xref: /petsc/include/petscmat.h (revision b1ae27ea635b58bc3a5a567f99a72fa63199efe4)
1 /* $Id: mat.h,v 1.170 1999/03/18 15:37:17 bsmith Exp bsmith $ */
2 /*
3      Include file for the matrix component of PETSc
4 */
5 #ifndef __MAT_H
6 #define __MAT_H
7 #include "vec.h"
8 
9 #define MAT_COOKIE         PETSC_COOKIE+5
10 
11 typedef struct _p_Mat*           Mat;
12 
13 #define MAX_MATRIX_TYPES 14
14 /*
15    The default matrix data storage formats and routines to create them.
16 
17    MATLASTTYPE is "end-of-list" marker that can be used to check that
18    MAX_MATRIX_TYPES is large enough.  The rule is
19    MAX_MATRIX_TYPES >= MATLASTTYPE .
20 
21    To do: add a test program that checks the consistency of these values.
22 */
23 typedef enum { MATSAME=-1,  MATSEQDENSE, MATSEQAIJ,   MATMPIAIJ,   MATSHELL,
24                MATMPIROWBS, MATSEQBDIAG, MATMPIBDIAG, MATMPIDENSE, MATSEQBAIJ,
25                MATMPIBAIJ,  MATMPICSN,   MATSEQCSN,   MATSEQADJ,   MATMPIADJ,
26                MATLASTTYPE } MatType;
27 
28 extern int MatCreate(MPI_Comm,int,int,Mat*);
29 extern int MatCreateSeqDense(MPI_Comm,int,int,Scalar*,Mat*);
30 extern int MatCreateMPIDense(MPI_Comm,int,int,int,int,Scalar*,Mat*);
31 extern int MatCreateSeqAIJ(MPI_Comm,int,int,int,int*,Mat*);
32 extern int MatCreateMPIAIJ(MPI_Comm,int,int,int,int,int,int*,int,int*,Mat*);
33 extern int MatCreateMPIRowbs(MPI_Comm,int,int,int,int*,void*,Mat*);
34 extern int MatCreateSeqBDiag(MPI_Comm,int,int,int,int,int*,Scalar**,Mat*);
35 extern int MatCreateMPIBDiag(MPI_Comm,int,int,int,int,int,int*,Scalar**,Mat*);
36 extern int MatCreateSeqBAIJ(MPI_Comm,int,int,int,int,int*,Mat*);
37 extern int MatCreateMPIBAIJ(MPI_Comm,int,int,int,int,int,int,int*,int,int*,Mat*);
38 extern int MatCreateSeqAdj(MPI_Comm,int,int,int*,int*,Mat *);
39 extern int MatCreateMPIAdj(MPI_Comm,int,int,int*,int*,Mat*);
40 
41 extern int MatDestroy(Mat);
42 
43 extern int MatCreateShell(MPI_Comm,int,int,int,int,void *,Mat*);
44 extern int MatShellGetContext(Mat,void **);
45 
46 extern int MatPrintHelp(Mat);
47 extern int MatGetMaps(Mat,Map*,Map*);
48 
49 /* ------------------------------------------------------------*/
50 extern int MatSetValues(Mat,int,int*,int,int*,Scalar*,InsertMode);
51 extern int MatSetValuesBlocked(Mat,int,int*,int,int*,Scalar*,InsertMode);
52 
53 typedef enum {MAT_FLUSH_ASSEMBLY=1,MAT_FINAL_ASSEMBLY=0} MatAssemblyType;
54 extern int MatAssemblyBegin(Mat,MatAssemblyType);
55 extern int MatAssemblyEnd(Mat,MatAssemblyType);
56 #define MatSetValue(v,i,j,va,mode) \
57 {int _ierr,_row = i,_col = j; Scalar _va = va; \
58   _ierr = MatSetValues(v,1,&_row,1,&_col,&_va,mode);CHKERRQ(_ierr); \
59 }
60 #define MatGetValue(v,i,j,va) \
61 {int _ierr,_row = i,_col = j; \
62   _ierr = MatGetValues(v,1,&_row,1,&_col,&va);CHKERRQ(_ierr); \
63 }
64 /*
65    Any additions/changes here MUST also be made in include/finclude/mat.h
66 */
