Actual source code: ex1f.F
petsc-3.7.1 2016-05-15
1: !
2: ! Description: This example solves a nonlinear system on 1 processor with SNES.
3: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
4: ! domain. The command line options include:
5: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
6: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
7: ! -mx <xg>, where <xg> = number of grid points in the x-direction
8: ! -my <yg>, where <yg> = number of grid points in the y-direction
9: !
10: !/*T
11: ! Concepts: SNES^sequential Bratu example
12: ! Processors: 1
13: !T*/
14: !
15: ! --------------------------------------------------------------------------
16: !
17: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
18: ! the partial differential equation
19: !
20: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
21: !
22: ! with boundary conditions
23: !
24: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
25: !
26: ! A finite difference approximation with the usual 5-point stencil
27: ! is used to discretize the boundary value problem to obtain a nonlinear
28: ! system of equations.
29: !
30: ! The parallel version of this code is snes/examples/tutorials/ex5f.F
31: !
32: ! --------------------------------------------------------------------------
34: program main
35: implicit none
37: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
38: ! Include files
39: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: !
41: ! The following include statements are generally used in SNES Fortran
42: ! programs:
43: ! petscsys.h - base PETSc routines
44: ! petscvec.h - vectors
45: ! petscmat.h - matrices
46: ! petscksp.h - Krylov subspace methods
47: ! petscpc.h - preconditioners
48: ! petscsnes.h - SNES interface
49: ! In addition, we need the following for use of PETSc drawing routines
50: ! petscdraw.h - drawing routines
51: ! Other include statements may be needed if using additional PETSc
52: ! routines in a Fortran program, e.g.,
53: ! petscviewer.h - viewers
54: ! petscis.h - index sets
55: !
56: #include <petsc/finclude/petscsys.h>
57: #include <petsc/finclude/petscvec.h>
58: #include <petsc/finclude/petscis.h>
59: #include <petsc/finclude/petscdraw.h>
60: #include <petsc/finclude/petscmat.h>
61: #include <petsc/finclude/petscksp.h>
62: #include <petsc/finclude/petscpc.h>
63: #include <petsc/finclude/petscsnes.h>
64: !
65: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
66: ! Variable declarations
67: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
68: !
69: ! Variables:
70: ! snes - nonlinear solver
71: ! x, r - solution, residual vectors
72: ! J - Jacobian matrix
73: ! its - iterations for convergence
74: ! matrix_free - flag - 1 indicates matrix-free version
75: ! lambda - nonlinearity parameter
76: ! draw - drawing context
77: !
78: SNES snes
79: MatColoring mc
80: Vec x,r
81: PetscDraw draw
82: Mat J
83: PetscBool matrix_free,flg,fd_coloring
84: PetscErrorCode ierr
85: PetscInt its,N, mx,my,i5
86: PetscMPIInt size,rank
87: PetscReal lambda_max,lambda_min,lambda
88: MatFDColoring fdcoloring
89: ISColoring iscoloring
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(PETSC_COMM_SELF,1,' ',ierr)
116: endif
118: ! Initialize problem parameters
119: i5 = 5
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_OBJECT,PETSC_NULL_CHARACTER, &
126: & '-mx',mx,flg,ierr)
127: call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER, &
128: & '-my',my,flg,ierr)
129: call PetscOptionsGetReal(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER, &
130: & '-par',lambda,flg,ierr)
131: if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
132: if (rank .eq. 0) write(6,*) 'Lambda is out of range'
133: SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
134: endif
135: N = mx*my
137: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138: ! Create nonlinear solver context
139: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
143: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: ! Create vector data structures; set function evaluation routine
145: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: call VecCreate(PETSC_COMM_WORLD,x,ierr)
148: call VecSetSizes(x,PETSC_DECIDE,N,ierr)
149: call VecSetFromOptions(x,ierr)
150: call VecDuplicate(x,r,ierr)
152: ! Set function evaluation routine and vector. Whenever the nonlinear
153: ! solver needs to evaluate the nonlinear function, it will call this
154: ! routine.
155: ! - Note that the final routine argument is the user-defined
156: ! context that provides application-specific data for the
157: ! function evaluation routine.
159: call SNESSetFunction(snes,r,FormFunction,PETSC_NULL_OBJECT,ierr)
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: ! Create matrix data structure; set Jacobian evaluation routine
163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: ! Create matrix. Here we only approximately preallocate storage space
166: ! for the Jacobian. See the users manual for a discussion of better
167: ! techniques for preallocating matrix memory.
