xref: /petsc/include/petscmat.h (revision 9d47de495d3c23378050c1b4a410c12a375cb6c6)

/*
     Include file for the matrix component of PETSc
*/
#pragma once

#include <petscvec.h>

/* SUBMANSEC = Mat */

/*S
   Mat - Abstract PETSc matrix object used to manage all linear operators in PETSc, even those without
         an explicit sparse representation (such as matrix-free operators). Also used to hold representations of graphs
         for graph operations such as coloring, `MatColoringCreate()`

   Level: beginner

   Note:
   See [](doc_matrix), [](ch_matrices) and `MatType` for available matrix types

.seealso: [](doc_matrix), [](ch_matrices), `MatCreate()`, `MatType`, `MatSetType()`, `MatDestroy()`
S*/
typedef struct _p_Mat *Mat;

/*J
   MatType - String with the name of a PETSc matrix type. These are all the matrix formats that PETSc provides.

   Level: beginner

   Notes:
   [](doc_matrix) for a table of available matrix types

   Use `MatSetType()` or the options database keys `-mat_type` or `-dm_mat_type` to set the matrix format to use for a given `Mat`

.seealso: [](doc_matrix), [](ch_matrices), `MatSetType()`, `Mat`, `MatSolverType`, `MatRegister()`
J*/
typedef const char *MatType;
#define MATSAME                      "same"
#define MATMAIJ                      "maij"
#define MATSEQMAIJ                   "seqmaij"
#define MATMPIMAIJ                   "mpimaij"
#define MATKAIJ                      "kaij"
#define MATSEQKAIJ                   "seqkaij"
#define MATMPIKAIJ                   "mpikaij"
#define MATIS                        "is"
#define MATAIJ                       "aij"
#define MATSEQAIJ                    "seqaij"
#define MATMPIAIJ                    "mpiaij"
#define MATAIJCRL                    "aijcrl"
#define MATSEQAIJCRL                 "seqaijcrl"
#define MATMPIAIJCRL                 "mpiaijcrl"
#define MATAIJCUSPARSE               "aijcusparse"
#define MATSEQAIJCUSPARSE            "seqaijcusparse"
#define MATMPIAIJCUSPARSE            "mpiaijcusparse"
#define MATAIJHIPSPARSE              "aijhipsparse"
#define MATSEQAIJHIPSPARSE           "seqaijhipsparse"
#define MATMPIAIJHIPSPARSE           "mpiaijhipsparse"
#define MATAIJKOKKOS                 "aijkokkos"
#define MATSEQAIJKOKKOS              "seqaijkokkos"
#define MATMPIAIJKOKKOS              "mpiaijkokkos"
#define MATAIJVIENNACL               "aijviennacl"
#define MATSEQAIJVIENNACL            "seqaijviennacl"
#define MATMPIAIJVIENNACL            "mpiaijviennacl"
#define MATAIJPERM                   "aijperm"
#define MATSEQAIJPERM                "seqaijperm"
#define MATMPIAIJPERM                "mpiaijperm"
#define MATAIJSELL                   "aijsell"
#define MATSEQAIJSELL                "seqaijsell"
#define MATMPIAIJSELL                "mpiaijsell"
#define MATAIJMKL                    "aijmkl"
#define MATSEQAIJMKL                 "seqaijmkl"
#define MATMPIAIJMKL                 "mpiaijmkl"
#define MATBAIJMKL                   "baijmkl"
#define MATSEQBAIJMKL                "seqbaijmkl"
#define MATMPIBAIJMKL                "mpibaijmkl"
#define MATSHELL                     "shell"
#define MATCENTERING                 "centering"
#define MATDENSE                     "dense"
#define MATDENSECUDA                 "densecuda"
#define MATDENSEHIP                  "densehip"
#define MATSEQDENSE                  "seqdense"
#define MATSEQDENSECUDA              "seqdensecuda"
#define MATSEQDENSEHIP               "seqdensehip"
#define MATMPIDENSE                  "mpidense"
#define MATMPIDENSECUDA              "mpidensecuda"
#define MATMPIDENSEHIP               "mpidensehip"
#define MATELEMENTAL                 "elemental"
#define MATSCALAPACK                 "scalapack"
#define MATBAIJ                      "baij"
#define MATSEQBAIJ                   "seqbaij"
#define MATMPIBAIJ                   "mpibaij"
#define MATMPIADJ                    "mpiadj"
#define MATSBAIJ                     "sbaij"
#define MATSEQSBAIJ                  "seqsbaij"
#define MATMPISBAIJ                  "mpisbaij"
#define MATMFFD                      "mffd"
#define MATNORMAL                    "normal"
#define MATNORMALHERMITIAN           "normalh"
#define MATLRC                       "lrc"
#define MATSCATTER                   "scatter"
#define MATBLOCKMAT                  "blockmat"
#define MATCOMPOSITE                 "composite"
#define MATFFT                       "fft"
#define MATFFTW                      "fftw"
#define MATSEQCUFFT                  "seqcufft"
#define MATSEQHIPFFT                 "seqhipfft"
#define MATTRANSPOSEMAT              PETSC_DEPRECATED_MACRO(3, 18, 0, "MATTRANSPOSEVIRTUAL", ) "transpose"
#define MATTRANSPOSEVIRTUAL          "transpose"
#define MATHERMITIANTRANSPOSEVIRTUAL "hermitiantranspose"
#define MATSCHURCOMPLEMENT           "schurcomplement"
#define MATPYTHON                    "python"
#define MATHYPRE                     "hypre"
#define MATHYPRESTRUCT               "hyprestruct"
#define MATHYPRESSTRUCT              "hypresstruct"
#define MATSUBMATRIX                 "submatrix"
#define MATLOCALREF                  "localref"
#define MATNEST                      "nest"
#define MATPREALLOCATOR              "preallocator"
#define MATSELL                      "sell"
#define MATSEQSELL                   "seqsell"
#define MATMPISELL                   "mpisell"
#define MATSELLCUDA                  "sellcuda"
#define MATSEQSELLCUDA               "seqsellcuda"
#define MATMPISELLCUDA               "mpisellcuda"
#define MATSELLHIP                   "sellhip"
#define MATSEQSELLHIP                "seqsellhip"
#define MATMPISELLHIP                "mpisellhip"
#define MATDUMMY                     "dummy"
#define MATLMVM                      "lmvm"
#define MATLMVMDFP                   "lmvmdfp"
#define MATLMVMDDFP                  "lmvmddfp"
#define MATLMVMBFGS                  "lmvmbfgs"
#define MATLMVMDBFGS                 "lmvmdbfgs"
#define MATLMVMDQN                   "lmvmdqn"
#define MATLMVMSR1                   "lmvmsr1"
#define MATLMVMBROYDEN               "lmvmbroyden"
#define MATLMVMBADBROYDEN            "lmvmbadbroyden"
#define MATLMVMSYMBROYDEN            "lmvmsymbroyden"
#define MATLMVMSYMBADBROYDEN         "lmvmsymbadbroyden"
#define MATLMVMDIAGBROYDEN           "lmvmdiagbroyden"
#define MATCONSTANTDIAGONAL          "constantdiagonal"
#define MATDIAGONAL                  "diagonal"
#define MATHTOOL                     "htool"
#define MATH2OPUS                    "h2opus"

/*J
   MatSolverType - String with the name of a PETSc factorization-based matrix solver type.

   For example: "petsc" indicates what PETSc provides, "superlu_dist" the parallel SuperLU_DIST package etc

   Level: beginner

   Note:
   `MATSOLVERUMFPACK`, `MATSOLVERCHOLMOD`, `MATSOLVERKLU`, `MATSOLVERSPQR` form the SuiteSparse package; you can use `--download-suitesparse` as
   a ./configure option to install them

.seealso: [](sec_matfactor), [](ch_matrices), `MatGetFactor()`, `PCFactorSetMatSolverType()`, `PCFactorGetMatSolverType()`
J*/
typedef const char *MatSolverType;
#define MATSOLVERSUPERLU      "superlu"
#define MATSOLVERSUPERLU_DIST "superlu_dist"
#define MATSOLVERSTRUMPACK    "strumpack"
#define MATSOLVERUMFPACK      "umfpack"
#define MATSOLVERCHOLMOD      "cholmod"
#define MATSOLVERKLU          "klu"
#define MATSOLVERELEMENTAL    "elemental"
#define MATSOLVERSCALAPACK    "scalapack"
#define MATSOLVERESSL         "essl"
#define MATSOLVERLUSOL        "lusol"
#define MATSOLVERMUMPS        "mumps"
#define MATSOLVERMKL_PARDISO  "mkl_pardiso"
#define MATSOLVERMKL_CPARDISO "mkl_cpardiso"
#define MATSOLVERPASTIX       "pastix"
#define MATSOLVERMATLAB       "matlab"
#define MATSOLVERPETSC        "petsc"
#define MATSOLVERBAS          "bas"
#define MATSOLVERCUSPARSE     "cusparse"
#define MATSOLVERCUDA         "cuda"
#define MATSOLVERHIPSPARSE    "hipsparse"
#define MATSOLVERHIP          "hip"
#define MATSOLVERKOKKOS       "kokkos"
#define MATSOLVERSPQR         "spqr"
#define MATSOLVERHTOOL        "htool"

/*E
    MatFactorType - indicates what type of factorization is requested

    Values:
+  `MAT_FACTOR_LU`       - LU factorization
.  `MAT_FACTOR_CHOLESKY` - Cholesky factorization
.  `MAT_FACTOR_ILU`      - ILU factorization
.  `MAT_FACTOR_ICC`      - incomplete Cholesky factorization
.  `MAT_FACTOR_ILUDT`    - ILU factorization with drop tolerance
-  `MAT_FACTOR_QR`       - QR factorization

    Level: beginner

.seealso: [](ch_matrices), `MatSolverType`, `MatGetFactor()`, `MatGetFactorAvailable()`, `MatSolverTypeRegister()`
E*/
typedef enum {
  MAT_FACTOR_NONE,
  MAT_FACTOR_LU,
  MAT_FACTOR_CHOLESKY,
  MAT_FACTOR_ILU,
  MAT_FACTOR_ICC,
  MAT_FACTOR_ILUDT,
  MAT_FACTOR_QR,
  MAT_FACTOR_NUM_TYPES
} MatFactorType;
PETSC_EXTERN const char *const MatFactorTypes[];

PETSC_EXTERN PetscErrorCode MatGetFactor(Mat, MatSolverType, MatFactorType, Mat *);
PETSC_EXTERN PetscErrorCode MatGetFactorAvailable(Mat, MatSolverType, MatFactorType, PetscBool *);
PETSC_EXTERN PetscErrorCode MatFactorGetCanUseOrdering(Mat, PetscBool *);
PETSC_DEPRECATED_FUNCTION(3, 15, 0, "MatFactorGetCanUseOrdering()", ) static inline PetscErrorCode MatFactorGetUseOrdering(Mat A, PetscBool *b)
{
  return MatFactorGetCanUseOrdering(A, b);
}
PETSC_EXTERN PetscErrorCode                 MatFactorGetSolverType(Mat, MatSolverType *);
PETSC_EXTERN PetscErrorCode                 MatGetFactorType(Mat, MatFactorType *);
PETSC_EXTERN PetscErrorCode                 MatSetFactorType(Mat, MatFactorType);
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatSolverFn(Mat, MatFactorType, Mat *);
PETSC_EXTERN_TYPEDEF typedef MatSolverFn   *MatSolverFunction;

PETSC_EXTERN PetscErrorCode MatSolverTypeRegister(MatSolverType, MatType, MatFactorType, MatSolverFn *);
PETSC_EXTERN PetscErrorCode MatSolverTypeGet(MatSolverType, MatType, MatFactorType, PetscBool *, PetscBool *, MatSolverFn **);
typedef MatSolverType       MatSolverPackage PETSC_DEPRECATED_TYPEDEF(3, 9, 0, "MatSolverType", );
PETSC_DEPRECATED_FUNCTION(3, 9, 0, "MatSolverTypeRegister()", ) static inline PetscErrorCode MatSolverPackageRegister(MatSolverType stype, MatType mtype, MatFactorType ftype, MatSolverFn *f)
{
  return MatSolverTypeRegister(stype, mtype, ftype, f);
}
PETSC_DEPRECATED_FUNCTION(3, 9, 0, "MatSolverTypeGet()", ) static inline PetscErrorCode MatSolverPackageGet(MatSolverType stype, MatType mtype, MatFactorType ftype, PetscBool *foundmtype, PetscBool *foundstype, MatSolverFn **f)
{
  return MatSolverTypeGet(stype, mtype, ftype, foundmtype, foundstype, f);
}

/*E
    MatProductType - indicates what type of matrix product to compute

    Values:
+  `MATPRODUCT_AB`   - product of two matrices
.  `MATPRODUCT_AtB`  - product of the transpose of a given matrix with a matrix
.  `MATPRODUCT_ABt`  - product of a matrix with the transpose of another given matrix
.  `MATPRODUCT_PtAP` - the triple product of the transpose of a matrix with another matrix and itself
.  `MATPRODUCT_RARt` - the triple product of a matrix, another matrix and the transpose of the first matrix
-  `MATPRODUCT_ABC`  - the product of three matrices

    Level: beginner

.seealso: [](sec_matmatproduct), [](ch_matrices), `MatProductSetType()`
E*/
typedef enum {
  MATPRODUCT_UNSPECIFIED,
  MATPRODUCT_AB,
  MATPRODUCT_AtB,
  MATPRODUCT_ABt,
  MATPRODUCT_PtAP,
  MATPRODUCT_RARt,
  MATPRODUCT_ABC
} MatProductType;
PETSC_EXTERN const char *const MatProductTypes[];

/*J
    MatProductAlgorithm - String with the name of an algorithm for a PETSc matrix product implementation

   Level: beginner

.seealso: [](sec_matmatproduct), [](ch_matrices), `MatSetType()`, `Mat`, `MatProductSetAlgorithm()`, `MatProductType`
J*/
typedef const char *MatProductAlgorithm;
#define MATPRODUCTALGORITHMDEFAULT         "default"
#define MATPRODUCTALGORITHMSORTED          "sorted"
#define MATPRODUCTALGORITHMSCALABLE        "scalable"
#define MATPRODUCTALGORITHMSCALABLEFAST    "scalable_fast"
#define MATPRODUCTALGORITHMHEAP            "heap"
#define MATPRODUCTALGORITHMBHEAP           "btheap"
#define MATPRODUCTALGORITHMLLCONDENSED     "llcondensed"
#define MATPRODUCTALGORITHMROWMERGE        "rowmerge"
#define MATPRODUCTALGORITHMOUTERPRODUCT    "outerproduct"
#define MATPRODUCTALGORITHMATB             "at*b"
#define MATPRODUCTALGORITHMRAP             "rap"
#define MATPRODUCTALGORITHMNONSCALABLE     "nonscalable"
#define MATPRODUCTALGORITHMSEQMPI          "seqmpi"
#define MATPRODUCTALGORITHMBACKEND         "backend"
#define MATPRODUCTALGORITHMOVERLAPPING     "overlapping"
#define MATPRODUCTALGORITHMMERGED          "merged"
#define MATPRODUCTALGORITHMALLATONCE       "allatonce"
#define MATPRODUCTALGORITHMALLATONCEMERGED "allatonce_merged"
#define MATPRODUCTALGORITHMALLGATHERV      "allgatherv"
#define MATPRODUCTALGORITHMCYCLIC          "cyclic"
#define MATPRODUCTALGORITHMHYPRE           "hypre"

PETSC_EXTERN PetscErrorCode MatProductCreate(Mat, Mat, Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatProductCreateWithMat(Mat, Mat, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatProductSetType(Mat, MatProductType);
PETSC_EXTERN PetscErrorCode MatProductSetAlgorithm(Mat, MatProductAlgorithm);
PETSC_EXTERN PetscErrorCode MatProductGetAlgorithm(Mat, MatProductAlgorithm *);
PETSC_EXTERN PetscErrorCode MatProductSetFill(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatProductSetFromOptions(Mat);
PETSC_EXTERN PetscErrorCode MatProductSymbolic(Mat);
PETSC_EXTERN PetscErrorCode MatProductNumeric(Mat);
PETSC_EXTERN PetscErrorCode MatProductReplaceMats(Mat, Mat, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatProductClear(Mat);
PETSC_EXTERN PetscErrorCode MatProductView(Mat, PetscViewer);
PETSC_EXTERN PetscErrorCode MatProductGetType(Mat, MatProductType *);
PETSC_EXTERN PetscErrorCode MatProductGetMats(Mat, Mat *, Mat *, Mat *);

/* Logging support */
#define MAT_FILE_CLASSID 1211216 /* used to indicate matrices in binary files */
PETSC_EXTERN PetscClassId MAT_CLASSID;
PETSC_EXTERN PetscClassId MAT_COLORING_CLASSID;
PETSC_EXTERN PetscClassId MAT_FDCOLORING_CLASSID;
PETSC_EXTERN PetscClassId MAT_TRANSPOSECOLORING_CLASSID;
PETSC_EXTERN PetscClassId MAT_PARTITIONING_CLASSID;
PETSC_EXTERN PetscClassId MAT_COARSEN_CLASSID;
PETSC_EXTERN PetscClassId MAT_NULLSPACE_CLASSID;
PETSC_EXTERN PetscClassId MATMFFD_CLASSID;

/*E
   MatReuse - Indicates if matrices obtained from a previous call to `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatConvert()` or several other functions
   are to be reused to store the new matrix values.

   Values:
+  `MAT_INITIAL_MATRIX` - create a new matrix
.  `MAT_REUSE_MATRIX`   - reuse the matrix created with a previous call that used `MAT_INITIAL_MATRIX`
.  `MAT_INPLACE_MATRIX` - replace the first input matrix with the new matrix (not applicable to all functions)
-  `MAT_IGNORE_MATRIX`  - do not create a new matrix or reuse a given matrix, just ignore that matrix argument (not applicable to all functions)

    Level: beginner

.seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatDestroyMatrices()`, `MatConvert()`
E*/
typedef enum {
  MAT_INITIAL_MATRIX,
  MAT_REUSE_MATRIX,
  MAT_IGNORE_MATRIX,
  MAT_INPLACE_MATRIX
} MatReuse;

/*E
    MatCreateSubMatrixOption - Indicates if matrices obtained from a call to `MatCreateSubMatrices()`
    include the matrix values. Currently it is only used by `MatGetSeqNonzeroStructure()`.