67 typedef enum {MAT_ROW_ORIENTED=1,MAT_COLUMN_ORIENTED=2,MAT_ROWS_SORTED=4,
68               MAT_COLUMNS_SORTED=8,MAT_NO_NEW_NONZERO_LOCATIONS=16,
69               MAT_YES_NEW_NONZERO_LOCATIONS=32,MAT_SYMMETRIC=64,
70               MAT_STRUCTURALLY_SYMMETRIC=65,MAT_NO_NEW_DIAGONALS=66,
71               MAT_YES_NEW_DIAGONALS=67,MAT_INODE_LIMIT_1=68,MAT_INODE_LIMIT_2=69,
72               MAT_INODE_LIMIT_3=70,MAT_INODE_LIMIT_4=71,MAT_INODE_LIMIT_5=72,
73               MAT_IGNORE_OFF_PROC_ENTRIES=73,MAT_ROWS_UNSORTED=74,
74               MAT_COLUMNS_UNSORTED=75,MAT_NEW_NONZERO_LOCATION_ERR=76,
75               MAT_NEW_NONZERO_ALLOCATION_ERR=77,MAT_USE_HASH_TABLE=78} MatOption;
76 extern int MatSetOption(Mat,MatOption);
77 extern int MatGetType(Mat,MatType*,char**);
78 extern int MatGetTypeFromOptions(MPI_Comm,char*,MatType*,PetscTruth*);
79 
80 extern int MatGetValues(Mat,int,int*,int,int*,Scalar*);
81 extern int MatGetRow(Mat,int,int *,int **,Scalar**);
82 extern int MatRestoreRow(Mat,int,int *,int **,Scalar**);
83 extern int MatGetColumn(Mat,int,int *,int **,Scalar**);
84 extern int MatRestoreColumn(Mat,int,int *,int **,Scalar**);
85 extern int MatGetColumnVector(Mat,Vec,int);
86 extern int MatGetArray(Mat,Scalar **);
87 extern int MatRestoreArray(Mat,Scalar **);
88 extern int MatGetBlockSize(Mat,int *);
89 
90 extern int MatMult(Mat,Vec,Vec);
91 extern int MatMultAdd(Mat,Vec,Vec,Vec);
92 extern int MatMultTrans(Mat,Vec,Vec);
93 extern int MatMultTransAdd(Mat,Vec,Vec,Vec);
94 
95 typedef enum {MAT_DO_NOT_COPY_VALUES, MAT_COPY_VALUES} MatDuplicateOption;
96 
97 extern int MatConvert(Mat,MatType,Mat*);
98 extern int MatDuplicate(Mat,MatDuplicateOption,Mat*);
99 extern int MatConvertRegister(MatType,MatType,int (*)(Mat,MatType,Mat*));
100 extern int MatConvertRegisterAll(void);
101 
102 typedef enum {SAME_NONZERO_PATTERN,DIFFERENT_NONZERO_PATTERN,SAME_PRECONDITIONER} MatStructure;
103 
104 extern int MatCopy(Mat,Mat,MatStructure);
105 extern int MatView(Mat,Viewer);
106 extern int MatLoad(Viewer,MatType,Mat*);
107 extern int MatLoadRegister(MatType,int (*)(Viewer,MatType,Mat*));
108 extern int MatLoadRegisterAll(void);
109 
110 extern int MatGetRowIJ(Mat,int,PetscTruth,int*,int **,int **,PetscTruth *);
111 extern int MatRestoreRowIJ(Mat,int,PetscTruth,int *,int **,int **,PetscTruth *);
112 extern int MatGetColumnIJ(Mat,int,PetscTruth,int*,int **,int **,PetscTruth *);
113 extern int MatRestoreColumnIJ(Mat,int,PetscTruth,int *,int **,int **,PetscTruth *);
114 
115 /*
116    Context of matrix information, used with MatGetInfo()
117    Note: If any entries are added to this context, be sure
118          to adjust MAT_INFO_SIZE in finclude/mat.h
119  */
120 typedef struct {
121   PLogDouble rows_global, columns_global;         /* number of global rows and columns */
122   PLogDouble rows_local, columns_local;           /* number of local rows and columns */