169: call PetscOptionsHasName(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER, &
170: & '-snes_mf',matrix_free,ierr)
171: if (.not. matrix_free) then
172: call MatCreateSeqAIJ(PETSC_COMM_WORLD,N,N,i5,PETSC_NULL_INTEGER, &
173: & J,ierr)
174: endif
176: !
177: ! This option will cause the Jacobian to be computed via finite differences
178: ! efficiently using a coloring of the columns of the matrix.
179: !
180: fd_coloring = .false.
181: call PetscOptionsHasName(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER, &
182: & '-snes_fd_coloring',fd_coloring,ierr)
183: if (fd_coloring) then
185: !
186: ! This initializes the nonzero structure of the Jacobian. This is artificial
187: ! because clearly if we had a routine to compute the Jacobian we won't need
188: ! to use finite differences.
189: !
190: call FormJacobian(snes,x,J,J,0,ierr)
191: !
192: ! Color the matrix, i.e. determine groups of columns that share no common
193: ! rows. These columns in the Jacobian can all be computed simulataneously.
194: !
195: call MatColoringCreate(J,mc,ierr)
196: call MatColoringSetType(mc,MATCOLORINGNATURAL,ierr)
197: call MatColoringSetFromOptions(mc,ierr)
198: call MatColoringApply(mc,iscoloring,ierr)
199: call MatColoringDestroy(mc,ierr)
200: !
201: ! Create the data structure that SNESComputeJacobianDefaultColor() uses
202: ! to compute the actual Jacobians via finite differences.
203: !
204: call MatFDColoringCreate(J,iscoloring,fdcoloring,ierr)
205: call MatFDColoringSetFunction(fdcoloring,FormFunction, &
206: & PETSC_NULL_OBJECT,ierr)
207: call MatFDColoringSetFromOptions(fdcoloring,ierr)
208: call MatFDColoringSetUp(J,iscoloring,fdcoloring,ierr)
209: !
210: ! Tell SNES to use the routine SNESComputeJacobianDefaultColor()
211: ! to compute Jacobians.
212: !
213: call SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor, &
214: & fdcoloring,ierr)
215: call ISColoringDestroy(iscoloring,ierr)
217: else if (.not. matrix_free) then
219: ! Set Jacobian matrix data structure and default Jacobian evaluation
220: ! routine. Whenever the nonlinear solver needs to compute the
221: ! Jacobian matrix, it will call this routine.
222: ! - Note that the final routine argument is the user-defined
223: ! context that provides application-specific data for the
224: ! Jacobian evaluation routine.
225: ! - The user can override with:
226: ! -snes_fd : default finite differencing approximation of Jacobian
227: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
228: ! (unless user explicitly sets preconditioner)
229: ! -snes_mf_operator : form preconditioning matrix as set by the user,
230: ! but use matrix-free approx for Jacobian-vector
231: ! products within Newton-Krylov method
232: !
233: call SNESSetJacobian(snes,J,J,FormJacobian,PETSC_NULL_OBJECT, &
234: & ierr)
235: endif
237: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
238: ! Customize nonlinear solver; set runtime options
239: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
241: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
243: call SNESSetFromOptions(snes,ierr)
245: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
246: ! Evaluate initial guess; then solve nonlinear system.
247: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
249: ! Note: The user should initialize the vector, x, with the initial guess
250: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
251: ! to employ an initial guess of zero, the user should explicitly set
252: ! this vector to zero by calling VecSet().
254: call FormInitialGuess(x,ierr)
255: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
256: call SNESGetIterationNumber(snes,its,ierr);
257: if (rank .eq. 0) then
258: write(6,100) its
259: endif
260: 100 format('Number of SNES iterations = ',i1)
262: ! PetscDraw contour plot of solution
264: call PetscDrawCreate(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER, &
265: & 'Solution',300,0,300,300,draw,ierr)
266: call PetscDrawSetFromOptions(draw,ierr)
268: call VecGetArrayRead(x,lx_v,lx_i,ierr)
269: call PetscDrawTensorContour(draw,mx,my,PETSC_NULL_REAL, &
270: & PETSC_NULL_REAL,lx_v(lx_i+1),ierr)
271: call VecRestoreArrayRead(x,lx_v,lx_i,ierr)
273: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
274: ! Free work space. All PETSc objects should be destroyed when they
275: ! are no longer needed.