    Values:
+  `MAT_DO_NOT_GET_VALUES` - do not copy the matrix values
-  `MAT_GET_VALUES`        - copy the matrix values

    Level: developer

    Developer Note:
    Why is not just a boolean used for this information?

.seealso: [](ch_matrices), `Mat`, `MatDuplicateOption`, `PetscCopyMode`, `MatGetSeqNonzeroStructure()`
E*/
typedef enum {
  MAT_DO_NOT_GET_VALUES,
  MAT_GET_VALUES
} MatCreateSubMatrixOption;

PETSC_EXTERN PetscErrorCode MatInitializePackage(void);
PETSC_EXTERN PetscErrorCode MatFinalizePackage(void);

PETSC_EXTERN PetscErrorCode MatCreate(MPI_Comm, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateFromOptions(MPI_Comm, const char *, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatSetSizes(Mat, PetscInt, PetscInt, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode MatSetType(Mat, MatType);
PETSC_EXTERN PetscErrorCode MatGetVecType(Mat, VecType *);
PETSC_EXTERN PetscErrorCode MatSetVecType(Mat, VecType);
PETSC_EXTERN PetscErrorCode MatSetFromOptions(Mat);
PETSC_EXTERN PetscErrorCode MatViewFromOptions(Mat, PetscObject, const char[]);
PETSC_EXTERN PetscErrorCode MatRegister(const char[], PetscErrorCode (*)(Mat));
PETSC_EXTERN PetscErrorCode MatRegisterRootName(const char[], const char[], const char[]);
PETSC_EXTERN PetscErrorCode MatSetOptionsPrefix(Mat, const char[]);
PETSC_EXTERN PetscErrorCode MatSetOptionsPrefixFactor(Mat, const char[]);
PETSC_EXTERN PetscErrorCode MatAppendOptionsPrefixFactor(Mat, const char[]);
PETSC_EXTERN PetscErrorCode MatAppendOptionsPrefix(Mat, const char[]);
PETSC_EXTERN PetscErrorCode MatGetOptionsPrefix(Mat, const char *[]);
PETSC_EXTERN PetscErrorCode MatGetState(Mat, PetscObjectState *);
PETSC_EXTERN PetscErrorCode MatSetErrorIfFailure(Mat, PetscBool);

PETSC_EXTERN PetscFunctionList MatList;
PETSC_EXTERN PetscFunctionList MatColoringList;
PETSC_EXTERN PetscFunctionList MatPartitioningList;

/*E
   MatStructure - Indicates if two matrices have the same nonzero structure

   Values:
+  `SAME_NONZERO_PATTERN`      - the two matrices have identical nonzero patterns
.  `DIFFERENT_NONZERO_PATTERN` - the two matrices may have different nonzero patterns
.  `SUBSET_NONZERO_PATTERN`    - the nonzero pattern of the second matrix is a subset of the nonzero pattern of the first matrix
-  `UNKNOWN_NONZERO_PATTERN`   - there is no known relationship between the nonzero patterns. In this case the implementations
                                 may try to detect a relationship to optimize the operation

   Level: beginner

   Note:
   Certain matrix operations (such as `MatAXPY()`) can run much faster if the sparsity pattern of the matrices are the same. But actually determining if
   the patterns are the same may be costly. This provides a way for users who know something about the sparsity patterns to provide this information
   to certain PETSc routines.

.seealso: [](ch_matrices), `Mat`, `MatCopy()`, `MatAXPY()`, `MatAYPX()`
E*/
typedef enum {
  DIFFERENT_NONZERO_PATTERN,
  SUBSET_NONZERO_PATTERN,
  SAME_NONZERO_PATTERN,
  UNKNOWN_NONZERO_PATTERN
} MatStructure;
PETSC_EXTERN const char *const MatStructures[];

#if defined(PETSC_HAVE_MKL_SPARSE)
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJMKL(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJMKL(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateBAIJMKL(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqBAIJMKL(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
#endif

PETSC_EXTERN PetscErrorCode MatCreateMPIAIJPERM(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJPERM(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);

PETSC_EXTERN PetscErrorCode MatCreateSeqSELL(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSELL(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatSeqSELLSetPreallocation(Mat, PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatMPISELLSetPreallocation(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSeqSELLGetFillRatio(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatSeqSELLGetMaxSliceWidth(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode MatSeqSELLGetAvgSliceWidth(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatSeqSELLSetSliceHeight(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSeqSELLGetVarSliceSize(Mat, PetscReal *);

PETSC_EXTERN PetscErrorCode MatCreateSeqAIJSELL(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJSELL(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatMPISELLGetLocalMatCondensed(Mat, MatReuse, IS *, IS *, Mat *);
PETSC_EXTERN PetscErrorCode MatMPISELLGetSeqSELL(Mat, Mat *, Mat *, const PetscInt *[]);

PETSC_EXTERN PetscErrorCode MatCreateSeqDense(MPI_Comm, PetscInt, PetscInt, PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateDense(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJ(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateAIJ(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatUpdateMPIAIJWithArrays(Mat, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatUpdateMPIAIJWithArray(Mat, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJWithSplitArrays(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], PetscInt[], PetscInt[], PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm, PetscInt, PetscInt, Mat, Mat, PetscInt *, Mat *);

PETSC_EXTERN PetscErrorCode MatCreateSeqBAIJ(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateBAIJ(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIBAIJWithArrays(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], Mat *);

PETSC_EXTERN PetscErrorCode MatSetPreallocationCOO(Mat, PetscCount, PetscInt[], PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSetPreallocationCOOLocal(Mat, PetscCount, PetscInt[], PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSetValuesCOO(Mat, const PetscScalar[], InsertMode);

PETSC_EXTERN PetscErrorCode MatCreateMPIAdj(MPI_Comm, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqSBAIJ(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);

PETSC_EXTERN PetscErrorCode MatCreateSBAIJ(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPISBAIJWithArrays(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatSeqSBAIJSetPreallocationCSR(Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatMPISBAIJSetPreallocationCSR(Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatXAIJSetPreallocation(Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscInt[], const PetscInt[]);

PETSC_EXTERN PetscErrorCode MatCreateShell(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscCtx, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateCentering(MPI_Comm, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateNormal(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateNormalHermitian(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateLRC(Mat, Mat, Vec, Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatLRCGetMats(Mat, Mat *, Mat *, Vec *, Mat *);
PETSC_EXTERN PetscErrorCode MatLRCSetMats(Mat, Mat, Mat, Vec, Mat);
PETSC_EXTERN PetscErrorCode MatCreateIS(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, ISLocalToGlobalMapping, ISLocalToGlobalMapping, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJCRL(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJCRL(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);

PETSC_EXTERN PetscErrorCode MatCreateScatter(MPI_Comm, VecScatter, Mat *);
PETSC_EXTERN PetscErrorCode MatScatterSetVecScatter(Mat, VecScatter);
PETSC_EXTERN PetscErrorCode MatScatterGetVecScatter(Mat, VecScatter *);
PETSC_EXTERN PetscErrorCode MatCreateBlockMat(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt *, Mat *);
PETSC_EXTERN PetscErrorCode MatCompositeAddMat(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatCompositeMerge(Mat);
typedef enum {
  MAT_COMPOSITE_MERGE_RIGHT,
  MAT_COMPOSITE_MERGE_LEFT
} MatCompositeMergeType;
PETSC_EXTERN PetscErrorCode MatCompositeSetMergeType(Mat, MatCompositeMergeType);
PETSC_EXTERN PetscErrorCode MatCreateComposite(MPI_Comm, PetscInt, const Mat *, Mat *);
/*E
    MatCompositeType - indicates what type of `MATCOMPOSITE` is used

    Values:
+  `MAT_COMPOSITE_ADDITIVE`       - sum of matrices (default)
-  `MAT_COMPOSITE_MULTIPLICATIVE` - product of matrices

    Level: beginner

.seealso: [](ch_matrices), `MATCOMPOSITE`, `MatCompositeSetType()`, `MatCompositeGetType()`
E*/
typedef enum {
  MAT_COMPOSITE_ADDITIVE,
  MAT_COMPOSITE_MULTIPLICATIVE
} MatCompositeType;
PETSC_EXTERN PetscErrorCode MatCompositeSetType(Mat, MatCompositeType);
PETSC_EXTERN PetscErrorCode MatCompositeGetType(Mat, MatCompositeType *);
PETSC_EXTERN PetscErrorCode MatCompositeSetMatStructure(Mat, MatStructure);
PETSC_EXTERN PetscErrorCode MatCompositeGetMatStructure(Mat, MatStructure *);
PETSC_EXTERN PetscErrorCode MatCompositeGetNumberMat(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode MatCompositeGetMat(Mat, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatCompositeSetScalings(Mat, const PetscScalar *);

PETSC_EXTERN PetscErrorCode MatCreateFFT(MPI_Comm, PetscInt, const PetscInt[], MatType, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqCUFFT(MPI_Comm, PetscInt, const PetscInt[], Mat *);

PETSC_EXTERN PetscErrorCode MatCreateTranspose(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatTransposeGetMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateHermitianTranspose(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatHermitianTransposeGetMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatNormalGetMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatNormalHermitianGetMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSubMatrixVirtual(Mat, IS, IS, Mat *);
PETSC_EXTERN PetscErrorCode MatSubMatrixVirtualUpdate(Mat, Mat, IS, IS);
PETSC_EXTERN PetscErrorCode MatCreateLocalRef(Mat, IS, IS, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateConstantDiagonal(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateDiagonal(Vec, Mat *);
PETSC_EXTERN PetscErrorCode MatDiagonalGetDiagonal(Mat, Vec *);
PETSC_EXTERN PetscErrorCode MatDiagonalRestoreDiagonal(Mat, Vec *);
PETSC_EXTERN PetscErrorCode MatDiagonalGetInverseDiagonal(Mat, Vec *);
PETSC_EXTERN PetscErrorCode MatDiagonalRestoreInverseDiagonal(Mat, Vec *);
PETSC_EXTERN PetscErrorCode MatConstantDiagonalGetConstant(Mat, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatGetCurrentMemType(Mat, PetscMemType *);

#if defined(PETSC_HAVE_HYPRE)
PETSC_EXTERN PetscErrorCode MatHYPRESetPreallocation(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]);
#endif

PETSC_EXTERN PetscErrorCode MatPythonSetType(Mat, const char[]);
PETSC_EXTERN PetscErrorCode MatPythonGetType(Mat, const char *[]);
PETSC_EXTERN PetscErrorCode MatPythonCreate(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, const char[], Mat *);

PETSC_EXTERN PetscErrorCode MatResetPreallocation(Mat);
PETSC_EXTERN PetscErrorCode MatResetHash(Mat);
PETSC_EXTERN PetscErrorCode MatSetUp(Mat);
PETSC_EXTERN PetscErrorCode MatDestroy(Mat *);
PETSC_EXTERN PetscErrorCode MatGetNonzeroState(Mat, PetscObjectState *);

PETSC_EXTERN PetscErrorCode MatConjugate(Mat);
PETSC_EXTERN PetscErrorCode MatRealPart(Mat);
PETSC_EXTERN PetscErrorCode MatImaginaryPart(Mat);
PETSC_EXTERN PetscErrorCode MatGetDiagonalBlock(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatGetTrace(Mat, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatInvertBlockDiagonal(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatInvertVariableBlockDiagonal(Mat, PetscInt, const PetscInt *, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatInvertBlockDiagonalMat(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatInvertVariableBlockEnvelope(Mat, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatComputeVariableBlockEnvelope(Mat);

PETSC_EXTERN PetscErrorCode MatSetValues(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode MatSetValuesIS(Mat, IS, IS, const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode MatSetValuesBlocked(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode MatSetValuesRow(Mat, PetscInt, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatSetValuesRowLocal(Mat, PetscInt, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatSetValuesBatch(Mat, PetscInt, PetscInt, PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatSetRandom(Mat, PetscRandom);

/*S
   MatStencil - Data structure (C struct) for storing information about rows and
   columns of a matrix as indexed on an associated grid. These are arguments to `MatSetStencil()` and `MatSetBlockStencil()`

   Level: beginner

   Notes:
   The i,j, and k represent the logical coordinates over the entire grid (for 2 and 1 dimensional problems the k and j entries are ignored).
   The c represents the degrees of freedom at each grid point (the dof argument to `DMDASetDOF()`). If dof is 1 then this entry is ignored.

   For stencil access to vectors see `DMDAVecGetArray()`

   For staggered grids, see `DMStagStencil`

.seealso: [](ch_matrices), `Mat`, `MatSetValuesStencil()`, `MatSetStencil()`, `MatSetValuesBlockedStencil()`, `DMDAVecGetArray()`
          `DMStagStencil`
S*/
typedef struct {
  PetscInt k, j, i, c;
} MatStencil;

PETSC_EXTERN PetscErrorCode MatSetValuesStencil(Mat, PetscInt, const MatStencil[], PetscInt, const MatStencil[], const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode MatSetValuesBlockedStencil(Mat, PetscInt, const MatStencil[], PetscInt, const MatStencil[], const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode MatSetStencil(Mat, PetscInt, const PetscInt[], const PetscInt[], PetscInt);

/*E
    MatAssemblyType - Indicates if the process of setting values into the matrix is complete, and the matrix is ready for use

    Values:
+   `MAT_FLUSH_ASSEMBLY` - you will continue to put values into the matrix
-   `MAT_FINAL_ASSEMBLY` - you wish to use the matrix with the values currently inserted

    Level: beginner

.seealso: [](ch_matrices), `Mat`, `MatSetValues`, `MatAssemblyBegin()`, `MatAssemblyEnd()`
E*/
typedef enum {
  MAT_FLUSH_ASSEMBLY = 1,
  MAT_FINAL_ASSEMBLY = 0
} MatAssemblyType;

PETSC_EXTERN PetscErrorCode MatAssemblyBegin(Mat, MatAssemblyType);
PETSC_EXTERN PetscErrorCode MatAssemblyEnd(Mat, MatAssemblyType);
PETSC_EXTERN PetscErrorCode MatAssembled(Mat, PetscBool *);

/*E
   MatOption - Options that may be set for a matrix that indicate properties of the matrix or affect its behavior or storage

   Level: beginner

   Note:
   See `MatSetOption()` for the use of the options

   Developer Note:
   Entries that are negative need not be called collectively by all processes.

.seealso: [](ch_matrices), `Mat`, `MatSetOption()`
E*/
typedef enum {
  MAT_OPTION_MIN                  = -3,
  MAT_UNUSED_NONZERO_LOCATION_ERR = -2,
  MAT_ROW_ORIENTED                = -1,
  MAT_SYMMETRIC                   = 1,
  MAT_STRUCTURALLY_SYMMETRIC      = 2,
  MAT_FORCE_DIAGONAL_ENTRIES      = 3,
  MAT_IGNORE_OFF_PROC_ENTRIES     = 4,
  MAT_USE_HASH_TABLE              = 5,
  MAT_KEEP_NONZERO_PATTERN        = 6,
  MAT_IGNORE_ZERO_ENTRIES         = 7,
  MAT_USE_INODES                  = 8,
  MAT_HERMITIAN                   = 9,
  MAT_SYMMETRY_ETERNAL            = 10,
  MAT_NEW_NONZERO_LOCATION_ERR    = 11,
  MAT_IGNORE_LOWER_TRIANGULAR     = 12,
  MAT_ERROR_LOWER_TRIANGULAR      = 13,
  MAT_GETROW_UPPERTRIANGULAR      = 14,
  MAT_SPD                         = 15,
  MAT_NO_OFF_PROC_ZERO_ROWS       = 16,
  MAT_NO_OFF_PROC_ENTRIES         = 17,
  MAT_NEW_NONZERO_LOCATIONS       = 18,
  MAT_NEW_NONZERO_ALLOCATION_ERR  = 19,
  MAT_SUBSET_OFF_PROC_ENTRIES     = 20,
  MAT_SUBMAT_SINGLEIS             = 21,
  MAT_STRUCTURE_ONLY              = 22,
  MAT_SORTED_FULL                 = 23,
  MAT_FORM_EXPLICIT_TRANSPOSE     = 24,
  MAT_STRUCTURAL_SYMMETRY_ETERNAL = 25,
  MAT_SPD_ETERNAL                 = 26,
  MAT_OPTION_MAX                  = 27
} MatOption;

PETSC_EXTERN const char *const *MatOptions;
PETSC_EXTERN PetscErrorCode     MatSetOption(Mat, MatOption, PetscBool);
PETSC_EXTERN PetscErrorCode     MatGetOption(Mat, MatOption, PetscBool *);
PETSC_EXTERN PetscErrorCode     MatPropagateSymmetryOptions(Mat, Mat);
PETSC_EXTERN PetscErrorCode     MatGetType(Mat, MatType *);

