: ! (not used here)
410: !
411: ! Output Parameter:
412: ! F - vector with newly computed function
413: !
414: ! Notes:
415: ! This routine serves as a wrapper for the lower-level routine
416: ! "ApplicationFunction", where the actual computations are
417: ! done using the standard Fortran style of treating the local
418: ! vector data as a multidimensional array over the local mesh.
419: ! This routine merely accesses the local vector data via
420: ! VecGetArray() and VecRestoreArray().
421: !
422: subroutine FormFunction(snes,X,F,dummy,ierr)
423: implicit none
425: #include include/finclude/petsc.h
426: #include include/finclude/petscvec.h
427: #include include/finclude/petscsnes.h
429: ! Input/output variables:
430: SNES snes
431: Vec X,F
432: PetscFortranAddr dummy
433: integer ierr
435: ! Common blocks:
436: PetscReal lambda
437: integer mx,my
438: common /params/ lambda,mx,my
440: ! Declarations for use with local arrays:
441: PetscScalar lx_v(0:1),lf_v(0:1)
442: PetscOffset lx_i,lf_i
444: ! Get pointers to vector data.
445: ! - For default PETSc vectors, VecGetArray() returns a pointer to
446: ! the data array. Otherwise, the routine is implementation dependent.
447: ! - You MUST call VecRestoreArray() when you no longer need access to
448: ! the array.
449: ! - Note that the Fortran interface to VecGetArray() differs from the
450: ! C version. See the Fortran chapter of the users manual for details.
452: call VecGetArray(X,lx_v,lx_i,ierr)
453: call VecGetArray(F,lf_v,lf_i,ierr)
455: ! Compute function
457: call ApplicationFunction(lx_v(lx_i),lf_v(lf_i),ierr)
459: ! Restore vectors
461: call VecRestoreArray(X,lx_v,lx_i,ierr)
462: call VecRestoreArray(F,lf_v,lf_i,ierr)
464: call PetscLogFlops(11*mx*my,ierr)
466: return
467: end
469: ! ---------------------------------------------------------------------
470: !
471: ! ApplicationFunction - Computes nonlinear function, called by
472: ! the higher level routine FormFunction().
473: !
474: ! Input Parameter:
475: ! x - local vector data
476: !
477: ! Output Parameters:
478: ! f - local vector data, f(x)
479: ! ierr - error code
480: !
481: ! Notes:
482: ! This routine uses standard Fortran-style computations over a 2-dim array.
483: !
484: subroutine ApplicationFunction(x,f,ierr)
486: implicit none
488: ! Common blocks:
489: PetscReal lambda
490: integer mx,my
491: common /params/ lambda,mx,my
493: ! Input/output variables:
494: PetscScalar x(mx,my),f(mx,my)
495: integer ierr
497: ! Local variables:
498: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
499: PetscScalar u,uxx,uyy
500: integer i,j
502: 0
503: one = 1.0
504: two = 2.0
505: hx = one/dble(mx-1)
506: hy = one/dble(my-1)
507: sc = hx*hy*lambda
508: hxdhy = hx/hy
509: hydhx = hy/hx
511: ! Compute function
513: do 20 j=1,my
514: do 10 i=1,mx
515: if (i .eq. 1 .or. j .eq. 1 &
516: & .or. i .eq. mx .or. j .eq. my) then
517: f(i,j) = x(i,j)
518: else
519: u = x(i,j)
520: uxx = hydhx * (two*u &
521: & - x(i-1,j) - x(i+1,j))
522: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
523: f(i,j) = uxx + uyy - sc*exp(u)
524: endif
525: 10 continue
526: 20 continue
528: return
529: end
531: ! ---------------------------------------------------------------------
532: !
533: ! FormJacobian - Evaluates Jacobian matrix.
534: !
535: ! Input Parameters:
536: ! snes - the SNES context
537: ! x - input vector
538: ! dummy - optional user-defined context, as set by SNESSetJacobian()
539: ! (not used here)
540: !
541: ! Output Parameters:
542: ! jac - Jacobian matrix
543: ! jac_prec - optionally different preconditioning matrix (not used here)
544: ! flag - flag indicating matrix structure
545: !
546: ! Notes:
547: ! This routine serves as a wrapper for the lower-level routine
548: ! "ApplicationJacobian", where the actual computations are
549: ! done using the standard Fortran style of treating the local
550: ! vector data as a multidimensional array over the local mesh.
551: ! This routine merely accesses the local vector data via
552: ! VecGetArray() and VecRestoreArray().
553: !