276: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
278: if (.not. matrix_free) call MatDestroy(J,ierr)
279: if (fd_coloring) call MatFDColoringDestroy(fdcoloring,ierr)
281: call VecDestroy(x,ierr)
282: call VecDestroy(r,ierr)
283: call SNESDestroy(snes,ierr)
284: call PetscDrawDestroy(draw,ierr)
285: call PetscFinalize(ierr)
286: end
288: ! ---------------------------------------------------------------------
289: !
290: ! FormInitialGuess - Forms initial approximation.
291: !
292: ! Input Parameter:
293: ! X - vector
294: !
295: ! Output Parameters:
296: ! X - vector
297: ! ierr - error code
298: !
299: ! Notes:
300: ! This routine serves as a wrapper for the lower-level routine
301: ! "ApplicationInitialGuess", where the actual computations are
302: ! done using the standard Fortran style of treating the local
303: ! vector data as a multidimensional array over the local mesh.
304: ! This routine merely accesses the local vector data via
305: ! VecGetArray() and VecRestoreArray().
306: !
307: subroutine FormInitialGuess(X,ierr)
308: implicit none
310: #include <petsc/finclude/petscsys.h>
311: #include <petsc/finclude/petscvec.h>
312: #include <petsc/finclude/petscmat.h>
313: #include <petsc/finclude/petscsnes.h>
315: ! Input/output variables:
316: Vec X
317: PetscErrorCode ierr
319: ! Declarations for use with local arrays:
320: PetscScalar lx_v(0:1)
321: PetscOffset lx_i
323: 0
325: ! Get a pointer to vector data.
326: ! - For default PETSc vectors, VecGetArray() returns a pointer to
327: ! the data array. Otherwise, the routine is implementation dependent.
328: ! - You MUST call VecRestoreArray() when you no longer need access to
329: ! the array.
330: ! - Note that the Fortran interface to VecGetArray() differs from the
331: ! C version. See the users manual for details.
333: call VecGetArray(X,lx_v,lx_i,ierr)
335: ! Compute initial guess
337: call ApplicationInitialGuess(lx_v(lx_i),ierr)
339: ! Restore vector
341: call VecRestoreArray(X,lx_v,lx_i,ierr)
343: return
344: end
346: ! ---------------------------------------------------------------------
347: !
348: ! ApplicationInitialGuess - Computes initial approximation, called by
349: ! the higher level routine FormInitialGuess().
350: !
351: ! Input Parameter:
352: ! x - local vector data
353: !
354: ! Output Parameters:
355: ! f - local vector data, f(x)
356: ! ierr - error code
357: !
358: ! Notes:
359: ! This routine uses standard Fortran-style computations over a 2-dim array.
360: !
361: subroutine ApplicationInitialGuess(x,ierr)
363: implicit none
365: ! Common blocks:
366: PetscReal lambda
367: PetscInt mx,my
368: common /params/ lambda,mx,my
370: ! Input/output variables:
371: PetscScalar x(mx,my)
372: PetscErrorCode ierr
374: ! Local variables:
375: PetscInt i,j
376: PetscReal temp1,temp,hx,hy,one
378: ! Set parameters
380: 0
381: one = 1.0
382: hx = one/(mx-1)
383: hy = one/(my-1)
384: temp1 = lambda/(lambda + one)
386: do 20 j=1,my
387: temp = min(j-1,my-j)*hy
388: do 10 i=1,mx
389: if (i .eq. 1 .or. j .eq. 1 &
390: & .or. i .eq. mx .or. j .eq. my) then
391: x(i,j) = 0.0
392: else
393: x(i,j) = temp1 * &
394: & sqrt(min(min(i-1,mx-i)*hx,temp))
395: endif
396: 10 continue
397: 20 continue
399: return
400: end
402: ! ---------------------------------------------------------------------
403: !
404: ! FormFunction - Evaluates nonlinear function, F(x).
405: !
406: ! Input Parameters:
407: ! snes - the SNES context
408: ! X - input vector
409: ! dummy - optional user-defined context, as set by SNESSetFunction()
410: ! (not used here)
411: !
412: ! Output Parameter:
413: ! F - vector with newly computed function
414: !