PETSC_EXTERN PetscErrorCode    MatGetValues(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscScalar[]);
PETSC_EXTERN PetscErrorCode    MatGetRow(Mat, PetscInt, PetscInt *, const PetscInt *[], const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatRestoreRow(Mat, PetscInt, PetscInt *, const PetscInt *[], const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatGetRowUpperTriangular(Mat);
PETSC_EXTERN PetscErrorCode    MatRestoreRowUpperTriangular(Mat);
PETSC_EXTERN PetscErrorCode    MatGetColumnVector(Mat, Vec, PetscInt);
PETSC_EXTERN PetscErrorCode    MatSeqAIJGetArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqAIJGetArrayRead(Mat, const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqAIJGetArrayWrite(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqAIJRestoreArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqAIJRestoreArrayRead(Mat, const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqAIJRestoreArrayWrite(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqAIJGetMaxRowNonzeros(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode    MatSeqAIJSetValuesLocalFast(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode    MatSeqAIJSetType(Mat, MatType);
PETSC_EXTERN PetscErrorCode    MatSeqAIJKron(Mat, Mat, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode    MatSeqAIJRegister(const char[], PetscErrorCode (*)(Mat, MatType, MatReuse, Mat *));
PETSC_EXTERN PetscFunctionList MatSeqAIJList;
PETSC_EXTERN PetscErrorCode    MatSeqBAIJGetArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqBAIJRestoreArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqSBAIJGetArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatSeqSBAIJRestoreArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseGetArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseRestoreArray(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDensePlaceArray(Mat, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode    MatDenseReplaceArray(Mat, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode    MatDenseResetArray(Mat);
PETSC_EXTERN PetscErrorCode    MatDenseGetArrayRead(Mat, const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseRestoreArrayRead(Mat, const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseGetArrayWrite(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseRestoreArrayWrite(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseGetArrayAndMemType(Mat, PetscScalar *[], PetscMemType *);
PETSC_EXTERN PetscErrorCode    MatDenseRestoreArrayAndMemType(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseGetArrayReadAndMemType(Mat, const PetscScalar *[], PetscMemType *);
PETSC_EXTERN PetscErrorCode    MatDenseRestoreArrayReadAndMemType(Mat, const PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatDenseGetArrayWriteAndMemType(Mat, PetscScalar *[], PetscMemType *);
PETSC_EXTERN PetscErrorCode    MatDenseRestoreArrayWriteAndMemType(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode    MatGetBlockSize(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode    MatSetBlockSize(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode    MatGetBlockSizes(Mat, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode    MatSetBlockSizes(Mat, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode    MatSetBlockSizesFromMats(Mat, Mat, Mat);
PETSC_EXTERN PetscErrorCode    MatSetVariableBlockSizes(Mat, PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode    MatGetVariableBlockSizes(Mat, PetscInt *, const PetscInt *[]);
PETSC_EXTERN PetscErrorCode    MatSelectVariableBlockSizes(Mat, Mat, IS);

PETSC_EXTERN PetscErrorCode MatDenseGetColumn(Mat, PetscInt, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode MatDenseRestoreColumn(Mat, PetscScalar *[]);
PETSC_EXTERN PetscErrorCode MatDenseGetColumnVec(Mat, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode MatDenseRestoreColumnVec(Mat, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode MatDenseGetColumnVecRead(Mat, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode MatDenseRestoreColumnVecRead(Mat, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode MatDenseGetColumnVecWrite(Mat, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode MatDenseRestoreColumnVecWrite(Mat, PetscInt, Vec *);
PETSC_EXTERN PetscErrorCode MatDenseGetSubMatrix(Mat, PetscInt, PetscInt, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatDenseRestoreSubMatrix(Mat, Mat *);

PETSC_EXTERN PetscErrorCode MatMult(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMultDiagonalBlock(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMultAdd(Mat, Vec, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMultTranspose(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMultHermitianTranspose(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatIsTranspose(Mat, Mat, PetscReal, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsHermitianTranspose(Mat, Mat, PetscReal, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultTransposeAdd(Mat, Vec, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMultHermitianTransposeAdd(Mat, Vec, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMatSolve(Mat, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatMatSolveTranspose(Mat, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatMatTransposeSolve(Mat, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatResidual(Mat, Vec, Vec, Vec);

/*E
  MatDuplicateOption - Indicates if a duplicated sparse matrix should have
  its numerical values copied over or just its nonzero structure.

  Values:
+ `MAT_DO_NOT_COPY_VALUES`    - Create a matrix using the same nonzero pattern as the original matrix,
                                with zeros for the numerical values
. `MAT_COPY_VALUES`           - Create a matrix with the same nonzero pattern as the original matrix
                                and with the same numerical values.
- `MAT_SHARE_NONZERO_PATTERN` - Create a matrix that shares the nonzero structure with the previous matrix
                                and does not copy it, using zeros for the numerical values. The parent and
                                child matrices will share their index (i and j) arrays, and you cannot
                                insert new nonzero entries into either matrix

  Level: beginner

  Note:
  Many matrix types (including `MATSEQAIJ`) do not support the `MAT_SHARE_NONZERO_PATTERN` optimization; in
  this case the behavior is as if `MAT_DO_NOT_COPY_VALUES` has been specified.

.seealso: [](ch_matrices), `Mat`, `MatDuplicate()`
E*/
typedef enum {
  MAT_DO_NOT_COPY_VALUES,
  MAT_COPY_VALUES,
  MAT_SHARE_NONZERO_PATTERN
} MatDuplicateOption;

PETSC_EXTERN PetscErrorCode MatConvert(Mat, MatType, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatDuplicate(Mat, MatDuplicateOption, Mat *);

PETSC_EXTERN PetscErrorCode MatCopy(Mat, Mat, MatStructure);
PETSC_EXTERN PetscErrorCode MatView(Mat, PetscViewer);
PETSC_EXTERN PetscErrorCode MatIsSymmetric(Mat, PetscReal, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsStructurallySymmetric(Mat, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsHermitian(Mat, PetscReal, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsSymmetricKnown(Mat, PetscBool *, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsHermitianKnown(Mat, PetscBool *, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsStructurallySymmetricKnown(Mat, PetscBool *, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsSPDKnown(Mat, PetscBool *, PetscBool *);
PETSC_EXTERN PetscErrorCode MatLoad(Mat, PetscViewer);

PETSC_EXTERN PetscErrorCode MatGetRowIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_EXTERN PetscErrorCode MatRestoreRowIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_EXTERN PetscErrorCode MatGetColumnIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_EXTERN PetscErrorCode MatRestoreColumnIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);

/*S
   MatInfo - Context of matrix information, used with `MatGetInfo()`

   Level: intermediate

   Fortran Note:
   `MatInfo` is a derived type, use e.g. `matinfo%nz_allocated` to access its components.

.seealso: [](ch_matrices), `Mat`, `MatGetInfo()`, `MatInfoType`
S*/
typedef struct {
  PetscLogDouble block_size;                          /* block size */
  PetscLogDouble nz_allocated, nz_used, nz_unneeded;  /* number of nonzeros */
  PetscLogDouble memory;                              /* memory allocated */
  PetscLogDouble assemblies;                          /* number of matrix assemblies called */
  PetscLogDouble mallocs;                             /* number of mallocs during MatSetValues() */
  PetscLogDouble fill_ratio_given, fill_ratio_needed; /* fill ratio for LU/ILU */
  PetscLogDouble factor_mallocs;                      /* number of mallocs during factorization */
} MatInfo;

/*E
    MatInfoType - Indicates if you want information about the local part of the matrix,
    the entire parallel matrix or the maximum over all the local parts.

    Values:
+   `MAT_LOCAL`      - values for each MPI process part of the matrix
.   `MAT_GLOBAL_MAX` - maximum of each value over all MPI processes
-   `MAT_GLOBAL_SUM` - sum of each value over all MPI processes

    Level: beginner

.seealso: [](ch_matrices), `MatGetInfo()`, `MatInfo`
E*/
typedef enum {
  MAT_LOCAL      = 1,
  MAT_GLOBAL_MAX = 2,
  MAT_GLOBAL_SUM = 3
} MatInfoType;
PETSC_EXTERN PetscErrorCode MatGetInfo(Mat, MatInfoType, MatInfo *);
PETSC_EXTERN PetscErrorCode MatGetDiagonal(Mat, Vec);
PETSC_EXTERN PetscErrorCode MatGetRowMax(Mat, Vec, PetscInt[]);
PETSC_EXTERN PetscErrorCode MatGetRowMin(Mat, Vec, PetscInt[]);
PETSC_EXTERN PetscErrorCode MatGetRowMaxAbs(Mat, Vec, PetscInt[]);
PETSC_EXTERN PetscErrorCode MatGetRowSumAbs(Mat, Vec);
PETSC_EXTERN PetscErrorCode MatGetRowMinAbs(Mat, Vec, PetscInt[]);
PETSC_EXTERN PetscErrorCode MatGetRowSum(Mat, Vec);
PETSC_EXTERN PetscErrorCode MatTranspose(Mat, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatTransposeSymbolic(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatTransposeSetPrecursor(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatHermitianTranspose(Mat, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatPermute(Mat, IS, IS, Mat *);
PETSC_EXTERN PetscErrorCode MatDiagonalScale(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatDiagonalSet(Mat, Vec, InsertMode);

PETSC_EXTERN PetscErrorCode MatEqual(Mat, Mat, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultEqual(Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultAddEqual(Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultTransposeEqual(Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultTransposeAddEqual(Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultHermitianTransposeEqual(Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMultHermitianTransposeAddEqual(Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMatMultEqual(Mat, Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatTransposeMatMultEqual(Mat, Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatMatTransposeMultEqual(Mat, Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatPtAPMultEqual(Mat, Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatRARtMultEqual(Mat, Mat, Mat, PetscInt, PetscBool *);
PETSC_EXTERN PetscErrorCode MatIsLinear(Mat, PetscInt, PetscBool *);

PETSC_EXTERN PetscErrorCode MatNorm(Mat, NormType, PetscReal *);
PETSC_EXTERN PetscErrorCode MatGetColumnNorms(Mat, NormType, PetscReal *);
PETSC_EXTERN PetscErrorCode MatGetColumnSums(Mat, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatGetColumnSumsRealPart(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatGetColumnSumsImaginaryPart(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatGetColumnMeans(Mat, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatGetColumnMeansRealPart(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatGetColumnMeansImaginaryPart(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatGetColumnReductions(Mat, PetscInt, PetscReal *);
PETSC_EXTERN PetscErrorCode MatZeroEntries(Mat);
PETSC_EXTERN PetscErrorCode MatSetInf(Mat);
PETSC_EXTERN PetscErrorCode MatZeroRows(Mat, PetscInt, const PetscInt[], PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsIS(Mat, IS, PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsStencil(Mat, PetscInt, const MatStencil[], PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsColumnsStencil(Mat, PetscInt, const MatStencil[], PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsColumns(Mat, PetscInt, const PetscInt[], PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsColumnsIS(Mat, IS, PetscScalar, Vec, Vec);

PETSC_EXTERN PetscErrorCode MatGetSize(Mat, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatGetLocalSize(Mat, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatGetOwnershipRange(Mat, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatGetOwnershipRanges(Mat, const PetscInt **);
PETSC_EXTERN PetscErrorCode MatGetOwnershipRangeColumn(Mat, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatGetOwnershipRangesColumn(Mat, const PetscInt **);
PETSC_EXTERN PetscErrorCode MatGetOwnershipIS(Mat, IS *, IS *);

PETSC_EXTERN PetscErrorCode MatCreateSubMatrices(Mat, PetscInt, const IS[], const IS[], MatReuse, Mat *[]);
PETSC_DEPRECATED_FUNCTION(3, 8, 0, "MatCreateSubMatrices()", ) static inline PetscErrorCode MatGetSubMatrices(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
{
  return MatCreateSubMatrices(mat, n, irow, icol, scall, submat);
}
PETSC_EXTERN PetscErrorCode MatCreateSubMatricesMPI(Mat, PetscInt, const IS[], const IS[], MatReuse, Mat *[]);
PETSC_DEPRECATED_FUNCTION(3, 8, 0, "MatCreateSubMatricesMPI()", ) static inline PetscErrorCode MatGetSubMatricesMPI(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
{
  return MatCreateSubMatricesMPI(mat, n, irow, icol, scall, submat);
}
PETSC_EXTERN PetscErrorCode MatDestroyMatrices(PetscInt, Mat *[]);
PETSC_EXTERN PetscErrorCode MatDestroySubMatrices(PetscInt, Mat *[]);
PETSC_EXTERN PetscErrorCode MatCreateSubMatrix(Mat, IS, IS, MatReuse, Mat *);
PETSC_DEPRECATED_FUNCTION(3, 8, 0, "MatCreateSubMatrix()", ) static inline PetscErrorCode MatGetSubMatrix(Mat mat, IS isrow, IS iscol, MatReuse cll, Mat *newmat)
{
  return MatCreateSubMatrix(mat, isrow, iscol, cll, newmat);
}
PETSC_EXTERN PetscErrorCode MatGetLocalSubMatrix(Mat, IS, IS, Mat *);
PETSC_EXTERN PetscErrorCode MatRestoreLocalSubMatrix(Mat, IS, IS, Mat *);
PETSC_EXTERN PetscErrorCode MatGetSeqNonzeroStructure(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatDestroySeqNonzeroStructure(Mat *);

PETSC_EXTERN PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm, Mat, PetscInt, PetscInt, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm, Mat, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatMPIAIJGetLocalMat(Mat, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatAIJGetLocalMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat, MatReuse, IS *, IS *, Mat *);
PETSC_EXTERN PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat, MatReuse, IS *, Mat *);
PETSC_EXTERN PetscErrorCode MatMPIAIJGetNumberNonzeros(Mat, PetscCount *);
PETSC_EXTERN PetscErrorCode MatGetBrowsOfAcols(Mat, Mat, MatReuse, IS *, IS *, Mat *);
PETSC_EXTERN PetscErrorCode MatGetGhosts(Mat, PetscInt *, const PetscInt *[]);

PETSC_EXTERN PetscErrorCode MatIncreaseOverlap(Mat, PetscInt, IS[], PetscInt);
PETSC_EXTERN PetscErrorCode MatIncreaseOverlapSplit(Mat, PetscInt, IS[], PetscInt);
PETSC_EXTERN PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat, PetscBool);

PETSC_EXTERN PetscErrorCode MatMatMult(Mat, Mat, MatReuse, PetscReal, Mat *);

PETSC_EXTERN PetscErrorCode MatMatMatMult(Mat, Mat, Mat, MatReuse, PetscReal, Mat *);
PETSC_EXTERN PetscErrorCode MatGalerkin(Mat, Mat, Mat, MatReuse, PetscReal, Mat *);

PETSC_EXTERN PetscErrorCode MatPtAP(Mat, Mat, MatReuse, PetscReal, Mat *);
PETSC_EXTERN PetscErrorCode MatRARt(Mat, Mat, MatReuse, PetscReal, Mat *);

PETSC_EXTERN PetscErrorCode MatTransposeMatMult(Mat, Mat, MatReuse, PetscReal, Mat *);
PETSC_EXTERN PetscErrorCode MatMatTransposeMult(Mat, Mat, MatReuse, PetscReal, Mat *);

PETSC_EXTERN PetscErrorCode MatAXPY(Mat, PetscScalar, Mat, MatStructure);
PETSC_EXTERN PetscErrorCode MatAYPX(Mat, PetscScalar, Mat, MatStructure);

PETSC_EXTERN PetscErrorCode MatScale(Mat, PetscScalar);
PETSC_EXTERN PetscErrorCode MatShift(Mat, PetscScalar);

PETSC_EXTERN PetscErrorCode MatSetLocalToGlobalMapping(Mat, ISLocalToGlobalMapping, ISLocalToGlobalMapping);
PETSC_EXTERN PetscErrorCode MatGetLocalToGlobalMapping(Mat, ISLocalToGlobalMapping *, ISLocalToGlobalMapping *);
PETSC_EXTERN PetscErrorCode MatGetLayouts(Mat, PetscLayout *, PetscLayout *);
PETSC_EXTERN PetscErrorCode MatSetLayouts(Mat, PetscLayout, PetscLayout);
PETSC_EXTERN PetscErrorCode MatZeroRowsLocal(Mat, PetscInt, const PetscInt[], PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsLocalIS(Mat, IS, PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsColumnsLocal(Mat, PetscInt, const PetscInt[], PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatZeroRowsColumnsLocalIS(Mat, IS, PetscScalar, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatGetValuesLocal(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatSetValuesLocal(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);
PETSC_EXTERN PetscErrorCode MatSetValuesBlockedLocal(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);

PETSC_EXTERN PetscErrorCode MatStashSetInitialSize(Mat, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode MatStashGetInfo(Mat, PetscInt *, PetscInt *, PetscInt *, PetscInt *);

PETSC_EXTERN PetscErrorCode MatInterpolate(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatInterpolateAdd(Mat, Vec, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatRestrict(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMatInterpolate(Mat, Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatMatInterpolateAdd(Mat, Mat, Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatMatRestrict(Mat, Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateVecs(Mat, Vec *, Vec *);
PETSC_DEPRECATED_FUNCTION(3, 6, 0, "MatCreateVecs()", ) static inline PetscErrorCode MatGetVecs(Mat mat, Vec *x, Vec *y)
{
  return MatCreateVecs(mat, x, y);
}
PETSC_EXTERN PetscErrorCode MatCreateRedundantMatrix(Mat, PetscInt, MPI_Comm, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatGetMultiProcBlock(Mat, MPI_Comm, MatReuse, Mat *);
PETSC_EXTERN PetscErrorCode MatFindZeroDiagonals(Mat, IS *);
PETSC_EXTERN PetscErrorCode MatFindOffBlockDiagonalEntries(Mat, IS *);
PETSC_EXTERN PetscErrorCode MatCreateMPIMatConcatenateSeqMat(MPI_Comm, Mat, PetscInt, MatReuse, Mat *);

PETSC_EXTERN PetscErrorCode MatCopyHashToXAIJ(Mat A, Mat B);
/*@C
   MatSetValue - Set a single entry into a matrix.

   Not Collective

   Input Parameters:
+  mat  - the matrix
.  i    - the row location of the entry
.  j    - the column location of the entry
.  va   - the value to insert
-  mode - either `INSERT_VALUES` or `ADD_VALUES`

   Level: beginner

   Notes:
   This value may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
   MUST be called after all calls to `MatSetValue()` have been completed.

   For efficiency one should use `MatSetValues()` and set several values simultaneously.

.seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `InsertMode`, `MatGetValue()`, `MatSetValues()`,
          `MatSetValueLocal()`, `MatSetValuesLocal()`
@*/
static inline PetscErrorCode MatSetValue(Mat mat, PetscInt i, PetscInt j, PetscScalar va, InsertMode mode)
{
  return MatSetValues(mat, 1, &i, 1, &j, &va, mode);
}

/*@C
   MatGetValue - Gets a single value from a matrix

   Not Collective; can only return a value owned by the given process

   Input Parameters:
+  mat - the matrix
.  row - the row location of the entry
-  col - the column location of the entry

   Output Parameter:
.  va - the value

   Level: advanced

   Notes:
   The matrix must have been assembled with `MatAssemblyBegin()` and `MatAssemblyEnd()` before this call

   For efficiency one should use `MatGetValues()` and get several values simultaneously.

   See notes for `MatGetValues()`.

.seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValue()`, `MatGetValuesLocal()`, `MatGetValues()`
@*/
static inline PetscErrorCode MatGetValue(Mat mat, PetscInt row, PetscInt col, PetscScalar *va)
{
  return MatGetValues(mat, 1, &row, 1, &col, va);
}

/*@C
   MatSetValueLocal - Inserts or adds a single value into a matrix, using a local numbering of the nodes.

   Not Collective

   Input Parameters:
+  mat  - the matrix
.  i    - the row location of the entry
.  j    - the column location of the entry
.  va   - the value to insert
-  mode - either `INSERT_VALUES` or `ADD_VALUES`

   Level: intermediate

   Notes:
   For efficiency one should use `MatSetValuesLocal()` and set several values simultaneously.

   See notes for `MatSetValuesLocal()` for additional information on when and how this function can be used.

.seealso: [](ch_matrices), `MatSetValue()`, `MatSetValuesLocal()`
@*/
static inline PetscErrorCode MatSetValueLocal(Mat mat, PetscInt i, PetscInt j, PetscScalar va, InsertMode mode)
{
  return MatSetValuesLocal(mat, 1, &i, 1, &j, &va, mode);
}

/*MC
   MatPreallocateBegin - Begins the block of code that will count the number of nonzeros per
   row in a matrix providing the data that one can use to correctly preallocate the matrix.

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateBegin(MPI_Comm comm, PetscInt nrows, PetscInt ncols, PetscInt *dnz, PetscInt *onz)

   Collective

   Input Parameters:
+  comm  - the communicator that will share the eventually allocated matrix
.  nrows - the number of LOCAL rows in the matrix
-  ncols - the number of LOCAL columns in the matrix

   Output Parameters:
+  dnz - the array that will be passed to the matrix preallocation routines
-  onz - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   This is a macro that handles its own error checking, it does not return an error code.

   Do not malloc or free `dnz` and `onz`, that is handled internally by these routines

   Developer Note:
   This is a MACRO, not a function, because it has a leading { that is closed by `PetscPreallocateFinalize()`.

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`, `MatPreallocateSetLocal()`,
          `MatPreallocateSymmetricSetLocalBlock()`
M*/
#define MatPreallocateBegin(comm, nrows, ncols, dnz, onz) \
  do { \
    PetscInt              __nrows = (nrows), __ncols = (ncols), __rstart, __end = 0; \
    PetscInt PETSC_UNUSED __start; \
    PetscCall(PetscCalloc2(__nrows, &(dnz), __nrows, &(onz))); \
    PetscCallMPI(MPI_Scan(&__ncols, &__end, 1, MPIU_INT, MPI_SUM, comm)); \
    __start = __end - __ncols; \
    (void)__start; \
    PetscCallMPI(MPI_Scan(&__nrows, &__rstart, 1, MPIU_INT, MPI_SUM, comm)); \
  __rstart -= __nrows

#define MatPreallocateInitialize(...) PETSC_DEPRECATED_MACRO(3, 18, 0, "MatPreallocateBegin()", ) MatPreallocateBegin(__VA_ARGS__)

/*MC
   MatPreallocateSetLocal - Indicates the locations (rows and columns) in the matrix where nonzeros will be
   inserted using a local number of the rows and columns

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateSetLocal(ISLocalToGlobalMappping map,PetscInt nrows, PetscInt *rows,PetscInt ncols, PetscInt *cols,PetscInt *dnz, PetscInt *onz)

   Not Collective

   Input Parameters:
+  map   - the row mapping from local numbering to global numbering
.  nrows - the number of rows indicated
.  rows  - the indices of the rows
.  cmap  - the column mapping from local to global numbering
.  ncols - the number of columns in the matrix
.  cols  - the columns indicated
.  dnz   - the array that will be passed to the matrix preallocation routines
-  onz   - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz`, that is handled internally by these routines

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`
          `MatPreallocateBegin()`, `MatPreallocateSymmetricSetLocalBlock()`, `MatPreallocateSetLocalRemoveDups()`
M*/
#define MatPreallocateSetLocal(rmap, nrows, rows, cmap, ncols, cols, dnz, onz) \
  PetscMacroReturnStandard(PetscCall(ISLocalToGlobalMappingApply(rmap, nrows, rows, rows)); PetscCall(ISLocalToGlobalMappingApply(cmap, ncols, cols, cols)); for (PetscInt __l = 0; __l < nrows; __l++) PetscCall(MatPreallocateSet((rows)[__l], ncols, cols, dnz, onz));)

/*MC
   MatPreallocateSetLocalRemoveDups - Indicates the locations (rows and columns) in the matrix where nonzeros will be
   inserted using a local number of the rows and columns. This version removes any duplicate columns in cols

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateSetLocalRemoveDups(ISLocalToGlobalMappping map,PetscInt nrows, PetscInt *rows,PetscInt ncols, PetscInt *cols,PetscInt *dnz, PetscInt *onz)

   Not Collective

   Input Parameters:
+  map   - the row mapping from local numbering to global numbering
.  nrows - the number of rows indicated
.  rows  - the indices of the rows (these values are mapped to the global values)
.  cmap  - the column mapping from local to global numbering
.  ncols - the number of columns in the matrix   (this value will be changed if duplicate columns are found)
.  cols  - the columns indicated (these values are mapped to the global values, they are then sorted and duplicates removed)
.  dnz   - the array that will be passed to the matrix preallocation routines
-  onz   - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz`, that is handled internally by these routines

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`
          `MatPreallocateBegin()`, `MatPreallocateSymmetricSetLocalBlock()`, `MatPreallocateSetLocal()`
M*/
#define MatPreallocateSetLocalRemoveDups(rmap, nrows, rows, cmap, ncols, cols, dnz, onz) \
  PetscMacroReturnStandard(PetscCall(ISLocalToGlobalMappingApply(rmap, nrows, rows, rows)); PetscCall(ISLocalToGlobalMappingApply(cmap, ncols, cols, cols)); PetscCall(PetscSortRemoveDupsInt(&ncols, cols)); for (PetscInt __l = 0; __l < nrows; __l++) PetscCall(MatPreallocateSet((rows)[__l], ncols, cols, dnz, onz));)

/*MC
   MatPreallocateSetLocalBlock - Indicates the locations (rows and columns) in the matrix where nonzeros will be
   inserted using a local number of the rows and columns

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateSetLocalBlock(ISLocalToGlobalMappping map,PetscInt nrows, PetscInt *rows,PetscInt ncols, PetscInt *cols,PetscInt *dnz, PetscInt *onz)

   Not Collective

   Input Parameters:
+  map   - the row mapping from local numbering to global numbering
.  nrows - the number of rows indicated
.  rows  - the indices of the rows
.  cmap  - the column mapping from local to global numbering
.  ncols - the number of columns in the matrix
.  cols  - the columns indicated
.  dnz   - the array that will be passed to the matrix preallocation routines
-  onz   - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz`, that is handled internally by these routines

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`
          `MatPreallocateBegin()`, `MatPreallocateSymmetricSetLocalBlock()`
M*/
#define MatPreallocateSetLocalBlock(rmap, nrows, rows, cmap, ncols, cols, dnz, onz) \
  PetscMacroReturnStandard(PetscCall(ISLocalToGlobalMappingApplyBlock(rmap, nrows, rows, rows)); PetscCall(ISLocalToGlobalMappingApplyBlock(cmap, ncols, cols, cols)); for (PetscInt __l = 0; __l < nrows; __l++) PetscCall(MatPreallocateSet((rows)[__l], ncols, cols, dnz, onz));)

/*MC
   MatPreallocateSymmetricSetLocalBlock - Indicates the locations (rows and columns) in the matrix where nonzeros will be
   inserted using a local number of the rows and columns

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateSymmetricSetLocalBlock(ISLocalToGlobalMappping map,PetscInt nrows, PetscInt *rows,PetscInt ncols, PetscInt *cols,PetscInt *dnz, PetscInt *onz)

   Not Collective

   Input Parameters:
+  map   - the mapping between local numbering and global numbering
.  nrows - the number of rows indicated
.  rows  - the indices of the rows
.  ncols - the number of columns in the matrix
.  cols  - the columns indicated
.  dnz   - the array that will be passed to the matrix preallocation routines
-  onz   - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz` that is handled internally by these routines

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`
          `MatPreallocateBegin()`, `MatPreallocateSetLocal()`
M*/
#define MatPreallocateSymmetricSetLocalBlock(map, nrows, rows, ncols, cols, dnz, onz) \
  PetscMacroReturnStandard(PetscCall(ISLocalToGlobalMappingApplyBlock(map, nrows, rows, rows)); PetscCall(ISLocalToGlobalMappingApplyBlock(map, ncols, cols, cols)); for (PetscInt __l = 0; __l < nrows; __l++) PetscCall(MatPreallocateSymmetricSetBlock((rows)[__l], ncols, cols, dnz, onz));)

/*MC
   MatPreallocateSet - Indicates the locations (rows and columns) in the matrix where nonzeros will be
   inserted using a local number of the rows and columns

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateSet(PetscInt nrows, PetscInt *rows,PetscInt ncols, PetscInt *cols,PetscInt *dnz, PetscInt *onz)

   Not Collective

   Input Parameters:
+  row   - the row
.  ncols - the number of columns in the matrix
-  cols  - the columns indicated

   Output Parameters:
+  dnz - the array that will be passed to the matrix preallocation routines
-  onz - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz` that is handled internally by these routines

   This is a MACRO, not a function, because it uses variables declared in MatPreallocateBegin().

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`
          `MatPreallocateBegin()`, `MatPreallocateSetLocal()`
M*/
#define MatPreallocateSet(row, nc, cols, dnz, onz) \
  PetscMacroReturnStandard(PetscCheck(row >= __rstart, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Trying to set preallocation for row %" PetscInt_FMT " less than first local row %" PetscInt_FMT, row, __rstart); PetscCheck(row < __rstart + __nrows, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Trying to set preallocation for row %" PetscInt_FMT " greater than last local row %" PetscInt_FMT, row, __rstart + __nrows - 1); for (PetscInt __i = 0; __i < nc; ++__i) { \
    if ((cols)[__i] < __start || (cols)[__i] >= __end) onz[row - __rstart]++; \
    else if (dnz[row - __rstart] < __ncols) dnz[row - __rstart]++; \
  })

/*MC
   MatPreallocateSymmetricSetBlock - Indicates the locations (rows and columns) in the matrix where nonzeros will be
   inserted using a local number of the rows and columns

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateSymmetricSetBlock(PetscInt nrows, PetscInt *rows,PetscInt ncols, PetscInt *cols,PetscInt *dnz, PetscInt *onz)

   Not Collective

   Input Parameters:
+  nrows - the number of rows indicated
.  rows  - the indices of the rows
.  ncols - the number of columns in the matrix
.  cols  - the columns indicated
.  dnz   - the array that will be passed to the matrix preallocation routines
-  onz   - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz` that is handled internally by these routines

   This is a MACRO, not a function, because it uses variables declared in MatPreallocateBegin().

.seealso: [](ch_matrices), `MatPreallocateEnd()`, `MatPreallocateSet()`, `MatPreallocateBegin()`,
          `MatPreallocateSymmetricSetLocalBlock()`, `MatPreallocateSetLocal()`
M*/
#define MatPreallocateSymmetricSetBlock(row, nc, cols, dnz, onz) \
  PetscMacroReturnStandard(for (PetscInt __i = 0; __i < nc; __i++) { \
    if (cols[__i] >= __end) onz[row - __rstart]++; \
    else if (cols[__i] >= row && dnz[row - __rstart] < __ncols) dnz[row - __rstart]++; \
  })

/*MC
   MatPreallocateLocation -  An alternative to MatPreallocateSet() that puts the nonzero locations into the matrix if it exists

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateLocations(Mat A,PetscInt row,PetscInt ncols,PetscInt *cols,PetscInt *dnz,PetscInt *onz)

   Not Collective

   Input Parameters:
+  A     - matrix
.  row   - row where values exist (must be local to this process)
.  ncols - number of columns
.  cols  - columns with nonzeros
.  dnz   - the array that will be passed to the matrix preallocation routines
-  onz   - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz` that is handled internally by these routines

   Developer Note:
   This is a MACRO, not a function, because it uses a bunch of variables private to the MatPreallocation.... routines.

.seealso: [](ch_matrices), `MatPreallocateBegin()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`, `MatPreallocateSetLocal()`,
          `MatPreallocateSymmetricSetLocalBlock()`
M*/
#define MatPreallocateLocation(A, row, ncols, cols, dnz, onz) (A ? MatSetValues(A, 1, &row, ncols, cols, NULL, INSERT_VALUES) : MatPreallocateSet(row, ncols, cols, dnz, onz))

/*MC
   MatPreallocateEnd - Ends the block of code that will count the number of nonzeros per
   row in a matrix providing the data that one can use to correctly preallocate the matrix.

   Synopsis:
   #include <petscmat.h>
   PetscErrorCode MatPreallocateEnd(PetscInt *dnz, PetscInt *onz)

   Collective

   Input Parameters:
+  dnz - the array that was be passed to the matrix preallocation routines
-  onz - the other array passed to the matrix preallocation routines

   Level: deprecated (since v3.19)

   Notes:
   This routine is no longer needed since assembling matrices without explicit preallocation will not be slower than
   the use of this routine

   Do not malloc or free `dnz` and `onz`, that is handled internally by these routines

   Developer Note:
   This is a MACRO, not a function, because it closes the { started in MatPreallocateBegin().

.seealso: [](ch_matrices), `MatPreallocateBegin()`, `MatPreallocateSet()`, `MatPreallocateSymmetricSetBlock()`, `MatPreallocateSetLocal()`,
          `MatPreallocateSymmetricSetLocalBlock()`
M*/
#define MatPreallocateEnd(dnz, onz) \
  PetscCall(PetscFree2(dnz, onz)); \
  } \
  while (0)

#define MatPreallocateFinalize(...) PETSC_DEPRECATED_MACRO(3, 18, 0, "MatPreallocateEnd()", ) MatPreallocateEnd(__VA_ARGS__)

/* Routines unique to particular data structures */
PETSC_EXTERN PetscErrorCode MatShellGetContext(Mat, PetscCtxRt);

PETSC_EXTERN PetscErrorCode MatInodeAdjustForInodes(Mat, IS *, IS *);
PETSC_EXTERN PetscErrorCode MatInodeGetInodeSizes(Mat, PetscInt *, PetscInt *[], PetscInt *);

PETSC_EXTERN PetscErrorCode MatSeqAIJSetColumnIndices(Mat, PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSeqBAIJSetColumnIndices(Mat, PetscInt[]);
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJWithArrays(MPI_Comm, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqBAIJWithArrays(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqSBAIJWithArrays(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJFromTriple(MPI_Comm, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], Mat *, PetscCount, PetscBool);

#define MAT_SKIP_ALLOCATION -4

PETSC_EXTERN PetscErrorCode MatSeqBAIJSetPreallocation(Mat, PetscInt, PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSeqSBAIJSetPreallocation(Mat, PetscInt, PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSeqAIJSetPreallocation(Mat, PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSeqAIJSetTotalPreallocation(Mat, PetscInt);

PETSC_EXTERN PetscErrorCode MatMPIBAIJSetPreallocation(Mat, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatMPISBAIJSetPreallocation(Mat, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatMPIAIJSetPreallocation(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatSeqBAIJSetPreallocationCSR(Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatMPIAIJSetPreallocationCSR(Mat, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatMPIBAIJSetPreallocationCSR(Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatMPIAdjSetPreallocation(Mat, PetscInt[], PetscInt[], PetscInt[]);
PETSC_EXTERN PetscErrorCode MatMPIAdjToSeq(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatMPIAdjToSeqRankZero(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatMPIDenseSetPreallocation(Mat, PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatSeqDenseSetPreallocation(Mat, PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatMPIAIJGetSeqAIJ(Mat, Mat *, Mat *, const PetscInt *[]);
PETSC_EXTERN PetscErrorCode MatMPIBAIJGetSeqBAIJ(Mat, Mat *, Mat *, const PetscInt *[]);
PETSC_EXTERN PetscErrorCode MatMPIAdjCreateNonemptySubcommMat(Mat, Mat *);

PETSC_EXTERN PetscErrorCode MatDenseGetLDA(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode MatDenseSetLDA(Mat, PetscInt);
PETSC_DEPRECATED_FUNCTION(3, 14, 0, "MatDenseSetLDA()", ) static inline PetscErrorCode MatSeqDenseSetLDA(Mat A, PetscInt lda)
{
  return MatDenseSetLDA(A, lda);
}
PETSC_EXTERN PetscErrorCode MatDenseGetLocalMatrix(Mat, Mat *);

PETSC_EXTERN PetscErrorCode MatBlockMatSetPreallocation(Mat, PetscInt, PetscInt, const PetscInt[]);

PETSC_EXTERN PetscErrorCode MatStoreValues(Mat);
PETSC_EXTERN PetscErrorCode MatRetrieveValues(Mat);

PETSC_EXTERN PetscErrorCode MatFindNonzeroRows(Mat, IS *);
PETSC_EXTERN PetscErrorCode MatFindZeroRows(Mat, IS *);
/*
  These routines are not usually accessed directly, rather solving is
  done through the KSP and PC interfaces.
*/

/*J
   MatOrderingType - String with the name of a PETSc matrix ordering. These orderings are most commonly used
   to reduce fill in sparse factorizations.

   Level: beginner

   Notes:
   If `MATORDERINGEXTERNAL` is used then PETSc does not compute an ordering and instead the external factorization solver package called utilizes one
   of its own.