123   PLogDouble block_size;                          /* block size */
124   PLogDouble nz_allocated, nz_used, nz_unneeded;  /* number of nonzeros */
125   PLogDouble memory;                              /* memory allocated */
126   PLogDouble assemblies;                          /* number of matrix assemblies */
127   PLogDouble mallocs;                             /* number of mallocs during MatSetValues() */
128   PLogDouble fill_ratio_given, fill_ratio_needed; /* fill ratio for LU/ILU */
129   PLogDouble factor_mallocs;                      /* number of mallocs during factorization */
130 } MatInfo;
131 
132 typedef enum {MAT_LOCAL=1,MAT_GLOBAL_MAX=2,MAT_GLOBAL_SUM=3} MatInfoType;
133 extern int MatGetInfo(Mat,MatInfoType,MatInfo*);
134 extern int MatValid(Mat,PetscTruth*);
135 extern int MatGetDiagonal(Mat,Vec);
136 extern int MatTranspose(Mat,Mat*);
137 extern int MatPermute(Mat,IS,IS,Mat *);
138 extern int MatDiagonalScale(Mat,Vec,Vec);
139 extern int MatDiagonalShift(Mat,Vec);
140 extern int MatEqual(Mat,Mat, PetscTruth*);
141 
142 extern int MatNorm(Mat,NormType,double *);
143 extern int MatZeroEntries(Mat);
144 extern int MatZeroRows(Mat,IS,Scalar*);
145 extern int MatZeroColumns(Mat,IS,Scalar*);
146 
147 extern int MatUseScaledForm(Mat,PetscTruth);
148 extern int MatScaleSystem(Mat,Vec,Vec);
149 extern int MatUnScaleSystem(Mat,Vec,Vec);
150 
151 extern int MatGetSize(Mat,int*,int*);
152 extern int MatGetLocalSize(Mat,int*,int*);
153 extern int MatGetOwnershipRange(Mat,int*,int*);
154 
155 typedef enum {MAT_INITIAL_MATRIX, MAT_REUSE_MATRIX} MatReuse;
156 extern int MatGetSubMatrices(Mat,int,IS *,IS *,MatReuse,Mat **);
157 extern int MatDestroyMatrices(int, Mat **);
158 extern int MatGetSubMatrix(Mat,IS,IS,int,MatReuse,Mat *);
159 
160 extern int MatIncreaseOverlap(Mat,int,IS *,int);
161 
162 extern int MatAXPY(Scalar *,Mat,Mat);
163 extern int MatAYPX(Scalar *,Mat,Mat);
164 extern int MatCompress(Mat);
165 
166 extern int MatScale(Scalar *,Mat);
167 extern int MatShift(Scalar *,Mat);
168 
169 extern int MatSetLocalToGlobalMapping(Mat, ISLocalToGlobalMapping);
170 extern int MatSetLocalToGlobalMappingBlocked(Mat, ISLocalToGlobalMapping);
171 extern int MatZeroRowsLocal(Mat,IS,Scalar*);
172 extern int MatSetValuesLocal(Mat,int,int*,int,int*,Scalar*,InsertMode);
173 extern int MatSetValuesBlockedLocal(Mat,int,int*,int,int*,Scalar*,InsertMode);
174 
175 extern int MatSetStashInitialSize(Mat,int, int);
176 
177 /* Routines unique to particular data structures */
178 extern int MatBDiagGetData(Mat,int*,int*,int**,int**,Scalar***);
179 extern int MatSeqAIJSetColumnIndices(Mat,int *);
180 extern int MatSeqBAIJSetColumnIndices(Mat,int *);
181 
182 extern int MatStoreValues(Mat);
183 extern int MatRetrieveValues(Mat);
184 
185 /*
186   These routines are not usually accessed directly, rather solving is
187   done through the SLES, KSP and PC interfaces.
