Actual source code: ex1f.F90
petsc-3.10.5 2019-03-28
1: !
2: ! Description: Solves a tridiagonal linear system with KSP.
3: !
4: !/*T
5: ! Concepts: KSP^solving a system of linear equations
6: ! Processors: 1
7: !T*/
8: ! -----------------------------------------------------------------------
10: program main
11: #include <petsc/finclude/petscksp.h>
12: use petscksp
13: implicit none
15: !
16: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
17: ! Variable declarations
18: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
19: !
20: ! Variables:
21: ! ksp - linear solver context
22: ! ksp - Krylov subspace method context
23: ! pc - preconditioner context
24: ! x, b, u - approx solution, right-hand-side, exact solution vectors
25: ! A - matrix that defines linear system
26: ! its - iterations for convergence
27: ! norm - norm of error in solution
28: !
29: Vec x,b,u
30: Mat A
31: KSP ksp
32: PC pc
33: PetscReal norm,tol
34: PetscErrorCode ierr
35: PetscInt i,n,col(3),its,i1,i2,i3
36: PetscBool flg
37: PetscMPIInt size
38: PetscScalar none,one,value(3)
40: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: ! Beginning of program
42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
45: if (ierr .ne. 0) then
46: print*,'Unable to initialize PETSc'
47: stop
48: endif
49: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
50: if (size .ne. 1) then; SETERRA(PETSC_COMM_WORLD,1,'This is a uniprocessor example only'); endif
51: none = -1.0
52: one = 1.0
53: n = 10
54: i1 = 1
55: i2 = 2
56: i3 = 3
57: call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
59: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: ! Compute the matrix and right-hand-side vector that define
61: ! the linear system, Ax = b.
62: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
64: ! Create matrix. When using MatCreate(), the matrix format can
65: ! be specified at runtime.
67: call MatCreate(PETSC_COMM_WORLD,A,ierr)
68: call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n,ierr)
69: call MatSetFromOptions(A,ierr)
70: call MatSetUp(A,ierr)
72: ! Assemble matrix.
73: ! - Note that MatSetValues() uses 0-based row and column numbers
74: ! in Fortran as well as in C (as set here in the array "col").
76: value(1) = -1.0
77: value(2) = 2.0
78: value(3) = -1.0
79: do 50 i=1,n-2
80: col(1) = i-1
81: col(2) = i
82: col(3) = i+1
83: call MatSetValues(A,i1,i,i3,col,value,INSERT_VALUES,ierr)
84: 50 continue
85: i = n - 1
86: col(1) = n - 2
87: col(2) = n - 1
88: call MatSetValues(A,i1,i,i2,col,value,INSERT_VALUES,ierr)
89: i = 0
90: col(1) = 0
91: col(2) = 1
92: value(1) = 2.0
93: value(2) = -1.0
94: call MatSetValues(A,i1,i,i2,col,value,INSERT_VALUES,ierr)
95: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
96: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
98: ! Create vectors. Note that we form 1 vector from scratch and
99: ! then duplicate as needed.
101: call VecCreate(PETSC_COMM_WORLD,x,ierr)
102: call VecSetSizes(x,PETSC_DECIDE,n,ierr)
103: call VecSetFromOptions(x,ierr)
104: call VecDuplicate(x,b,ierr)
105: call VecDuplicate(x,u,ierr)
107: ! Set exact solution; then compute right-hand-side vector.
109: call VecSet(u,one,ierr)
110: call MatMult(A,u,b,ierr)
112: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: ! Create the linear solver and set various options
114: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: ! Create linear solver context
118: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
120: ! Set operators. Here the matrix that defines the linear system
121: ! also serves as the preconditioning matrix.
123: call KSPSetOperators(ksp,A,A,ierr)
125: ! Set linear solver defaults for this problem (optional).
126: ! - By extracting the KSP and PC contexts from the KSP context,
127: ! we can then directly directly call any KSP and PC routines
128: ! to set various options.
129: ! - The following four statements are optional; all of these
130: ! parameters could alternatively be specified at runtime via
131: ! KSPSetFromOptions();
133: call KSPGetPC(ksp,pc,ierr)
134: call PCSetType(pc,PCJACOBI,ierr)
135: tol = .0000001
136: call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL, &
137: & PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
139: ! Set runtime options, e.g.,
140: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
141: ! These options will override those specified above as long as
142: ! KSPSetFromOptions() is called _after_ any other customization
143: ! routines.
145: call KSPSetFromOptions(ksp,ierr)
147: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: ! Solve the linear system
149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: call KSPSolve(ksp,b,x,ierr)
153: ! View solver info; we could instead use the option -ksp_view
155: call KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD,ierr)
157: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: ! Check solution and clean up
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: ! Check the error
163: call VecAXPY(x,none,u,ierr)
164: call VecNorm(x,NORM_2,norm,ierr)
165: call KSPGetIterationNumber(ksp,its,ierr)
166: if (norm .gt. 1.e-12) then
167: write(6,100) norm,its
168: else
169: write(6,200) its
170: endif
171: 100 format('Norm of error ',e11.4,', Iterations = ',i5)
172: 200 format('Norm of error < 1.e-12, Iterations = ',i5)
174: ! Free work space. All PETSc objects should be destroyed when they
175: ! are no longer needed.
177: call VecDestroy(x,ierr)
178: call VecDestroy(u,ierr)
179: call VecDestroy(b,ierr)
180: call MatDestroy(A,ierr)
181: call KSPDestroy(ksp,ierr)
182: call PetscFinalize(ierr)
184: end
186: !/*TEST
187: !
188: ! test:
189: ! args: -ksp_monitor_short
190: !
191: !TEST*/