   There is no `MatOrdering` object, the ordering is obtained directly from the matrix with `MatGetOrdering()`

   Developer Note:
   This API should be converted to an API similar to those for `MatColoring` and `MatPartitioning`

.seealso: [](ch_matrices), [](sec_graph), `MatGetFactor()`, `MatGetOrdering()`, `MatColoringType`, `MatPartitioningType`, `MatCoarsenType`, `MatCoarsenType`,
          `PCFactorSetOrderingType()`
J*/
typedef const char *MatOrderingType;
#define MATORDERINGNATURAL       "natural"
#define MATORDERINGND            "nd"
#define MATORDERING1WD           "1wd"
#define MATORDERINGRCM           "rcm"
#define MATORDERINGQMD           "qmd"
#define MATORDERINGROWLENGTH     "rowlength"
#define MATORDERINGWBM           "wbm"
#define MATORDERINGSPECTRAL      "spectral"
#define MATORDERINGAMD           "amd"           /* only works if UMFPACK is installed with PETSc */
#define MATORDERINGMETISND       "metisnd"       /* only works if METIS is installed with PETSc */
#define MATORDERINGNATURAL_OR_ND "natural_or_nd" /* special coase used for Cholesky and ICC, allows ND when AIJ matrix is used but Natural when SBAIJ is used */
#define MATORDERINGEXTERNAL      "external"      /* uses an ordering type internal to the factorization package */

PETSC_EXTERN PetscErrorCode    MatGetOrdering(Mat, MatOrderingType, IS *, IS *);
PETSC_EXTERN PetscErrorCode    MatGetOrderingList(PetscFunctionList *);
PETSC_EXTERN PetscErrorCode    MatOrderingRegister(const char[], PetscErrorCode (*)(Mat, MatOrderingType, IS *, IS *));
PETSC_EXTERN PetscFunctionList MatOrderingList;

#include "petscmatcoarsen.h"

PETSC_EXTERN PetscErrorCode MatReorderForNonzeroDiagonal(Mat, PetscReal, IS, IS);
PETSC_EXTERN PetscErrorCode MatCreateLaplacian(Mat, PetscReal, PetscBool, Mat *);

PETSC_EXTERN PetscErrorCode MatFactorGetPreferredOrdering(Mat, MatFactorType, MatOrderingType *);

/*S
   MatFactorShiftType - Type of numeric shift used for factorizations

   Values:
+  `MAT_SHIFT_NONE`              - do not shift the matrix diagonal entries
.  `MAT_SHIFT_NONZERO`           - shift the entries to be non-zero
.  `MAT_SHIFT_POSITIVE_DEFINITE` - shift the entries to force the factorization to be positive definite
-  `MAT_SHIFT_INBLOCKS`          - only shift the factors inside the small dense diagonal blocks of the matrix, for example with `MATBAIJ`

   Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `PCFactorSetShiftType()`
S*/
typedef enum {
  MAT_SHIFT_NONE,
  MAT_SHIFT_NONZERO,
  MAT_SHIFT_POSITIVE_DEFINITE,
  MAT_SHIFT_INBLOCKS
} MatFactorShiftType;
PETSC_EXTERN const char *const MatFactorShiftTypes[];
PETSC_EXTERN const char *const MatFactorShiftTypesDetail[];

/*S
    MatFactorError - indicates what type of error was generated in a matrix factorization

    Values:
+   `MAT_FACTOR_NOERROR`           - there was no error during the factorization
.   `MAT_FACTOR_STRUCT_ZEROPIVOT`  - there was a missing entry in a diagonal location of the matrix
.   `MAT_FACTOR_NUMERIC_ZEROPIVOT` - there was a (near) zero pivot during the factorization
.   `MAT_FACTOR_OUTMEMORY`         - the factorization has run out of memory
-   `MAT_FACTOR_OTHER`             - some other error has occurred.

    Level: intermediate

    Note:
    When a factorization is done in a preconditioner `PC` the error may be propagated up to a `PCFailedReason` or a `KSPConvergedReason`

.seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorGetError()`, `MatFactorGetErrorZeroPivot()`, `MatFactorClearError()`,
          `PCFailedReason`, `PCGetFailedReason()`, `KSPConvergedReason`
S*/
typedef enum {
  MAT_FACTOR_NOERROR,
  MAT_FACTOR_STRUCT_ZEROPIVOT,
  MAT_FACTOR_NUMERIC_ZEROPIVOT,
  MAT_FACTOR_OUTMEMORY,
  MAT_FACTOR_OTHER
} MatFactorError;

PETSC_EXTERN PetscErrorCode MatFactorGetError(Mat, MatFactorError *);
PETSC_EXTERN PetscErrorCode MatFactorClearError(Mat);
PETSC_EXTERN PetscErrorCode MatFactorGetErrorZeroPivot(Mat, PetscReal *, PetscInt *);

/*S
   MatFactorInfo - Data passed into the matrix factorization routines, and information about the resulting factorization

   Level: developer

   Note:
   You can use `MatFactorInfoInitialize()` to set default values.

   Fortran Note:
   `MatFactorInfo` is a derived type, use e.g. `matfactorinfo%dt` to access its components.

.seealso: [](ch_matrices), `Mat`, `MatInfo`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatILUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`,
          `MatICCFactorSymbolic()`, `MatICCFactor()`, `MatFactorInfoInitialize()`
S*/
typedef struct {
  PetscReal diagonal_fill; /* force diagonal to fill in if initially not filled */
  PetscReal usedt;
  PetscReal dt;            /* drop tolerance */
  PetscReal dtcol;         /* tolerance for pivoting */
  PetscReal dtcount;       /* maximum nonzeros to be allowed per row */
  PetscReal fill;          /* expected fill, nonzeros in factored matrix/nonzeros in original matrix */
  PetscReal levels;        /* ICC/ILU(levels) */
  PetscReal pivotinblocks; /* BAIJ and SBAIJ matrices pivot in factorization on blocks, default 1.0 factorization may be faster if do not pivot */
  PetscReal zeropivot;     /* pivot is called zero if less than this */
  PetscReal shifttype;     /* type of shift added to matrix factor to prevent zero pivots */
  PetscReal shiftamount;   /* how large the shift is */
  PetscBool factoronhost;  /* do factorization on host instead of device (for device matrix types) */
  PetscBool solveonhost;   /* do mat solve on host with the factor (for device matrix types) */
} MatFactorInfo;

PETSC_EXTERN PetscErrorCode MatFactorInfoInitialize(MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatCholeskyFactor(Mat, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatCholeskyFactorSymbolic(Mat, Mat, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatCholeskyFactorNumeric(Mat, Mat, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatLUFactor(Mat, IS, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatILUFactor(Mat, IS, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatLUFactorSymbolic(Mat, Mat, IS, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatILUFactorSymbolic(Mat, Mat, IS, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatICCFactorSymbolic(Mat, Mat, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatICCFactor(Mat, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatLUFactorNumeric(Mat, Mat, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatQRFactor(Mat, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatQRFactorSymbolic(Mat, Mat, IS, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatQRFactorNumeric(Mat, Mat, const MatFactorInfo *);
PETSC_EXTERN PetscErrorCode MatGetInertia(Mat, PetscInt *, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatSolve(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatForwardSolve(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatBackwardSolve(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatSolveAdd(Mat, Vec, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatSolveTranspose(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatSolveTransposeAdd(Mat, Vec, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatSolves(Mat, Vecs, Vecs);
PETSC_EXTERN PetscErrorCode MatSetUnfactored(Mat);

typedef enum {
  MAT_FACTOR_SCHUR_UNFACTORED,
  MAT_FACTOR_SCHUR_FACTORED,
  MAT_FACTOR_SCHUR_INVERTED
} MatFactorSchurStatus;
PETSC_EXTERN PetscErrorCode MatFactorSetSchurIS(Mat, IS);
PETSC_EXTERN PetscErrorCode MatFactorGetSchurComplement(Mat, Mat *, MatFactorSchurStatus *);
PETSC_EXTERN PetscErrorCode MatFactorRestoreSchurComplement(Mat, Mat *, MatFactorSchurStatus);
PETSC_EXTERN PetscErrorCode MatFactorInvertSchurComplement(Mat);
PETSC_EXTERN PetscErrorCode MatFactorCreateSchurComplement(Mat, Mat *, MatFactorSchurStatus *);
PETSC_EXTERN PetscErrorCode MatFactorSolveSchurComplement(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatFactorSolveSchurComplementTranspose(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatFactorFactorizeSchurComplement(Mat);

PETSC_EXTERN PetscErrorCode MatSeqDenseInvert(Mat);
/*E
   MatSORType - What type of (S)SOR to perform

   Values:
+  `SOR_FORWARD_SWEEP`         - do a sweep from the first row of the matrix to the last
.  `SOR_BACKWARD_SWEEP`        - do a sweep from the last row to the first
.  `SOR_SYMMETRIC_SWEEP`       - do a sweep from the first row to the last and then back to the first
.  `SOR_LOCAL_FORWARD_SWEEP`   - each MPI process does its own forward sweep with no communication
.  `SOR_LOCAL_BACKWARD_SWEEP`  - each MPI process does its own backward sweep with no communication
.  `SOR_LOCAL_SYMMETRIC_SWEEP` - each MPI process does its own symmetric sweep with no communication
.  `SOR_ZERO_INITIAL_GUESS`    - indicates the initial solution is zero so the sweep can avoid unneeded computation
.  `SOR_EISENSTAT`             - apply the Eisentat application of SOR, see `PCEISENSTAT`
.  `SOR_APPLY_UPPER`           - multiply by the upper triangular portion of the matrix
-  `SOR_APPLY_LOWER`           - multiply by the lower triangular portion of the matrix

   Level: beginner

   Note:
   These may be bitwise ORd together

   Developer Note:
   Since `MatSORType` may be bitwise ORd together, so do not change the numerical values below

.seealso: [](ch_matrices), `MatSOR()`
E*/
typedef enum {
  SOR_FORWARD_SWEEP         = 1,
  SOR_BACKWARD_SWEEP        = 2,
  SOR_SYMMETRIC_SWEEP       = 3,
  SOR_LOCAL_FORWARD_SWEEP   = 4,
  SOR_LOCAL_BACKWARD_SWEEP  = 8,
  SOR_LOCAL_SYMMETRIC_SWEEP = 12,
  SOR_ZERO_INITIAL_GUESS    = 16,
  SOR_EISENSTAT             = 32,
  SOR_APPLY_UPPER           = 64,
  SOR_APPLY_LOWER           = 128
} MatSORType;
PETSC_EXTERN PetscErrorCode MatSOR(Mat, Vec, PetscReal, MatSORType, PetscReal, PetscInt, PetscInt, Vec);

/*S
   MatColoring - Object for managing the coloring of matrices.

   Level: beginner

   Notes:
   Coloring of matrices can be computed directly from the sparse matrix nonzero structure via the `MatColoring` object or from the mesh from which the
   matrix comes from via `DMCreateColoring()`. In general using the mesh produces a more optimal coloring (fewer colors).

   Once a coloring is available `MatFDColoringCreate()` creates an object that can be used to efficiently compute Jacobians using that coloring. This
   same object can also be used to efficiently convert data created by Automatic Differentiation tools to PETSc sparse matrices.

.seealso: [](ch_matrices), [](sec_graph), `MatFDColoringCreate()`, `MatColoringWeightType`, `ISColoring`, `MatFDColoring`, `DMCreateColoring()`, `MatColoringCreate()`,
          `MatPartitioning`, `MatColoringType`, `MatPartitioningType`, `MatOrderingType`, `MatColoringSetWeightType()`,
          `MatColoringSetWeights()`, `MatCoarsenType`, `MatCoarsen`
S*/
typedef struct _p_MatColoring *MatColoring;

/*J
   MatColoringType - String with the name of a PETSc matrix coloring

   Level: beginner

.seealso: [](ch_matrices), [](sec_graph), `Mat`, `MatFDColoringCreate()`, `MatColoringSetType()`, `MatColoring`
J*/
typedef const char *MatColoringType;
#define MATCOLORINGJP      "jp"
#define MATCOLORINGPOWER   "power"
#define MATCOLORINGNATURAL "natural"
#define MATCOLORINGSL      "sl"
#define MATCOLORINGLF      "lf"
#define MATCOLORINGID      "id"
#define MATCOLORINGGREEDY  "greedy"

/*E
   MatColoringWeightType - Type of weight scheme used for the coloring algorithm

   Values:
+  `MAT_COLORING_RANDOM`  - Random weights
.  `MAT_COLORING_LEXICAL` - Lexical weighting based upon global numbering.
-  `MAT_COLORING_LF`      - Last-first weighting.

    Level: intermediate

.seealso: [](ch_matrices), `MatColoring`, `MatColoringCreate()`, `MatColoringSetWeightType()`, `MatColoringSetWeights()`
E*/
typedef enum {
  MAT_COLORING_WEIGHT_RANDOM,
  MAT_COLORING_WEIGHT_LEXICAL,
  MAT_COLORING_WEIGHT_LF,
  MAT_COLORING_WEIGHT_SL
} MatColoringWeightType;

PETSC_EXTERN PetscErrorCode MatColoringCreate(Mat, MatColoring *);
PETSC_EXTERN PetscErrorCode MatColoringGetDegrees(Mat, PetscInt, PetscInt *);
PETSC_EXTERN PetscErrorCode MatColoringDestroy(MatColoring *);
PETSC_EXTERN PetscErrorCode MatColoringView(MatColoring, PetscViewer);
PETSC_EXTERN PetscErrorCode MatColoringSetType(MatColoring, MatColoringType);
PETSC_EXTERN PetscErrorCode MatColoringSetFromOptions(MatColoring);
PETSC_EXTERN PetscErrorCode MatColoringSetDistance(MatColoring, PetscInt);
PETSC_EXTERN PetscErrorCode MatColoringGetDistance(MatColoring, PetscInt *);
PETSC_EXTERN PetscErrorCode MatColoringSetMaxColors(MatColoring, PetscInt);
PETSC_EXTERN PetscErrorCode MatColoringGetMaxColors(MatColoring, PetscInt *);
PETSC_EXTERN PetscErrorCode MatColoringApply(MatColoring, ISColoring *);
PETSC_EXTERN PetscErrorCode MatColoringRegister(const char[], PetscErrorCode (*)(MatColoring));
PETSC_EXTERN PetscErrorCode MatColoringPatch(Mat, PetscInt, PetscInt, ISColoringValue[], ISColoring *);
PETSC_EXTERN PetscErrorCode MatColoringSetWeightType(MatColoring, MatColoringWeightType);
PETSC_EXTERN PetscErrorCode MatColoringSetWeights(MatColoring, PetscReal *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatColoringCreateWeights(MatColoring, PetscReal **, PetscInt **lperm);
PETSC_EXTERN PetscErrorCode MatColoringTest(MatColoring, ISColoring);
PETSC_DEPRECATED_FUNCTION(3, 10, 0, "MatColoringTest()", ) static inline PetscErrorCode MatColoringTestValid(MatColoring matcoloring, ISColoring iscoloring)
{
  return MatColoringTest(matcoloring, iscoloring);
}
PETSC_EXTERN PetscErrorCode MatISColoringTest(Mat, ISColoring);

/*S
   MatFDColoring - Object for computing a sparse Jacobian via finite differences with coloring

   Level: beginner

   Options Database Key:
.  -snes_fd_coloring - cause the Jacobian needed by `SNES` to be computed via a use of this object

   Note:
   This object is created utilizing a coloring provided by the `MatColoring` object or `DMCreateColoring()`

.seealso: [](ch_matrices), `Mat`, `MatFDColoringCreate()`, `MatFDColoringSetFunction()`, `MatColoring`, `DMCreateColoring()`
S*/
typedef struct _p_MatFDColoring *MatFDColoring;

/*S
  MatFDColoringFn - Function provided to `MatFDColoringSetFunction()` that computes the function being differenced

  Level: advanced

  Calling Sequence:
+ snes - either a `SNES` object if used within `SNES` otherwise an unused parameter
. in   - the location where the Jacobian is to be computed
. out  - the location to put the computed function value
- fctx - the function context passed into `MatFDColoringSetFunction()`

.seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`, `MatMFFDSetFunction()`, `MatMFFDiFn`, `MatMFFDiBaseFn`
S*/
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatFDColoringFn(void *snes, Vec x, Vec y, void *fctx);

PETSC_EXTERN PetscErrorCode MatFDColoringCreate(Mat, ISColoring, MatFDColoring *);
PETSC_EXTERN PetscErrorCode MatFDColoringDestroy(MatFDColoring *);
PETSC_EXTERN PetscErrorCode MatFDColoringView(MatFDColoring, PetscViewer);
PETSC_EXTERN PetscErrorCode MatFDColoringSetFunction(MatFDColoring, MatFDColoringFn *, void *);
PETSC_EXTERN PetscErrorCode MatFDColoringGetFunction(MatFDColoring, MatFDColoringFn **, void **);
PETSC_EXTERN PetscErrorCode MatFDColoringSetParameters(MatFDColoring, PetscReal, PetscReal);
PETSC_EXTERN PetscErrorCode MatFDColoringSetFromOptions(MatFDColoring);
PETSC_EXTERN PetscErrorCode MatFDColoringApply(Mat, MatFDColoring, Vec, void *);
PETSC_EXTERN PetscErrorCode MatFDColoringSetF(MatFDColoring, Vec);
PETSC_EXTERN PetscErrorCode MatFDColoringGetPerturbedColumns(MatFDColoring, PetscInt *, const PetscInt *[]);
PETSC_EXTERN PetscErrorCode MatFDColoringSetUp(Mat, ISColoring, MatFDColoring);
PETSC_EXTERN PetscErrorCode MatFDColoringSetBlockSize(MatFDColoring, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode MatFDColoringSetValues(Mat, MatFDColoring, const PetscScalar *);

/*S
   MatTransposeColoring - Object for computing a sparse matrix product $C = A*B^T$ via coloring

   Level: developer

.seealso: [](ch_matrices), `Mat`, `MatProductType`, `MatTransposeColoringCreate()`
S*/
typedef struct _p_MatTransposeColoring *MatTransposeColoring;

PETSC_EXTERN PetscErrorCode MatTransposeColoringCreate(Mat, ISColoring, MatTransposeColoring *);
PETSC_EXTERN PetscErrorCode MatTransColoringApplySpToDen(MatTransposeColoring, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatTransColoringApplyDenToSp(MatTransposeColoring, Mat, Mat);
PETSC_EXTERN PetscErrorCode MatTransposeColoringDestroy(MatTransposeColoring *);

/*S
   MatPartitioning - Object for managing the partitioning of a matrix or graph

   Level: beginner

   Note:
   There is also a `PetscPartitioner` object that provides the same functionality. It can utilize the `MatPartitioning` operations
   via `PetscPartitionerSetType`(p,`PETSCPARTITIONERMATPARTITIONING`)

   Developer Note:
   It is an extra maintenance and documentation cost to have two objects with the same functionality. `PetscPartitioner` should be removed