188 */
189 
190 typedef enum {ORDER_NATURAL=0,ORDER_ND=1,ORDER_1WD=2,ORDER_RCM=3,
191               ORDER_QMD=4,ORDER_ROWLENGTH=5,ORDER_FLOW,ORDER_NEW} MatOrderingType;
192 extern int MatGetOrdering(Mat,MatOrderingType,IS*,IS*);
193 extern int MatGetOrderingTypeFromOptions(char *,MatOrderingType*);
194 extern int MatOrderingRegister(MatOrderingType,MatOrderingType*,char*,
195                                  int(*)(Mat,MatOrderingType,IS*,IS*));
196 extern int MatOrderingGetName(MatOrderingType,char **);
197 extern int MatOrderingRegisterDestroy(void);
198 extern int MatOrderingRegisterAll(void);
199 extern int MatOrderingRegisterAllCalled;
200 
201 extern int MatReorderForNonzeroDiagonal(Mat,double,IS,IS);
202 
203 extern int MatCholeskyFactor(Mat,IS,double);
204 extern int MatCholeskyFactorSymbolic(Mat,IS,double,Mat*);
205 extern int MatCholeskyFactorNumeric(Mat,Mat*);
206 
207 /*
208    Context of matrix information, used with MatILUFactor() and MatILUFactorSymbolic()
209    Note: If any entries are added to this context, be sure
210          to adjust MAT_ILUINFO_SIZE in finclude/mat.h
211 
212    Note: The integer values below are passed in double to allow easy use from
213          Fortran
214  */
215 typedef struct {
216   double levels;  /* ILU(levels) */
217   double fill;    /* expected fill; nonzeros in factored matrix/nonzeros in original matrix*/
218   double diagonal_fill;  /* force diagonal to fill in if initially not filled */
219 } MatILUInfo;
220 
221 extern int MatLUFactor(Mat,IS,IS,double);
222 extern int MatILUFactor(Mat,IS,IS,MatILUInfo*);
223 extern int MatLUFactorSymbolic(Mat,IS,IS,double,Mat*);
224 extern int MatILUFactorSymbolic(Mat,IS,IS,MatILUInfo*,Mat*);
225 extern int MatIncompleteCholeskyFactorSymbolic(Mat,IS,double,int,Mat*);
226 extern int MatLUFactorNumeric(Mat,Mat*);
227 extern int MatILUDTFactor(Mat,double,int,IS,IS,Mat *);
228 
229 extern int MatSolve(Mat,Vec,Vec);
230 extern int MatForwardSolve(Mat,Vec,Vec);
231 extern int MatBackwardSolve(Mat,Vec,Vec);
232 extern int MatSolveAdd(Mat,Vec,Vec,Vec);
233 extern int MatSolveTrans(Mat,Vec,Vec);
234 extern int MatSolveTransAdd(Mat,Vec,Vec,Vec);
235 
236 extern int MatSetUnfactored(Mat);
237 
238 typedef enum {SOR_FORWARD_SWEEP=1,SOR_BACKWARD_SWEEP=2,SOR_SYMMETRIC_SWEEP=3,
239               SOR_LOCAL_FORWARD_SWEEP=4,SOR_LOCAL_BACKWARD_SWEEP=8,
240               SOR_LOCAL_SYMMETRIC_SWEEP=12,SOR_ZERO_INITIAL_GUESS=16,
241               SOR_EISENSTAT=32,SOR_APPLY_UPPER=64,SOR_APPLY_LOWER=128} MatSORType;
242 extern int MatRelax(Mat,Vec,double,MatSORType,double,int,Vec);
243 
244 
245 /*
246     These routines are for efficiently computing Jacobians via finite differences.
247 */
248 typedef enum {COLORING_NATURAL, COLORING_SL, COLORING_LF, COLORING_ID,
249               COLORING_NEW} MatColoringType;
250 extern int MatGetColoring(Mat,MatColoringType,ISColoring*);
251 extern int MatGetColoringTypeFromOptions(char *,MatColoringType*);
252 extern int MatColoringRegister(MatColoringType,MatColoringType*,char*,int(*)(Mat,MatColoringType,ISColoring *));
253 extern int MatColoringRegisterAll(void);
254 extern int MatColoringRegisterAllCalled;
255 extern int MatColoringRegisterDestroy(void);
256 extern int MatColoringPatch(Mat,int,int *,ISColoring*);
257 
258 /*
259     Data structures used to compute Jacobian vector products
260   efficiently using finite differences.