415: ! Notes:
416: ! This routine serves as a wrapper for the lower-level routine
417: ! "ApplicationFunction", where the actual computations are
418: ! done using the standard Fortran style of treating the local
419: ! vector data as a multidimensional array over the local mesh.
420: ! This routine merely accesses the local vector data via
421: ! VecGetArray() and VecRestoreArray().
422: !
423: subroutine FormFunction(snes,X,F,dummy,ierr)
424: implicit none
426: #include <petsc/finclude/petscsys.h>
427: #include <petsc/finclude/petscvec.h>
428: #include <petsc/finclude/petscsnes.h>
430: ! Input/output variables:
431: SNES snes
432: Vec X,F
433: PetscFortranAddr dummy
434: PetscErrorCode ierr
436: ! Common blocks:
437: PetscReal lambda
438: PetscInt mx,my
439: common /params/ lambda,mx,my
441: ! Declarations for use with local arrays:
442: PetscScalar lx_v(0:1),lf_v(0:1)
443: PetscOffset lx_i,lf_i
445: ! Get pointers to vector data.
446: ! - For default PETSc vectors, VecGetArray() returns a pointer to
447: ! the data array. Otherwise, the routine is implementation dependent.
448: ! - You MUST call VecRestoreArray() when you no longer need access to
449: ! the array.
450: ! - Note that the Fortran interface to VecGetArray() differs from the
451: ! C version. See the Fortran chapter of the users manual for details.
453: call VecGetArrayRead(X,lx_v,lx_i,ierr)
454: call VecGetArray(F,lf_v,lf_i,ierr)
456: ! Compute function
458: call ApplicationFunction(lx_v(lx_i),lf_v(lf_i),ierr)
460: ! Restore vectors
462: call VecRestoreArrayRead(X,lx_v,lx_i,ierr)
463: call VecRestoreArray(F,lf_v,lf_i,ierr)
465: call PetscLogFlops(11.0d0*mx*my,ierr)
467: return
468: end
470: ! ---------------------------------------------------------------------
471: !
472: ! ApplicationFunction - Computes nonlinear function, called by
473: ! the higher level routine FormFunction().
474: !
475: ! Input Parameter:
476: ! x - local vector data
477: !
478: ! Output Parameters:
479: ! f - local vector data, f(x)
480: ! ierr - error code
481: !
482: ! Notes:
483: ! This routine uses standard Fortran-style computations over a 2-dim array.
484: !
485: subroutine ApplicationFunction(x,f,ierr)
487: implicit none
489: ! Common blocks:
490: PetscReal lambda
491: PetscInt mx,my
492: common /params/ lambda,mx,my
494: ! Input/output variables:
495: PetscScalar x(mx,my),f(mx,my)
496: PetscErrorCode ierr
498: ! Local variables:
499: PetscScalar two,one,hx,hy
500: PetscScalar hxdhy,hydhx,sc
501: PetscScalar u,uxx,uyy
502: PetscInt i,j
504: 0
505: one = 1.0
506: two = 2.0
507: hx = one/(mx-1)
508: hy = one/(my-1)
509: sc = hx*hy*lambda
510: hxdhy = hx/hy
511: hydhx = hy/hx
513: ! Compute function
515: do 20 j=1,my
516: do 10 i=1,mx
517: if (i .eq. 1 .or. j .eq. 1 &
518: & .or. i .eq. mx .or. j .eq. my) then
519: f(i,j) = x(i,j)
520: else
521: u = x(i,j)
522: uxx = hydhx * (two*u &
523: & - x(i-1,j) - x(i+1,j))
524: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
525: f(i,j) = uxx + uyy - sc*exp(u)
526: endif
527: 10 continue
528: 20 continue
530: return
531: end
533: ! ---------------------------------------------------------------------
534: !
535: ! FormJacobian - Evaluates Jacobian matrix.
536: !
537: ! Input Parameters:
538: ! snes - the SNES context
539: ! x - input vector
540: ! dummy - optional user-defined context, as set by SNESSetJacobian()
541: ! (not used here)
542: !
543: ! Output Parameters:
544: ! jac - Jacobian matrix
545: ! jac_prec - optionally different preconditioning matrix (not used here)
546: ! flag - flag indicating matrix structure
547: !
548: ! Notes:
549: ! This routine serves as a wrapper for the lower-level routine
550: ! "ApplicationJacobian", where the actual computations are
551: ! done using the standard Fortran style of treating the local
552: ! vector data as a multidimensional array over the local mesh.