.seealso: [](ch_matrices), [](sec_graph), `Mat`, `MatPartitioningCreate()`, `MatPartitioningType`, `MatColoring`, `MatGetOrdering()`, `MatOrderingType`,
          `MatCoarsenType`, `MatCoarsenType`
S*/
typedef struct _p_MatPartitioning *MatPartitioning;

/*J
    MatPartitioningType - String with the name of a PETSc matrix partitioning

   Level: beginner
dm
.seealso: [](ch_matrices), [](sec_graph), `Mat`, `MatPartitioningCreate()`, `MatPartitioning`, `MatPartitioningSetType()`, `MatColoringType`, `MatOrderingType`,
          `MatCoarsenType`, `MatCoarsenType`
J*/
typedef const char *MatPartitioningType;
#define MATPARTITIONINGCURRENT  "current"
#define MATPARTITIONINGAVERAGE  "average"
#define MATPARTITIONINGSQUARE   "square"
#define MATPARTITIONINGPARMETIS "parmetis"
#define MATPARTITIONINGCHACO    "chaco"
#define MATPARTITIONINGPARTY    "party"
#define MATPARTITIONINGPTSCOTCH "ptscotch"
#define MATPARTITIONINGHIERARCH "hierarch"

PETSC_EXTERN PetscErrorCode MatPartitioningCreate(MPI_Comm, MatPartitioning *);
PETSC_EXTERN PetscErrorCode MatPartitioningSetType(MatPartitioning, MatPartitioningType);
PETSC_EXTERN PetscErrorCode MatPartitioningSetNParts(MatPartitioning, PetscInt);
PETSC_EXTERN PetscErrorCode MatPartitioningSetAdjacency(MatPartitioning, Mat);
PETSC_EXTERN PetscErrorCode MatPartitioningSetNumberVertexWeights(MatPartitioning, PetscInt);
PETSC_EXTERN PetscErrorCode MatPartitioningSetVertexWeights(MatPartitioning, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatPartitioningSetPartitionWeights(MatPartitioning, const PetscReal[]);
PETSC_EXTERN PetscErrorCode MatPartitioningSetUseEdgeWeights(MatPartitioning, PetscBool);
PETSC_EXTERN PetscErrorCode MatPartitioningGetUseEdgeWeights(MatPartitioning, PetscBool *);
PETSC_EXTERN PetscErrorCode MatPartitioningApply(MatPartitioning, IS *);
PETSC_EXTERN PetscErrorCode MatPartitioningImprove(MatPartitioning, IS *);
PETSC_EXTERN PetscErrorCode MatPartitioningViewImbalance(MatPartitioning, IS);
PETSC_EXTERN PetscErrorCode MatPartitioningApplyND(MatPartitioning, IS *);
PETSC_EXTERN PetscErrorCode MatPartitioningDestroy(MatPartitioning *);
PETSC_EXTERN PetscErrorCode MatPartitioningRegister(const char[], PetscErrorCode (*)(MatPartitioning));
PETSC_EXTERN PetscErrorCode MatPartitioningView(MatPartitioning, PetscViewer);
PETSC_EXTERN PetscErrorCode MatPartitioningViewFromOptions(MatPartitioning, PetscObject, const char[]);
PETSC_EXTERN PetscErrorCode MatPartitioningSetFromOptions(MatPartitioning);
PETSC_EXTERN PetscErrorCode MatPartitioningGetType(MatPartitioning, MatPartitioningType *);

PETSC_EXTERN PetscErrorCode MatPartitioningParmetisSetRepartition(MatPartitioning);
PETSC_EXTERN PetscErrorCode MatPartitioningParmetisSetCoarseSequential(MatPartitioning);
PETSC_EXTERN PetscErrorCode MatPartitioningParmetisGetEdgeCut(MatPartitioning, PetscInt *);

typedef enum {
  MP_CHACO_MULTILEVEL = 1,
  MP_CHACO_SPECTRAL   = 2,
  MP_CHACO_LINEAR     = 4,
  MP_CHACO_RANDOM     = 5,
  MP_CHACO_SCATTERED  = 6
} MPChacoGlobalType;
PETSC_EXTERN const char *const MPChacoGlobalTypes[];
typedef enum {
  MP_CHACO_KERNIGHAN = 1,
  MP_CHACO_NONE      = 2
} MPChacoLocalType;
PETSC_EXTERN const char *const MPChacoLocalTypes[];
typedef enum {
  MP_CHACO_LANCZOS = 0,
  MP_CHACO_RQI     = 1
} MPChacoEigenType;
PETSC_EXTERN const char *const MPChacoEigenTypes[];

PETSC_EXTERN PetscErrorCode MatPartitioningChacoSetGlobal(MatPartitioning, MPChacoGlobalType);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoGetGlobal(MatPartitioning, MPChacoGlobalType *);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoSetLocal(MatPartitioning, MPChacoLocalType);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoGetLocal(MatPartitioning, MPChacoLocalType *);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoSetCoarseLevel(MatPartitioning, PetscReal);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoSetEigenSolver(MatPartitioning, MPChacoEigenType);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoGetEigenSolver(MatPartitioning, MPChacoEigenType *);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoSetEigenTol(MatPartitioning, PetscReal);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoGetEigenTol(MatPartitioning, PetscReal *);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoSetEigenNumber(MatPartitioning, PetscInt);
PETSC_EXTERN PetscErrorCode MatPartitioningChacoGetEigenNumber(MatPartitioning, PetscInt *);

#define MP_PARTY_OPT "opt"
#define MP_PARTY_LIN "lin"
#define MP_PARTY_SCA "sca"
#define MP_PARTY_RAN "ran"
#define MP_PARTY_GBF "gbf"
#define MP_PARTY_GCF "gcf"
#define MP_PARTY_BUB "bub"
#define MP_PARTY_DEF "def"
PETSC_EXTERN PetscErrorCode MatPartitioningPartySetGlobal(MatPartitioning, const char *);
#define MP_PARTY_HELPFUL_SETS  "hs"
#define MP_PARTY_KERNIGHAN_LIN "kl"
#define MP_PARTY_NONE          "no"
PETSC_EXTERN PetscErrorCode MatPartitioningPartySetLocal(MatPartitioning, const char *);
PETSC_EXTERN PetscErrorCode MatPartitioningPartySetCoarseLevel(MatPartitioning, PetscReal);
PETSC_EXTERN PetscErrorCode MatPartitioningPartySetBipart(MatPartitioning, PetscBool);
PETSC_EXTERN PetscErrorCode MatPartitioningPartySetMatchOptimization(MatPartitioning, PetscBool);

typedef enum {
  MP_PTSCOTCH_DEFAULT,
  MP_PTSCOTCH_QUALITY,
  MP_PTSCOTCH_SPEED,
  MP_PTSCOTCH_BALANCE,
  MP_PTSCOTCH_SAFETY,
  MP_PTSCOTCH_SCALABILITY
} MPPTScotchStrategyType;
PETSC_EXTERN const char *const MPPTScotchStrategyTypes[];

PETSC_EXTERN PetscErrorCode MatPartitioningPTScotchSetImbalance(MatPartitioning, PetscReal);
PETSC_EXTERN PetscErrorCode MatPartitioningPTScotchGetImbalance(MatPartitioning, PetscReal *);
PETSC_EXTERN PetscErrorCode MatPartitioningPTScotchSetStrategy(MatPartitioning, MPPTScotchStrategyType);
PETSC_EXTERN PetscErrorCode MatPartitioningPTScotchGetStrategy(MatPartitioning, MPPTScotchStrategyType *);

/*
 * hierarchical partitioning
 */
PETSC_EXTERN PetscErrorCode MatPartitioningHierarchicalGetFineparts(MatPartitioning, IS *);
PETSC_EXTERN PetscErrorCode MatPartitioningHierarchicalGetCoarseparts(MatPartitioning, IS *);
PETSC_EXTERN PetscErrorCode MatPartitioningHierarchicalSetNcoarseparts(MatPartitioning, PetscInt);
PETSC_EXTERN PetscErrorCode MatPartitioningHierarchicalSetNfineparts(MatPartitioning, PetscInt);

PETSC_EXTERN PetscErrorCode MatMeshToCellGraph(Mat, PetscInt, Mat *);

/*
    If any of the enum values are changed, also update dMatOps dict at src/binding/petsc4py/src/petsc4py/PETSc/libpetsc4py.pyx
*/
typedef enum {
  MATOP_SET_VALUES                = 0,
  MATOP_GET_ROW                   = 1,
  MATOP_RESTORE_ROW               = 2,
  MATOP_MULT                      = 3,
  MATOP_MULT_ADD                  = 4,
  MATOP_MULT_TRANSPOSE            = 5,
  MATOP_MULT_TRANSPOSE_ADD        = 6,
  MATOP_SOLVE                     = 7,
  MATOP_SOLVE_ADD                 = 8,
  MATOP_SOLVE_TRANSPOSE           = 9,
  MATOP_SOLVE_TRANSPOSE_ADD       = 10,
  MATOP_LUFACTOR                  = 11,
  MATOP_CHOLESKYFACTOR            = 12,
  MATOP_SOR                       = 13,
  MATOP_TRANSPOSE                 = 14,
  MATOP_GETINFO                   = 15,
  MATOP_EQUAL                     = 16,
  MATOP_GET_DIAGONAL              = 17,
  MATOP_DIAGONAL_SCALE            = 18,
  MATOP_NORM                      = 19,
  MATOP_ASSEMBLY_BEGIN            = 20,
  MATOP_ASSEMBLY_END              = 21,
  MATOP_SET_OPTION                = 22,
  MATOP_ZERO_ENTRIES              = 23,
  MATOP_ZERO_ROWS                 = 24,
  MATOP_LUFACTOR_SYMBOLIC         = 25,
  MATOP_LUFACTOR_NUMERIC          = 26,
  MATOP_CHOLESKY_FACTOR_SYMBOLIC  = 27,
  MATOP_CHOLESKY_FACTOR_NUMERIC   = 28,
  MATOP_SETUP                     = 29,
  MATOP_ILUFACTOR_SYMBOLIC        = 30,
  MATOP_ICCFACTOR_SYMBOLIC        = 31,
  MATOP_GET_DIAGONAL_BLOCK        = 32,
  MATOP_SET_INF                   = 33,
  MATOP_DUPLICATE                 = 34,
  MATOP_FORWARD_SOLVE             = 35,
  MATOP_BACKWARD_SOLVE            = 36,
  MATOP_ILUFACTOR                 = 37,
  MATOP_ICCFACTOR                 = 38,
  MATOP_AXPY                      = 39,
  MATOP_CREATE_SUBMATRICES        = 40,
  MATOP_INCREASE_OVERLAP          = 41,
  MATOP_GET_VALUES                = 42,
  MATOP_COPY                      = 43,
  MATOP_GET_ROW_MAX               = 44,
  MATOP_SCALE                     = 45,
  MATOP_SHIFT                     = 46,
  MATOP_DIAGONAL_SET              = 47,
  MATOP_ZERO_ROWS_COLUMNS         = 48,
  MATOP_SET_RANDOM                = 49,
  MATOP_GET_ROW_IJ                = 50,
  MATOP_RESTORE_ROW_IJ            = 51,
  MATOP_GET_COLUMN_IJ             = 52,
  MATOP_RESTORE_COLUMN_IJ         = 53,
  MATOP_FDCOLORING_CREATE         = 54,
  MATOP_COLORING_PATCH            = 55,
  MATOP_SET_UNFACTORED            = 56,
  MATOP_PERMUTE                   = 57,
  MATOP_SET_VALUES_BLOCKED        = 58,
  MATOP_CREATE_SUBMATRIX          = 59,
  MATOP_DESTROY                   = 60,
  MATOP_VIEW                      = 61,
  MATOP_CONVERT_FROM              = 62,
  MATOP_MATMAT_MULT_SYMBOLIC      = 63,
  MATOP_MATMAT_MULT_NUMERIC       = 64,
  MATOP_SET_LOCAL_TO_GLOBAL_MAP   = 65,
  MATOP_SET_VALUES_LOCAL          = 66,
  MATOP_ZERO_ROWS_LOCAL           = 67,
  MATOP_GET_ROW_MAX_ABS           = 68,
  MATOP_GET_ROW_MIN_ABS           = 69,
  MATOP_CONVERT                   = 70,
  MATOP_HAS_OPERATION             = 71,
  MATOP_FD_COLORING_APPLY         = 72,
  MATOP_SET_FROM_OPTIONS          = 73,
  MATOP_FIND_ZERO_DIAGONALS       = 74,
  MATOP_MULT_MULTIPLE             = 75,
  MATOP_SOLVE_MULTIPLE            = 76,
  MATOP_GET_INERTIA               = 77,
  MATOP_LOAD                      = 78,
  MATOP_IS_SYMMETRIC              = 79,
  MATOP_IS_HERMITIAN              = 80,
  MATOP_IS_STRUCTURALLY_SYMMETRIC = 81,
  MATOP_SET_VALUES_BLOCKEDLOCAL   = 82,
  MATOP_CREATE_VECS               = 83,
  MATOP_MAT_MULT_SYMBOLIC         = 84,
  MATOP_MAT_MULT_NUMERIC          = 85,
  MATOP_PTAP_NUMERIC              = 86,
  MATOP_MAT_TRANSPOSE_MULT_SYMBO  = 87,
  MATOP_MAT_TRANSPOSE_MULT_NUMER  = 88,
  MATOP_BIND_TO_CPU               = 89,
  MATOP_PRODUCTSETFROMOPTIONS     = 90,
  MATOP_PRODUCTSYMBOLIC           = 91,
  MATOP_PRODUCTNUMERIC            = 92,
  MATOP_CONJUGATE                 = 93,
  MATOP_VIEW_NATIVE               = 94,
  MATOP_SET_VALUES_ROW            = 95,
  MATOP_REAL_PART                 = 96,
  MATOP_IMAGINARY_PART            = 97,
  MATOP_GET_ROW_UPPER_TRIANGULAR  = 98,
  MATOP_RESTORE_ROW_UPPER_TRIANG  = 99,
  MATOP_MAT_SOLVE                 = 100,
  MATOP_MAT_SOLVE_TRANSPOSE       = 101,
  MATOP_GET_ROW_MIN               = 102,
  MATOP_GET_COLUMN_VECTOR         = 103,
  MATOP_GET_SEQ_NONZERO_STRUCTUR  = 104,
  MATOP_CREATE                    = 105,
  MATOP_GET_GHOSTS                = 106,
  MATOP_GET_LOCAL_SUB_MATRIX      = 107,
  MATOP_RESTORE_LOCALSUB_MATRIX   = 108,
  MATOP_MULT_DIAGONAL_BLOCK       = 109,
  MATOP_HERMITIAN_TRANSPOSE       = 110,
  MATOP_MULT_HERMITIAN_TRANSPOSE  = 111,
  MATOP_MULT_HERMITIAN_TRANS_ADD  = 112,
  MATOP_GET_MULTI_PROC_BLOCK      = 113,
  MATOP_FIND_NONZERO_ROWS         = 114,
  MATOP_GET_COLUMN_NORMS          = 115,
  MATOP_INVERT_BLOCK_DIAGONAL     = 116,
  MATOP_INVERT_VBLOCK_DIAGONAL    = 117,
  MATOP_CREATE_SUB_MATRICES_MPI   = 118,
  MATOP_SET_VALUES_BATCH          = 119,
  MATOP_TRANSPOSE_MAT_MULT_SYMBO  = 120,
  MATOP_TRANSPOSE_MAT_MULT_NUMER  = 121,
  MATOP_TRANSPOSE_COLORING_CREAT  = 122,
  MATOP_TRANS_COLORING_APPLY_SPT  = 123,
  MATOP_TRANS_COLORING_APPLY_DEN  = 124,
  MATOP_RART_NUMERIC              = 125,
  MATOP_SET_BLOCK_SIZES           = 126,
  MATOP_RESIDUAL                  = 127,
  MATOP_FDCOLORING_SETUP          = 128,
  MATOP_FIND_OFFBLOCK_ENTRIES     = 129,
  MATOP_MPICONCATENATESEQ         = 130,
  MATOP_DESTROYSUBMATRICES        = 131,
  MATOP_MAT_TRANSPOSE_SOLVE       = 132,
  MATOP_GET_VALUES_LOCAL          = 133,
  MATOP_CREATE_GRAPH              = 134,
  MATOP_TRANSPOSE_SYMBOLIC        = 135,
  MATOP_ELIMINATE_ZEROS           = 136,
  MATOP_GET_ROW_SUM_ABS           = 137,
  MATOP_GET_FACTOR                = 138,
  MATOP_GET_BLOCK_DIAGONAL        = 139, /* NOTE: caller of the two op functions owns the returned matrix */
  MATOP_GET_VBLOCK_DIAGONAL       = 140, /* and need to destroy it after use. */
  MATOP_COPY_HASH_TO_XAIJ         = 141,
  MATOP_GET_CURRENT_MEM_TYPE      = 142,
  MATOP_ZERO_ROWS_COLUMNS_LOCAL   = 143
} MatOperation;

PETSC_EXTERN PetscErrorCode MatSetOperation(Mat, MatOperation, PetscErrorCodeFn *);
PETSC_EXTERN PetscErrorCode MatGetOperation(Mat, MatOperation, PetscErrorCodeFn **);
PETSC_EXTERN PetscErrorCode MatHasOperation(Mat, MatOperation, PetscBool *);
PETSC_EXTERN PetscErrorCode MatHasCongruentLayouts(Mat, PetscBool *);
PETSC_DEPRECATED_FUNCTION(3, 14, 0, "MatProductClear()", ) static inline PetscErrorCode MatFreeIntermediateDataStructures(Mat A)
{
  return MatProductClear(A);
}
PETSC_EXTERN PetscErrorCode MatShellSetOperation(Mat, MatOperation, PetscErrorCodeFn *);
PETSC_EXTERN PetscErrorCode MatShellGetOperation(Mat, MatOperation, PetscErrorCodeFn **);
PETSC_EXTERN PetscErrorCode MatShellSetContext(Mat, PetscCtx);
PETSC_EXTERN PetscErrorCode MatShellSetContextDestroy(Mat, PetscCtxDestroyFn *);
PETSC_EXTERN PetscErrorCode MatShellSetVecType(Mat, VecType);
PETSC_EXTERN PetscErrorCode MatShellTestMult(Mat, PetscErrorCode (*)(void *, Vec, Vec), Vec, void *, PetscBool *);
PETSC_EXTERN PetscErrorCode MatShellTestMultTranspose(Mat, PetscErrorCode (*)(void *, Vec, Vec), Vec, void *, PetscBool *);
PETSC_EXTERN PetscErrorCode MatShellSetManageScalingShifts(Mat);
PETSC_EXTERN PetscErrorCode MatShellSetMatProductOperation(Mat, MatProductType, PetscErrorCode (*)(Mat, Mat, Mat, void **), PetscErrorCode (*)(Mat, Mat, Mat, void *), PetscCtxDestroyFn *, MatType, MatType);
PETSC_EXTERN PetscErrorCode MatIsShell(Mat, PetscBool *);