261 */
262 #define MAT_FDCOLORING_COOKIE PETSC_COOKIE + 22
263 
264 typedef struct _p_MatFDColoring *MatFDColoring;
265 
266 extern int MatFDColoringCreate(Mat,ISColoring,MatFDColoring *);
267 extern int MatFDColoringDestroy(MatFDColoring);
268 extern int MatFDColoringView(MatFDColoring,Viewer);
269 extern int MatFDColoringSetFunction(MatFDColoring,int (*)(void),void*);
270 extern int MatFDColoringSetParameters(MatFDColoring,double,double);
271 extern int MatFDColoringSetFrequency(MatFDColoring,int);
272 extern int MatFDColoringGetFrequency(MatFDColoring,int*);
273 extern int MatFDColoringSetFromOptions(MatFDColoring);
274 extern int MatFDColoringPrintHelp(MatFDColoring);
275 extern int MatFDColoringApply(Mat,MatFDColoring,Vec,MatStructure*,void *);
276 extern int MatFDColoringApplyTS(Mat,MatFDColoring,double,Vec,MatStructure*,void *);
277 
278 /*
279     These routines are for partitioning matrices: currently used only
280   for adjacency matrix, MatCreateSeqAdj() or MatCreateMPIAdj().
281 */
282 #define MATPARTITIONING_COOKIE PETSC_COOKIE + 25
283 
284 typedef struct _p_MatPartitioning *MatPartitioning;
285 
286 typedef enum {MATPARTITIONING_CURRENT,MATPARTITIONING_PARMETIS,MATPARTITIONING_NEW} MatPartitioningType;
287 
288 extern int MatPartitioningCreate(MPI_Comm,MatPartitioning*);
289 extern int MatPartitioningSetType(MatPartitioning,MatPartitioningType);
290 extern int MatPartitioningSetAdjacency(MatPartitioning,Mat);
291 extern int MatPartitioningSetVertexWeights(MatPartitioning,double*);
292 extern int MatPartitioningApply(MatPartitioning,IS*);
293 extern int MatPartitioningDestroy(MatPartitioning);
294 extern int MatPartitioningRegister(MatPartitioningType,MatPartitioningType *,char*,int(*)(MatPartitioning));
295 extern int MatPartitioningRegisterAll(void);
296 extern int MatPartitioningRegisterAllCalled;
297 extern int MatPartitioningRegisterDestroy(void);
298 extern int MatPartitioningView(MatPartitioning,Viewer);
299 extern int MatPartitioningSetFromOptions(MatPartitioning);
300 extern int MatPartitioningPrintHelp(MatPartitioning);
301 extern int MatPartitioningGetType(MatPartitioning,MatPartitioningType*,char**);
302 
303 extern int MatPartitioningParmetisSetCoarseSequential(MatPartitioning);
304 
305 /*
306     If you add entries here you must also add them to finclude/mat.h
307 */
308 typedef enum { MATOP_SET_VALUES=0,
309                MATOP_GET_ROW=1,
310                MATOP_RESTORE_ROW=2,
311                MATOP_MULT=3,
312                MATOP_MULT_ADD=4,
313                MATOP_MULT_TRANS=5,
314                MATOP_MULT_TRANS_ADD=6,
315                MATOP_SOLVE=7,
316                MATOP_SOLVE_ADD=8,
317                MATOP_SOLVE_TRANS=9,
318                MATOP_SOLVE_TRANS_ADD=10,
319                MATOP_LUFACTOR=11,
320                MATOP_CHOLESKYFACTOR=12,
321                MATOP_RELAX=13,
322                MATOP_TRANSPOSE=14,
323                MATOP_GETINFO=15,
324                MATOP_EQUAL=16,
325                MATOP_GET_DIAGONAL=17,
326                MATOP_DIAGONAL_SCALE=18,
327                MATOP_NORM=19,
328                MATOP_ASSEMBLY_BEGIN=20,
329                MATOP_ASSEMBLY_END=21,
330                MATOP_COMPRESS=22,
331                MATOP_SET_OPTION=23,
332                MATOP_ZERO_ENTRIES=24,
333                MATOP_ZERO_ROWS=25,
334                MATOP_LUFACTOR_SYMBOLIC=26,
335                MATOP_LUFACTOR_NUMERIC=27,
336                MATOP_CHOLESKY_FACTOR_SYMBOLIC=28,
337                MATOP_CHOLESKY_FACTOR_NUMERIC=29,
338                MATOP_GET_SIZE=30,
339                MATOP_GET_LOCAL_SIZE=31,