554: subroutine FormJacobian(snes,X,jac,jac_prec,flag,dummy,ierr)
555: implicit none
557: #include include/finclude/petsc.h
558: #include include/finclude/petscvec.h
559: #include include/finclude/petscmat.h
560: #include include/finclude/petscpc.h
561: #include include/finclude/petscsnes.h
563: ! Input/output variables:
564: SNES snes
565: Vec X
566: Mat jac,jac_prec
567: MatStructure flag
568: integer dummy,ierr
570: ! Common blocks:
571: PetscReal lambda
572: integer mx,my
573: common /params/ lambda,mx,my
575: ! Declarations for use with local array:
576: PetscScalar lx_v(0:1)
577: PetscOffset lx_i
579: ! Get a pointer to vector data
581: call VecGetArray(X,lx_v,lx_i,ierr)
583: ! Compute Jacobian entries
585: call ApplicationJacobian(lx_v(lx_i),jac,jac_prec,ierr)
587: ! Restore vector
589: call VecRestoreArray(X,lx_v,lx_i,ierr)
591: ! Assemble matrix
593: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
594: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
596: ! Set flag to indicate that the Jacobian matrix retains an identical
597: ! nonzero structure throughout all nonlinear iterations (although the
598: ! values of the entries change). Thus, we can save some work in setting
599: ! up the preconditioner (e.g., no need to redo symbolic factorization for
600: ! ILU/ICC preconditioners).
601: ! - If the nonzero structure of the matrix is different during
602: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
603: ! must be used instead. If you are unsure whether the matrix
604: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
605: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
606: ! believes your assertion and does not check the structure
607: ! of the matrix. If you erroneously claim that the structure
608: ! is the same when it actually is not, the new preconditioner
609: ! will not function correctly. Thus, use this optimization
610: ! feature with caution!
612: flag = SAME_NONZERO_PATTERN
614: return
615: end
617: ! ---------------------------------------------------------------------
618: !
619: ! ApplicationJacobian - Computes Jacobian matrix, called by
620: ! the higher level routine FormJacobian().
621: !
622: ! Input Parameters:
623: ! x - local vector data
624: !
625: ! Output Parameters:
626: ! jac - Jacobian matrix
627: ! jac_prec - optionally different preconditioning matrix (not used here)
628: ! ierr - error code
629: !
630: ! Notes:
631: ! This routine uses standard Fortran-style computations over a 2-dim array.
632: !
633: subroutine ApplicationJacobian(x,jac,jac_prec,ierr)
634: implicit none
636: #include include/finclude/petsc.h
637: #include include/finclude/petscvec.h
638: #include include/finclude/petscmat.h
639: #include include/finclude/petscpc.h
640: #include include/finclude/petscsnes.h
642: ! Common blocks:
643: PetscReal lambda
644: integer mx,my
645: common /params/ lambda,mx,my
647: ! Input/output variables:
648: PetscScalar x(mx,my)
649: Mat jac,jac_prec
650: integer ierr
652: ! Local variables:
653: integer i,j,row,col(5)
654: PetscScalar two,one, hx,hy,hxdhy,hydhx,sc,v(5)
656: ! Set parameters
658: one = 1.0
659: two = 2.0
660: hx = one/dble(mx-1)
661: hy = one/dble(my-1)
662: sc = hx*hy
663: hxdhy = hx/hy
664: hydhx = hy/hx
666: ! Compute entries of the Jacobian matrix
667: ! - Here, we set all entries for a particular row at once.
668: ! - Note that MatSetValues() uses 0-based row and column numbers
669: ! in Fortran as well as in C.
671: do 20 j=1,my
672: row = (j-1)*mx - 1
673: do 10 i=1,mx
674: row = row + 1
675: ! boundary points
676: if (i .eq. 1 .or. j .eq. 1 &
677: & .or. i .eq. mx .or. j .eq. my) then
678: call MatSetValues(jac_prec,1,row,1,row,one, &
679: & INSERT_VALUES,ierr)
680: ! interior grid points
681: else
682: v(1) = -hxdhy
683: v(2) = -hydhx
684: v(3) = two*(hydhx + hxdhy) &
685: & - sc*lambda*exp(x(i,j))
686: v(4) = -hydhx
687: v(5) = -hxdhy
688: col(1) = row - mx
689: col(2) = row - 1
690: col(3) = row
691: col(4) = row + 1
692: col(5) = row + mx
693: call MatSetValues(jac_prec,1,row,5,col,v, &
694: & INSERT_VALUES,ierr)
695: endif
696: 10 continue
697: 20 continue
699: return
700: end