/*
   Codes for matrices stored on disk. By default they are
   stored in a universal format. By changing the format with
   PetscViewerPushFormat(viewer,PETSC_VIEWER_NATIVE); the matrices will
   be stored in a way natural for the matrix, for example dense matrices
   would be stored as dense. Matrices stored this way may only be
   read into matrices of the same type.
*/
#define MATRIX_BINARY_FORMAT_DENSE -1

PETSC_EXTERN PetscErrorCode MatMPIBAIJSetHashTableFactor(Mat, PetscReal);

PETSC_EXTERN PetscErrorCode MatISSetLocalMatType(Mat, MatType);
PETSC_EXTERN PetscErrorCode MatISSetPreallocation(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]);
PETSC_EXTERN PetscErrorCode MatISSetAllowRepeated(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatISGetAllowRepeated(Mat, PetscBool *);
PETSC_EXTERN PetscErrorCode MatISStoreL2L(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatISFixLocalEmpty(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatISGetLocalMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatISRestoreLocalMat(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatISSetLocalMat(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatISGetLocalToGlobalMapping(Mat, ISLocalToGlobalMapping *, ISLocalToGlobalMapping *);

/*S
   MatNullSpace - Object that removes a null space from a vector, i.e.
                  orthogonalizes the vector to a subspace

   Level: advanced

.seealso: [](ch_matrices), `Mat`, `MatNullSpaceCreate()`, `MatNullSpaceSetFunction()`, `MatGetNullSpace()`, `MatSetNullSpace()`
S*/
typedef struct _p_MatNullSpace *MatNullSpace;

/*S
  MatNullSpaceRemoveFn - Function provided to `MatNullSpaceSetFunction()` that removes the null space from a vector

  Level: advanced

  Calling Sequence:
+ nsp - the `MatNullSpace` object
. x   - the vector from which to remove the null space
- ctx - [optional] user-defined function context provided with `MatNullSpaceSetFunction()`

.seealso: [](ch_matrices), `Mat`, `MatNullSpaceCreate()`, `MatNullSpaceSetFunction()`, `MatGetNullSpace()`, `MatSetNullSpace()`
S*/
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatNullSpaceRemoveFn(MatNullSpace nsp, Vec x, PetscCtx ctx);

PETSC_EXTERN PetscErrorCode MatNullSpaceCreate(MPI_Comm, PetscBool, PetscInt, const Vec[], MatNullSpace *);
PETSC_EXTERN PetscErrorCode MatNullSpaceSetFunction(MatNullSpace, MatNullSpaceRemoveFn *, void *);
PETSC_EXTERN PetscErrorCode MatNullSpaceDestroy(MatNullSpace *);
PETSC_EXTERN PetscErrorCode MatNullSpaceRemove(MatNullSpace, Vec);
PETSC_EXTERN PetscErrorCode MatGetNullSpace(Mat, MatNullSpace *);
PETSC_EXTERN PetscErrorCode MatGetTransposeNullSpace(Mat, MatNullSpace *);
PETSC_EXTERN PetscErrorCode MatSetTransposeNullSpace(Mat, MatNullSpace);
PETSC_EXTERN PetscErrorCode MatSetNullSpace(Mat, MatNullSpace);
PETSC_EXTERN PetscErrorCode MatSetNearNullSpace(Mat, MatNullSpace);
PETSC_EXTERN PetscErrorCode MatGetNearNullSpace(Mat, MatNullSpace *);
PETSC_EXTERN PetscErrorCode MatGetNullSpaces(PetscInt, Mat[], MatNullSpace *[]);
PETSC_EXTERN PetscErrorCode MatRestoreNullSpaces(PetscInt, Mat[], MatNullSpace *[]);
PETSC_EXTERN PetscErrorCode MatNullSpaceTest(MatNullSpace, Mat, PetscBool *);
PETSC_EXTERN PetscErrorCode MatNullSpaceView(MatNullSpace, PetscViewer);
PETSC_EXTERN PetscErrorCode MatNullSpaceGetVecs(MatNullSpace, PetscBool *, PetscInt *, const Vec **);
PETSC_EXTERN PetscErrorCode MatNullSpaceCreateRigidBody(Vec, MatNullSpace *);

PETSC_EXTERN PetscErrorCode MatReorderingSeqSBAIJ(Mat, IS);
PETSC_EXTERN PetscErrorCode MatMPISBAIJSetHashTableFactor(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatSeqSBAIJSetColumnIndices(Mat, PetscInt *);

PETSC_EXTERN PetscErrorCode MatCreateMAIJ(Mat, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatMAIJRedimension(Mat, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatMAIJGetAIJ(Mat, Mat *);

PETSC_EXTERN PetscErrorCode MatComputeOperator(Mat, MatType, Mat *);
PETSC_EXTERN PetscErrorCode MatComputeOperatorTranspose(Mat, MatType, Mat *);

PETSC_DEPRECATED_FUNCTION(3, 12, 0, "MatComputeOperator()", ) static inline PetscErrorCode MatComputeExplicitOperator(Mat A, Mat *B)
{
  return MatComputeOperator(A, PETSC_NULLPTR, B);
}
PETSC_DEPRECATED_FUNCTION(3, 12, 0, "MatComputeOperatorTranspose()", ) static inline PetscErrorCode MatComputeExplicitOperatorTranspose(Mat A, Mat *B)
{
  return MatComputeOperatorTranspose(A, PETSC_NULLPTR, B);
}

PETSC_EXTERN PetscErrorCode MatCreateKAIJ(Mat, PetscInt, PetscInt, const PetscScalar[], const PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatKAIJGetAIJ(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatKAIJGetS(Mat, PetscInt *, PetscInt *, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJGetSRead(Mat, PetscInt *, PetscInt *, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJRestoreS(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJRestoreSRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJGetT(Mat, PetscInt *, PetscInt *, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJGetTRead(Mat, PetscInt *, PetscInt *, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJRestoreT(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJRestoreTRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatKAIJSetAIJ(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatKAIJSetS(Mat, PetscInt, PetscInt, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatKAIJSetT(Mat, PetscInt, PetscInt, const PetscScalar[]);
PETSC_EXTERN PetscErrorCode MatKAIJGetScaledIdentity(Mat, PetscBool *);

PETSC_EXTERN PetscErrorCode MatDiagonalScaleLocal(Mat, Vec);

PETSC_EXTERN PetscErrorCode MatMFFDInitializePackage(void);
PETSC_EXTERN PetscErrorCode MatMFFDFinalizePackage(void);

/*S
  MatMFFDFn - Function provided to `MatMFFDSetFunction()` that computes the function being differenced

  Level: advanced

  Calling Sequence:
+ ctx - [optional] user-defined function context provided with `MatMFFDSetFunction()`
. x   - input vector
- y   - output vector

.seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`, `MatMFFDSetFunction()`, `MatMFFDiFn`, `MatMFFDiBaseFn`
S*/
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatMFFDFn(PetscCtx ctx, Vec x, Vec y);

/*S
  MatMFFDiFn - Function provided to `MatMFFDSetFunctioni()` that computes the function being differenced at a single point

  Level: advanced

  Calling Sequence:
+ ctx    - [optional] user-defined function context provided with `MatMFFDSetFunction()`
. i      - the component of the vector to compute
. x      - input vector
- result - the value of the function at that component (output)

.seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`, `MatMFFDSetFunction()`, `MatMFFDFn`, `MatMFFDiBaseFn`
S*/
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatMFFDiFn(PetscCtx ctx, PetscInt i, Vec x, PetscScalar *result);

/*S
  MatMFFDiBaseFn - Function provided to `MatMFFDSetFunctioniBase()` that computes the base of the function evaluations
  that will be used for differencing

  Level: advanced

  Calling Sequence:
+ ctx - [optional] user-defined function context provided with `MatMFFDSetFunction()`
- x   - input base vector

.seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`, `MatMFFDSetFunction()`, `MatMFFDSetFunctioniBase()`, `MatMFFDFn`, `MatMFFDiFn`
S*/
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatMFFDiBaseFn(PetscCtx ctx, Vec x);

/*S
  MatMFFDCheckhFn - Function provided to `MatMFFDSetCheckh()` that checks and possibly adjusts the value of `h` to ensure some property.
  that will be used for differencing

  Level: advanced

  Calling Sequence:
+ ctx - [optional] user-defined function context provided with `MatMFFDSetCheckh()`
. x   - input base vector
. y   - input step vector that the product is computed with
- h   - input tentative step, output possibly adjusted step

  Note:
  `MatMFFDCheckPositivity()` is one such function

.seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`,  `MatMFFDSetCheckh()`, `MatMFFDCheckPositivity()`
S*/
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode MatMFFDCheckhFn(PetscCtx ctx, Vec x, Vec y, PetscScalar *h);

PETSC_EXTERN PetscErrorCode MatCreateMFFD(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatMFFDSetBase(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatMFFDSetFunction(Mat, MatMFFDFn *, void *);
PETSC_EXTERN PetscErrorCode MatMFFDSetFunctioni(Mat, MatMFFDiFn *);
PETSC_EXTERN PetscErrorCode MatMFFDSetFunctioniBase(Mat, MatMFFDiBaseFn *);
PETSC_EXTERN PetscErrorCode MatMFFDSetHHistory(Mat, PetscScalar[], PetscInt);
PETSC_EXTERN PetscErrorCode MatMFFDResetHHistory(Mat);
PETSC_EXTERN PetscErrorCode MatMFFDSetFunctionError(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatMFFDSetPeriod(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatMFFDGetH(Mat, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatMFFDSetOptionsPrefix(Mat, const char[]);
PETSC_EXTERN PetscErrorCode MatMFFDCheckPositivity(void *, Vec, Vec, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatMFFDSetCheckh(Mat, MatMFFDCheckhFn *, void *);

/*S
    MatMFFD - A data structured used to manage the computation of the h differencing parameter for matrix-free
              Jacobian vector products

    Level: developer

    Notes:
    `MATMFFD` is a specific `MatType` which uses the `MatMFFD` data structure

     MatMFFD*() methods actually take the `Mat` as their first argument. Not a `MatMFFD` data structure

    This functionality is often obtained using `MatCreateSNESMF()` or with `SNES` solvers using `-snes_mf` or `-snes_mf_operator`

.seealso: [](ch_matrices), `MatMFFDType`, `MATMFFD`, `MatCreateMFFD()`, `MatMFFDSetFuction()`, `MatMFFDSetType()`, `MatMFFDRegister()`,
          `MatCreateSNESMF()`, `SNES`, `-snes_mf`, `-snes_mf_operator`
S*/
typedef struct _p_MatMFFD *MatMFFD;

/*J
   MatMFFDType - algorithm used to compute the `h` used in computing matrix-vector products via differencing of a function

   Values:
+   `MATMFFD_DS` - an algorithm described by Dennis and Schnabel {cite}`dennis:83`
-   `MATMFFD_WP` - the Walker-Pernice {cite}`pw98` strategy.

   Level: beginner

.seealso: [](ch_matrices), `MatMFFDSetType()`, `MatMFFDRegister()`, `MatMFFDSetFunction()`, `MatCreateMFFD()`
J*/
typedef const char *MatMFFDType;
#define MATMFFD_DS "ds"
#define MATMFFD_WP "wp"

PETSC_EXTERN PetscErrorCode MatMFFDSetType(Mat, MatMFFDType);
PETSC_EXTERN PetscErrorCode MatMFFDRegister(const char[], PetscErrorCode (*)(MatMFFD));

PETSC_EXTERN PetscErrorCode MatMFFDDSSetUmin(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatMFFDWPSetComputeNormU(Mat, PetscBool);

PETSC_EXTERN PetscErrorCode MatFDColoringSetType(MatFDColoring, MatMFFDType);

PETSC_EXTERN PetscErrorCode PetscViewerMathematicaPutMatrix(PetscViewer, PetscInt, PetscInt, PetscReal *);
PETSC_EXTERN PetscErrorCode PetscViewerMathematicaPutCSRMatrix(PetscViewer, PetscInt, PetscInt, PetscInt *, PetscInt *, PetscReal *);

#ifdef PETSC_HAVE_H2OPUS
PETSC_EXTERN_TYPEDEF typedef PetscScalar(MatH2OpusKernelFn)(PetscInt, PetscReal[], PetscReal[], void *);
PETSC_EXTERN_TYPEDEF typedef MatH2OpusKernelFn *MatH2OpusKernel;

PETSC_EXTERN PetscErrorCode MatCreateH2OpusFromKernel(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscReal[], PetscBool, MatH2OpusKernelFn *, void *, PetscReal, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatCreateH2OpusFromMat(Mat, PetscInt, const PetscReal[], PetscBool, PetscReal, PetscInt, PetscInt, PetscInt, PetscReal, Mat *);
PETSC_EXTERN PetscErrorCode MatH2OpusSetSamplingMat(Mat, Mat, PetscInt, PetscReal);
PETSC_EXTERN PetscErrorCode MatH2OpusOrthogonalize(Mat);
PETSC_EXTERN PetscErrorCode MatH2OpusCompress(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatH2OpusSetNativeMult(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatH2OpusGetNativeMult(Mat, PetscBool *);
PETSC_EXTERN PetscErrorCode MatH2OpusGetIndexMap(Mat, IS *);
PETSC_EXTERN PetscErrorCode MatH2OpusMapVec(Mat, PetscBool, Vec, Vec *);
PETSC_EXTERN PetscErrorCode MatH2OpusLowRankUpdate(Mat, Mat, Mat, PetscScalar);
#endif

#ifdef PETSC_HAVE_HTOOL
PETSC_EXTERN_TYPEDEF typedef PetscErrorCode    MatHtoolKernelFn(PetscInt, PetscInt, PetscInt, const PetscInt *, const PetscInt *, PetscScalar *, void *);
PETSC_EXTERN_TYPEDEF typedef MatHtoolKernelFn *MatHtoolKernel;

PETSC_EXTERN PetscErrorCode MatCreateHtoolFromKernel(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscReal[], const PetscReal[], MatHtoolKernelFn *, void *, Mat *);
PETSC_EXTERN PetscErrorCode MatHtoolSetKernel(Mat, MatHtoolKernelFn *, void *);
PETSC_EXTERN PetscErrorCode MatHtoolGetPermutationSource(Mat, IS *);
PETSC_EXTERN PetscErrorCode MatHtoolGetPermutationTarget(Mat, IS *);
PETSC_EXTERN PetscErrorCode MatHtoolUsePermutation(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatHtoolUseRecompression(Mat, PetscBool);

/*E
   MatHtoolCompressorType - Indicates the type of compressor used by a `MATHTOOL`

   Values:
+  `MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA` (default) - symmetric partial adaptive cross approximation
.  `MAT_HTOOL_COMPRESSOR_FULL_ACA`                 - full adaptive cross approximation
-  `MAT_HTOOL_COMPRESSOR_SVD`                      - singular value decomposition

   Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreateHtoolFromKernel()`, `MATHTOOL`, `MatHtoolClusteringType`
E*/
typedef enum {
  MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA,
  MAT_HTOOL_COMPRESSOR_FULL_ACA,
  MAT_HTOOL_COMPRESSOR_SVD
} MatHtoolCompressorType;

/*E
   MatHtoolClusteringType - Indicates the type of clustering used by a `MATHTOOL`

   Values:
+  `MAT_HTOOL_CLUSTERING_PCA_REGULAR` (default)    - axis computed via principle component analysis, split uniformly
.  `MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC`            - axis computed via principle component analysis, split barycentrically
.  `MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR`   - axis along the largest extent of the bounding box, split uniformly
-  `MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC` - axis along the largest extent of the bounding box, split barycentrically

   Level: intermediate

   Note:
   Higher-dimensional clustering is not yet supported in Htool, but once it is, one should add BOUNDING_BOX_{2,3} types

.seealso: [](ch_matrices), `Mat`, `MatCreateHtoolFromKernel()`, `MATHTOOL`, `MatHtoolCompressorType`
E*/
typedef enum {
  MAT_HTOOL_CLUSTERING_PCA_REGULAR,
  MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC,
  MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR,
  MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC
} MatHtoolClusteringType;
#endif

#ifdef PETSC_HAVE_MUMPS
PETSC_EXTERN PetscErrorCode MatMumpsSetIcntl(Mat, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode MatMumpsGetIcntl(Mat, PetscInt, PetscInt *);
PETSC_EXTERN PetscErrorCode MatMumpsSetCntl(Mat, PetscInt, PetscReal);
PETSC_EXTERN PetscErrorCode MatMumpsGetCntl(Mat, PetscInt, PetscReal *);

PETSC_EXTERN PetscErrorCode MatMumpsGetInfo(Mat, PetscInt, PetscInt *);
PETSC_EXTERN PetscErrorCode MatMumpsGetInfog(Mat, PetscInt, PetscInt *);
PETSC_EXTERN PetscErrorCode MatMumpsGetRinfo(Mat, PetscInt, PetscReal *);
PETSC_EXTERN PetscErrorCode MatMumpsGetRinfog(Mat, PetscInt, PetscReal *);
PETSC_EXTERN PetscErrorCode MatMumpsGetNullPivots(Mat, PetscInt *, PetscInt **);
PETSC_EXTERN PetscErrorCode MatMumpsGetInverse(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatMumpsGetInverseTranspose(Mat, Mat);
PETSC_EXTERN PetscErrorCode MatMumpsSetBlk(Mat, PetscInt, const PetscInt[], const PetscInt[]);