553: ! This routine merely accesses the local vector data via
554: ! VecGetArray() and VecRestoreArray().
555: !
556: subroutine FormJacobian(snes,X,jac,jac_prec,dummy,ierr)
557: implicit none
559: #include <petsc/finclude/petscsys.h>
560: #include <petsc/finclude/petscvec.h>
561: #include <petsc/finclude/petscmat.h>
562: #include <petsc/finclude/petscpc.h>
563: #include <petsc/finclude/petscsnes.h>
565: ! Input/output variables:
566: SNES snes
567: Vec X
568: Mat jac,jac_prec
569: PetscErrorCode ierr
570: integer dummy
572: ! Common blocks:
573: PetscReal lambda
574: PetscInt mx,my
575: common /params/ lambda,mx,my
577: ! Declarations for use with local array:
578: PetscScalar lx_v(0:1)
579: PetscOffset lx_i
581: ! Get a pointer to vector data
583: call VecGetArrayRead(X,lx_v,lx_i,ierr)
585: ! Compute Jacobian entries
587: call ApplicationJacobian(lx_v(lx_i),jac,jac_prec,ierr)
589: ! Restore vector
591: call VecRestoreArrayRead(X,lx_v,lx_i,ierr)
593: ! Assemble matrix
595: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
596: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
599: return
600: end
602: ! ---------------------------------------------------------------------
603: !
604: ! ApplicationJacobian - Computes Jacobian matrix, called by
605: ! the higher level routine FormJacobian().
606: !
607: ! Input Parameters:
608: ! x - local vector data
609: !
610: ! Output Parameters:
611: ! jac - Jacobian matrix
612: ! jac_prec - optionally different preconditioning matrix (not used here)
613: ! ierr - error code
614: !
615: ! Notes:
616: ! This routine uses standard Fortran-style computations over a 2-dim array.
617: !
618: subroutine ApplicationJacobian(x,jac,jac_prec,ierr)
619: implicit none
621: #include <petsc/finclude/petscsys.h>
622: #include <petsc/finclude/petscvec.h>
623: #include <petsc/finclude/petscmat.h>
624: #include <petsc/finclude/petscpc.h>
625: #include <petsc/finclude/petscsnes.h>
627: ! Common blocks:
628: PetscReal lambda
629: PetscInt mx,my
630: common /params/ lambda,mx,my
632: ! Input/output variables:
633: PetscScalar x(mx,my)
634: Mat jac,jac_prec
635: PetscErrorCode ierr
637: ! Local variables:
638: PetscInt i,j,row(1),col(5),i1,i5
639: PetscScalar two,one, hx,hy
640: PetscScalar hxdhy,hydhx,sc,v(5)
642: ! Set parameters
644: i1 = 1
645: i5 = 5
646: one = 1.0
647: two = 2.0
648: hx = one/(mx-1)
649: hy = one/(my-1)
650: sc = hx*hy
651: hxdhy = hx/hy
652: hydhx = hy/hx
654: ! Compute entries of the Jacobian matrix
655: ! - Here, we set all entries for a particular row at once.
656: ! - Note that MatSetValues() uses 0-based row and column numbers
657: ! in Fortran as well as in C.
659: do 20 j=1,my
660: row(1) = (j-1)*mx - 1
661: do 10 i=1,mx
662: row(1) = row(1) + 1
663: ! boundary points
664: if (i .eq. 1 .or. j .eq. 1 &
665: & .or. i .eq. mx .or. j .eq. my) then
666: call MatSetValues(jac_prec,i1,row,i1,row,one, &
667: & INSERT_VALUES,ierr)
668: ! interior grid points
669: else
670: v(1) = -hxdhy
671: v(2) = -hydhx
672: v(3) = two*(hydhx + hxdhy) &
673: & - sc*lambda*exp(x(i,j))
674: v(4) = -hydhx
675: v(5) = -hxdhy
676: col(1) = row(1) - mx
677: col(2) = row(1) - 1
678: col(3) = row(1)
679: col(4) = row(1) + 1
680: col(5) = row(1) + mx
681: call MatSetValues(jac_prec,i1,row,i5,col,v, &
682: & INSERT_VALUES,ierr)
683: endif
684: 10 continue
685: 20 continue
687: return
688: end