340                MATOP_GET_OWNERSHIP_RANGE=32,
341                MATOP_ILUFACTOR_SYMBOLIC=33,
342                MATOP_INCOMPLETECHOLESKYFACTOR_SYMBOLIC=34,
343                MATOP_GET_ARRAY=35,
344                MATOP_RESTORE_ARRAY=36,
345 
346                MATOP_CONVERT_SAME_TYPE=37,
347                MATOP_FORWARD_SOLVE=38,
348                MATOP_BACKWARD_SOLVE=39,
349                MATOP_ILUFACTOR=40,
350                MATOP_INCOMPLETECHOLESKYFACTOR=41,
351                MATOP_AXPY=42,
352                MATOP_GET_SUBMATRICES=43,
353                MATOP_INCREASE_OVERLAP=44,
354                MATOP_GET_VALUES=45,
355                MATOP_COPY=46,
356                MATOP_PRINT_HELP=47,
357                MATOP_SCALE=48,
358                MATOP_SHIFT=49,
359                MATOP_DIAGONAL_SHIFT=50,
360                MATOP_ILUDT_FACTOR=51,
361                MATOP_GET_BLOCK_SIZE=52,
362                MATOP_GET_ROW_IJ=53,
363                MATOP_RESTORE_ROW_IJ=54,
364                MATOP_GET_COLUMN_IJ=55,
365                MATOP_RESTORE_COLUMN_IJ=56,
366                MATOP_FDCOLORING_CREATE=57,
367                MATOP_COLORING_PATCH=58,
368                MATOP_SET_UNFACTORED=59,
369                MATOP_PERMUTE=60,
370                MATOP_SET_VALUES_BLOCKED=61,
371                MATOP_DESTROY=250,
372                MATOP_VIEW=251
373              } MatOperation;
374 extern int MatHasOperation(Mat,MatOperation,PetscTruth*);
375 extern int MatShellSetOperation(Mat,MatOperation,void *);
376 extern int MatShellGetOperation(Mat,MatOperation,void **);
377 
378 /*
379    Codes for matrices stored on disk. By default they are
380  stored in a universal format. By changing the format with
381  ViewerSetFormat(viewer,VIEWER_FORMAT_BINARY_NATIVE); the matrices will
382  be stored in a way natural for the matrix, for example dense matrices
383  would be stored as dense. Matrices stored this way may only be
384  read into matrices of the same time.
385 */
386 #define MATRIX_BINARY_FORMAT_DENSE -1
387 
388 /*
389      New matrix classes not yet distributed
390 */
391 /*
392     MatAIJIndices is a data structure for storing the nonzero location information
393   for sparse matrices. Several matrices with identical nonzero structure can share
394   the same MatAIJIndices.
395 */
396 typedef struct _p_MatAIJIndices* MatAIJIndices;
397 
398 extern int MatCreateAIJIndices(int,int,int*,int*,PetscTruth,MatAIJIndices*);
399 extern int MatCreateAIJIndicesEmpty(int,int,int*,PetscTruth,MatAIJIndices*);
400 extern int MatAttachAIJIndices(MatAIJIndices,MatAIJIndices*);
401 extern int MatDestroyAIJIndices(MatAIJIndices);
402 extern int MatCopyAIJIndices(MatAIJIndices,MatAIJIndices*);
403 extern int MatValidateAIJIndices(int,MatAIJIndices);
404 extern int MatShiftAIJIndices(MatAIJIndices);
405 extern int MatShrinkAIJIndices(MatAIJIndices);
406 extern int MatTransposeAIJIndices(MatAIJIndices, MatAIJIndices*);
407 
408 extern int MatCreateSeqCSN(MPI_Comm,int,int,int*,int,Mat*);
409 extern int MatCreateSeqCSN_Single(MPI_Comm,int,int,int*,int,Mat*);
410 extern int MatCreateSeqCSNWithPrecision(MPI_Comm,int,int,int*,int,ScalarPrecision,Mat*);
411 
412 extern int MatCreateSeqCSNIndices(MPI_Comm,MatAIJIndices,int,Mat *);
413 extern int MatCreateSeqCSNIndices_Single(MPI_Comm,MatAIJIndices,int,Mat *);
414 extern int MatCreateSeqCSNIndicesWithPrecision(MPI_Comm,MatAIJIndices,int,ScalarPrecision,Mat *);
415 
416 extern int MatMPIBAIJSetHashTableFactor(Mat,double);
417 extern int MatSeqAIJGetInodeSizes(Mat,int *,int *[],int *);
418 
419 
420 #endif
421 
422 
423 
424