PETSC_EXTERN PetscErrorCode MatMumpsSetOocTmpDir(Mat, const char *);
PETSC_EXTERN PetscErrorCode MatMumpsGetOocTmpDir(Mat, const char **);
#else
static inline PetscErrorCode MatMumpsSetIcntl(PETSC_UNUSED Mat F, PETSC_UNUSED PetscInt icntl, PETSC_UNUSED PetscInt ival)
{
  return PETSC_SUCCESS;
}
static inline PetscErrorCode MatMumpsSetCntl(PETSC_UNUSED Mat F, PETSC_UNUSED PetscInt icntl, PETSC_UNUSED PetscReal val)
{
  return PETSC_SUCCESS;
}
#endif

#ifdef PETSC_HAVE_MKL_PARDISO
PETSC_EXTERN PetscErrorCode MatMkl_PardisoSetCntl(Mat, PetscInt, PetscInt);
#endif

#ifdef PETSC_HAVE_MKL_CPARDISO
PETSC_EXTERN PetscErrorCode MatMkl_CPardisoSetCntl(Mat, PetscInt, PetscInt);
#endif

#ifdef PETSC_HAVE_SUPERLU
PETSC_EXTERN PetscErrorCode MatSuperluSetILUDropTol(Mat, PetscReal);
#endif

#ifdef PETSC_HAVE_SUPERLU_DIST
PETSC_EXTERN PetscErrorCode MatSuperluDistGetDiagU(Mat, PetscScalar *);
#endif

#ifdef PETSC_HAVE_STRUMPACK
/*E
    MatSTRUMPACKReordering - sparsity reducing ordering to be used in `MATSOLVERSTRUMPACK`

    Values:
+  `MAT_STRUMPACK_NATURAL`   - use the current ordering
.  `MAT_STRUMPACK_METIS`     - use MeTis to compute an ordering
.  `MAT_STRUMPACK_PARMETIS`  - use ParMeTis to compute an ordering
.  `MAT_STRUMPACK_SCOTCH`    - use Scotch to compute an ordering
.  `MAT_STRUMPACK_PTSCOTCH`  - use parallel Scotch to compute an ordering
.  `MAT_STRUMPACK_RCM`       - use an RCM ordering
.  `MAT_STRUMPACK_GEOMETRIC` - use a geometric ordering (needs mesh info from user)
.  `MAT_STRUMPACK_AMD`       - approximate minimum degree
.  `MAT_STRUMPACK_MMD`       - multiple minimum degree
.  `MAT_STRUMPACK_AND`       - approximate nested dissection
.  `MAT_STRUMPACK_MLF`       - minimum local fill
-  `MAT_STRUMPACK_SPECTRAL`  - spectral nested dissection

    Level: intermediate

    Developer Note:
    Should be called `MatSTRUMPACKReorderingType`

.seealso: `Mat`, `MATSOLVERSTRUMPACK`, `MatGetFactor()`, `MatSTRUMPACKSetReordering()`
E*/
typedef enum {
  MAT_STRUMPACK_NATURAL,
  MAT_STRUMPACK_METIS,
  MAT_STRUMPACK_PARMETIS,
  MAT_STRUMPACK_SCOTCH,
  MAT_STRUMPACK_PTSCOTCH,
  MAT_STRUMPACK_RCM,
  MAT_STRUMPACK_GEOMETRIC,
  MAT_STRUMPACK_AMD,
  MAT_STRUMPACK_MMD,
  MAT_STRUMPACK_AND,
  MAT_STRUMPACK_MLF,
  MAT_STRUMPACK_SPECTRAL
} MatSTRUMPACKReordering;

PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetReordering(Mat, MatSTRUMPACKReordering);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetReordering(Mat, MatSTRUMPACKReordering *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetGeometricNxyz(Mat, PetscInt, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetGeometricComponents(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetGeometricWidth(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetColPerm(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetColPerm(Mat, PetscBool *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetGPU(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetGPU(Mat, PetscBool *);

/*E
    MatSTRUMPACKCompressionType - Compression used in the approximate sparse factorization solver `MATSOLVERSTRUMPACK`

    Values:
+  `MAT_STRUMPACK_COMPRESSION_TYPE_NONE`          - no compression, direct solver
.  `MAT_STRUMPACK_COMPRESSION_TYPE_HSS`           - hierarchically semi-separable
.  `MAT_STRUMPACK_COMPRESSION_TYPE_BLR`           - block low rank
.  `MAT_STRUMPACK_COMPRESSION_TYPE_HODLR`         - hierarchically off-diagonal low rank (requires ButterfyPACK support, configure with --download-butterflypack)
.  `MAT_STRUMPACK_COMPRESSION_TYPE_BLR_HODLR`     - hybrid of BLR and HODLR (requires ButterfyPACK support, configure with --download-butterflypack)
.  `MAT_STRUMPACK_COMPRESSION_TYPE_ZFP_BLR_HODLR` - hybrid of lossy (ZFP), BLR and HODLR (requires ButterfyPACK and ZFP support, configure with --download-butterflypack --download-zfp)
.  `MAT_STRUMPACK_COMPRESSION_TYPE_LOSSLESS`      - lossless compression (requires ZFP support, configure with --download-zfp)
-  `MAT_STRUMPACK_COMPRESSION_TYPE_LOSSY`         - lossy compression (requires ZFP support, configure with --download-zfp)

    Level: intermediate

.seealso: `Mat`, `MATSOLVERSTRUMPACK`, `MatGetFactor()`, `MatSTRUMPACKSetCompression()`
E*/
typedef enum {
  MAT_STRUMPACK_COMPRESSION_TYPE_NONE,
  MAT_STRUMPACK_COMPRESSION_TYPE_HSS,
  MAT_STRUMPACK_COMPRESSION_TYPE_BLR,
  MAT_STRUMPACK_COMPRESSION_TYPE_HODLR,
  MAT_STRUMPACK_COMPRESSION_TYPE_BLR_HODLR,
  MAT_STRUMPACK_COMPRESSION_TYPE_ZFP_BLR_HODLR,
  MAT_STRUMPACK_COMPRESSION_TYPE_LOSSLESS,
  MAT_STRUMPACK_COMPRESSION_TYPE_LOSSY
} MatSTRUMPACKCompressionType;

PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompression(Mat, MatSTRUMPACKCompressionType);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompression(Mat, MatSTRUMPACKCompressionType *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompRelTol(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompRelTol(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompAbsTol(Mat, PetscReal);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompAbsTol(Mat, PetscReal *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompMinSepSize(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompMinSepSize(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompLeafSize(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompLeafSize(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompLossyPrecision(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompLossyPrecision(Mat, PetscInt *);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKSetCompButterflyLevels(Mat, PetscInt);
PETSC_EXTERN PetscErrorCode MatSTRUMPACKGetCompButterflyLevels(Mat, PetscInt *);
#endif

PETSC_EXTERN PetscErrorCode MatBindToCPU(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatBoundToCPU(Mat, PetscBool *);
PETSC_DEPRECATED_FUNCTION(3, 13, 0, "MatBindToCPU()", ) static inline PetscErrorCode MatPinToCPU(Mat A, PetscBool flg)
{
  return MatBindToCPU(A, flg);
}
PETSC_EXTERN PetscErrorCode MatSetBindingPropagates(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatGetBindingPropagates(Mat, PetscBool *);

#ifdef PETSC_HAVE_CUDA
/*E
    MatCUSPARSEStorageFormat - indicates the storage format for `MATAIJCUSPARSE` (GPU)
    matrices.

    Values:
+   `MAT_CUSPARSE_CSR` - Compressed Sparse Row
.   `MAT_CUSPARSE_ELL` - Ellpack (requires CUDA 4.2 or later).
-   `MAT_CUSPARSE_HYB` - Hybrid, a combination of Ellpack and Coordinate format (requires CUDA 4.2 or later).

    Level: intermediate

.seealso: [](ch_matrices), `MATAIJCUSPARSE`, `MatCUSPARSESetFormat()`, `MatCUSPARSEFormatOperation`
E*/

typedef enum {
  MAT_CUSPARSE_CSR,
  MAT_CUSPARSE_ELL,
  MAT_CUSPARSE_HYB
} MatCUSPARSEStorageFormat;

/* these will be strings associated with enumerated type defined above */
PETSC_EXTERN const char *const MatCUSPARSEStorageFormats[];

/*E
    MatCUSPARSEFormatOperation - indicates the operation of `MATAIJCUSPARSE` (GPU)
    matrices whose operation should use a particular storage format.

    Values:
+   `MAT_CUSPARSE_MULT_DIAG`    - sets the storage format for the diagonal matrix in the parallel `MatMult()`
.   `MAT_CUSPARSE_MULT_OFFDIAG` - sets the storage format for the off-diagonal matrix in the parallel `MatMult()`
.   `MAT_CUSPARSE_MULT`         - sets the storage format for the entire matrix in the serial (single GPU) `MatMult()`
-   `MAT_CUSPARSE_ALL`          - sets the storage format for all `MATAIJCUSPARSE` (GPU) matrices

    Level: intermediate

.seealso: [](ch_matrices), `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`
E*/
typedef enum {
  MAT_CUSPARSE_MULT_DIAG,
  MAT_CUSPARSE_MULT_OFFDIAG,
  MAT_CUSPARSE_MULT,
  MAT_CUSPARSE_ALL
} MatCUSPARSEFormatOperation;

PETSC_EXTERN PetscErrorCode MatCreateSeqAIJCUSPARSE(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateAIJCUSPARSE(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCUSPARSESetFormat(Mat, MatCUSPARSEFormatOperation, MatCUSPARSEStorageFormat);
PETSC_EXTERN PetscErrorCode MatCUSPARSESetUseCPUSolve(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSEGetIJ(Mat, PetscBool, const int **, const int **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSERestoreIJ(Mat, PetscBool, const int **, const int **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSEGetArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSERestoreArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSEGetArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSERestoreArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSEGetArray(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJCUSPARSERestoreArray(Mat, PetscScalar **);

PETSC_EXTERN PetscErrorCode MatCreateDenseCUDA(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqDenseCUDA(MPI_Comm, PetscInt, PetscInt, PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatDenseCUDAGetArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseCUDAGetArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseCUDAGetArray(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseCUDARestoreArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseCUDARestoreArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseCUDARestoreArray(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseCUDAPlaceArray(Mat, const PetscScalar *);
PETSC_EXTERN PetscErrorCode MatDenseCUDAReplaceArray(Mat, const PetscScalar *);
PETSC_EXTERN PetscErrorCode MatDenseCUDAResetArray(Mat);
PETSC_EXTERN PetscErrorCode MatDenseCUDASetPreallocation(Mat, PetscScalar *);

PETSC_EXTERN PetscErrorCode MatCreateSeqSELLCUDA(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSELLCUDA(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
#endif

#ifdef PETSC_HAVE_HIP
/*E
    MatHIPSPARSEStorageFormat - indicates the storage format for `MATAIJHIPSPARSE` (GPU)
    matrices.

    Values:
+   `MAT_HIPSPARSE_CSR` - Compressed Sparse Row
.   `MAT_HIPSPARSE_ELL` - Ellpack
-   `MAT_HIPSPARSE_HYB` - Hybrid, a combination of Ellpack and Coordinate format

    Level: intermediate

.seealso: [](ch_matrices), `MatHIPSPARSESetFormat()`, `MatHIPSPARSEFormatOperation`
E*/

typedef enum {
  MAT_HIPSPARSE_CSR,
  MAT_HIPSPARSE_ELL,
  MAT_HIPSPARSE_HYB
} MatHIPSPARSEStorageFormat;

/* these will be strings associated with enumerated type defined above */
PETSC_EXTERN const char *const MatHIPSPARSEStorageFormats[];

/*E
    MatHIPSPARSEFormatOperation - indicates the operation of `MATAIJHIPSPARSE` (GPU)
    matrices whose operation should use a particular storage format.

    Values:
+   `MAT_HIPSPARSE_MULT_DIAG`    - sets the storage format for the diagonal matrix in the parallel `MatMult()`
.   `MAT_HIPSPARSE_MULT_OFFDIAG` - sets the storage format for the off-diagonal matrix in the parallel `MatMult()`
.   `MAT_HIPSPARSE_MULT`         - sets the storage format for the entire matrix in the serial (single GPU) `MatMult()`
-   `MAT_HIPSPARSE_ALL`          - sets the storage format for all HIPSPARSE (GPU) matrices

    Level: intermediate

.seealso: [](ch_matrices), `MatHIPSPARSESetFormat()`, `MatHIPSPARSEStorageFormat`
E*/
typedef enum {
  MAT_HIPSPARSE_MULT_DIAG,
  MAT_HIPSPARSE_MULT_OFFDIAG,
  MAT_HIPSPARSE_MULT,
  MAT_HIPSPARSE_ALL
} MatHIPSPARSEFormatOperation;

PETSC_EXTERN PetscErrorCode MatCreateSeqAIJHIPSPARSE(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateAIJHIPSPARSE(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatHIPSPARSESetFormat(Mat, MatHIPSPARSEFormatOperation, MatHIPSPARSEStorageFormat);
PETSC_EXTERN PetscErrorCode MatHIPSPARSESetUseCPUSolve(Mat, PetscBool);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSEGetIJ(Mat, PetscBool, const int **, const int **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSERestoreIJ(Mat, PetscBool, const int **, const int **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSEGetArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSERestoreArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSEGetArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSERestoreArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSEGetArray(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatSeqAIJHIPSPARSERestoreArray(Mat, PetscScalar **);

PETSC_EXTERN PetscErrorCode MatCreateDenseHIP(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqDenseHIP(MPI_Comm, PetscInt, PetscInt, PetscScalar[], Mat *);
PETSC_EXTERN PetscErrorCode MatDenseHIPGetArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseHIPGetArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseHIPGetArray(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseHIPRestoreArrayWrite(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseHIPRestoreArrayRead(Mat, const PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseHIPRestoreArray(Mat, PetscScalar **);
PETSC_EXTERN PetscErrorCode MatDenseHIPPlaceArray(Mat, const PetscScalar *);
PETSC_EXTERN PetscErrorCode MatDenseHIPReplaceArray(Mat, const PetscScalar *);
PETSC_EXTERN PetscErrorCode MatDenseHIPResetArray(Mat);
PETSC_EXTERN PetscErrorCode MatDenseHIPSetPreallocation(Mat, PetscScalar *);
PETSC_EXTERN PetscErrorCode MatCreateSeqSELLHIP(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSELLHIP(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
#endif

#if defined(PETSC_HAVE_VIENNACL)
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJViennaCL(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateAIJViennaCL(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
#endif

#if PetscDefined(HAVE_KOKKOS)
PETSC_EXTERN PetscErrorCode MatCreateAIJKokkos(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatCreateSeqAIJKokkos(MPI_Comm, PetscInt, PetscInt, PetscInt, const PetscInt[], Mat *);
#endif

#if defined(PETSC_HAVE_FFTW)
PETSC_EXTERN PetscErrorCode VecScatterPetscToFFTW(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode VecScatterFFTWToPetsc(Mat, Vec, Vec);
PETSC_EXTERN PetscErrorCode MatCreateVecsFFTW(Mat, Vec *, Vec *, Vec *);
#endif

#if defined(PETSC_HAVE_SCALAPACK) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
PETSC_EXTERN PetscErrorCode MatCreateScaLAPACK(MPI_Comm, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatScaLAPACKSetBlockSizes(Mat, PetscInt, PetscInt);
PETSC_EXTERN PetscErrorCode MatScaLAPACKGetBlockSizes(Mat, PetscInt *, PetscInt *);
#endif

PETSC_EXTERN PetscErrorCode MatCreateNest(MPI_Comm, PetscInt, const IS[], PetscInt, const IS[], const Mat[], Mat *);
PETSC_EXTERN PetscErrorCode MatNestGetSize(Mat, PetscInt *, PetscInt *);
PETSC_EXTERN PetscErrorCode MatNestGetISs(Mat, IS[], IS[]);
PETSC_EXTERN PetscErrorCode MatNestGetLocalISs(Mat, IS[], IS[]);
PETSC_EXTERN PetscErrorCode MatNestGetSubMats(Mat, PetscInt *, PetscInt *, Mat ***);
PETSC_EXTERN PetscErrorCode MatNestGetSubMat(Mat, PetscInt, PetscInt, Mat *);
PETSC_EXTERN PetscErrorCode MatNestSetVecType(Mat, VecType);
PETSC_EXTERN PetscErrorCode MatNestSetSubMats(Mat, PetscInt, const IS[], PetscInt, const IS[], const Mat[]);
PETSC_EXTERN PetscErrorCode MatNestSetSubMat(Mat, PetscInt, PetscInt, Mat);

PETSC_EXTERN PetscErrorCode MatFilter(Mat, PetscReal, PetscBool, PetscBool);
PETSC_DEPRECATED_FUNCTION(3, 20, 0, "MatFilter()", ) static inline PetscErrorCode MatChop(Mat A, PetscReal tol)
{
  return MatFilter(A, tol, PETSC_FALSE, PETSC_FALSE);
}
PETSC_EXTERN PetscErrorCode MatComputeBandwidth(Mat, PetscReal, PetscInt *);

PETSC_EXTERN PetscErrorCode MatSubdomainsCreateCoalesce(Mat, PetscInt, PetscInt *, IS **);

PETSC_EXTERN PetscErrorCode MatPreallocatorPreallocate(Mat, PetscBool, Mat);

PETSC_EXTERN PetscErrorCode MatHeaderMerge(Mat, Mat *);
PETSC_EXTERN PetscErrorCode MatHeaderReplace(Mat, Mat *);

PETSC_EXTERN PetscErrorCode MatSeqAIJGetCSRAndMemType(Mat, const PetscInt **, const PetscInt **, PetscScalar **, PetscMemType *);

PETSC_EXTERN PetscErrorCode MatCreateGraph(Mat, PetscBool, PetscBool, PetscReal, PetscInt, PetscInt[], Mat *);
PETSC_EXTERN PetscErrorCode MatEliminateZeros(Mat, PetscBool);

PETSC_EXTERN PetscErrorCode MatCreateDenseFromVecType(MPI_Comm, VecType, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar *, Mat *);

PETSC_EXTERN PetscErrorCode MatSetHPL(Mat, int);
#define PETSCBMHPL "hpl"

PETSC_EXTERN PetscErrorCode MatDFischer(Mat, Vec, Vec, Vec, Vec, Vec, Vec, Vec, Vec);