#include /*I "petscmat.h" I*/ static PetscErrorCode MatTransposeAXPY_Private(Mat Y, PetscScalar a, Mat X, MatStructure str, Mat T) { Mat A, F; PetscErrorCode (*f)(Mat, Mat *); PetscFunctionBegin; PetscCall(PetscObjectQueryFunction((PetscObject)T, "MatTransposeGetMat_C", &f)); if (f) { PetscCall(MatTransposeGetMat(T, &A)); if (T == X) { PetscCall(PetscInfo(NULL, "Explicitly transposing X of type MATTRANSPOSEVIRTUAL to perform MatAXPY()\n")); PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &F)); A = Y; } else { PetscCall(PetscInfo(NULL, "Transposing X because Y of type MATTRANSPOSEVIRTUAL to perform MatAXPY()\n")); PetscCall(MatTranspose(X, MAT_INITIAL_MATRIX, &F)); } } else { PetscCall(MatHermitianTransposeGetMat(T, &A)); if (T == X) { PetscCall(PetscInfo(NULL, "Explicitly Hermitian transposing X of type MATHERITIANTRANSPOSEVIRTUAL to perform MatAXPY()\n")); PetscCall(MatHermitianTranspose(A, MAT_INITIAL_MATRIX, &F)); A = Y; } else { PetscCall(PetscInfo(NULL, "Hermitian transposing X because Y of type MATHERITIANTRANSPOSEVIRTUAL to perform MatAXPY()\n")); PetscCall(MatHermitianTranspose(X, MAT_INITIAL_MATRIX, &F)); } } PetscCall(MatAXPY(A, a, F, str)); PetscCall(MatDestroy(&F)); PetscFunctionReturn(0); } /*@ MatAXPY - Computes Y = a*X + Y. Logically Collective on Mat Input Parameters: + a - the scalar multiplier . X - the first matrix . Y - the second matrix - str - either SAME_NONZERO_PATTERN, DIFFERENT_NONZERO_PATTERN, UNKNOWN_NONZERO_PATTERN, or SUBSET_NONZERO_PATTERN (nonzeros of X is a subset of Y's) Note: No operation is performed when a is zero. Level: intermediate .seealso: `MatAYPX()` @*/ PetscErrorCode MatAXPY(Mat Y, PetscScalar a, Mat X, MatStructure str) { PetscInt M1, M2, N1, N2; PetscInt m1, m2, n1, n2; PetscBool sametype, transpose; PetscFunctionBegin; PetscValidHeaderSpecific(Y, MAT_CLASSID, 1); PetscValidLogicalCollectiveScalar(Y, a, 2); PetscValidHeaderSpecific(X, MAT_CLASSID, 3); PetscCheckSameComm(Y, 1, X, 3); PetscCall(MatGetSize(X, &M1, &N1)); PetscCall(MatGetSize(Y, &M2, &N2)); PetscCall(MatGetLocalSize(X, &m1, &n1)); PetscCall(MatGetLocalSize(Y, &m2, &n2)); PetscCheck(M1 == M2 && N1 == N2, PetscObjectComm((PetscObject)Y), PETSC_ERR_ARG_SIZ, "Non conforming matrix add: global sizes X %" PetscInt_FMT " x %" PetscInt_FMT ", Y %" PetscInt_FMT " x %" PetscInt_FMT, M1, N1, M2, N2); PetscCheck(m1 == m2 && n1 == n2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Non conforming matrix add: local sizes X %" PetscInt_FMT " x %" PetscInt_FMT ", Y %" PetscInt_FMT " x %" PetscInt_FMT, m1, n1, m2, n2); PetscCheck(Y->assembled, PetscObjectComm((PetscObject)Y), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix (Y)"); PetscCheck(X->assembled, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix (X)"); if (a == (PetscScalar)0.0) PetscFunctionReturn(0); if (Y == X) { PetscCall(MatScale(Y, 1.0 + a)); PetscFunctionReturn(0); } PetscCall(PetscObjectObjectTypeCompare((PetscObject)X, (PetscObject)Y, &sametype)); PetscCall(PetscLogEventBegin(MAT_AXPY, Y, 0, 0, 0)); if (Y->ops->axpy && (sametype || X->ops->axpy == Y->ops->axpy)) { PetscUseTypeMethod(Y, axpy, a, X, str); } else { PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &transpose, MATTRANSPOSEVIRTUAL, MATHERMITIANTRANSPOSEVIRTUAL, "")); if (transpose) { PetscCall(MatTransposeAXPY_Private(Y, a, X, str, X)); } else { PetscCall(PetscObjectTypeCompareAny((PetscObject)Y, &transpose, MATTRANSPOSEVIRTUAL, MATHERMITIANTRANSPOSEVIRTUAL, "")); if (transpose) { PetscCall(MatTransposeAXPY_Private(Y, a, X, str, Y)); } else { PetscCall(MatAXPY_Basic(Y, a, X, str)); } } } PetscCall(PetscLogEventEnd(MAT_AXPY, Y, 0, 0, 0)); PetscFunctionReturn(0); } PetscErrorCode MatAXPY_Basic_Preallocate(Mat Y, Mat X, Mat *B) { PetscErrorCode (*preall)(Mat, Mat, Mat *) = NULL; PetscFunctionBegin; /* look for any available faster alternative to the general preallocator */ PetscCall(PetscObjectQueryFunction((PetscObject)Y, "MatAXPYGetPreallocation_C", &preall)); if (preall) { PetscCall((*preall)(Y, X, B)); } else { /* Use MatPrellocator, assumes same row-col distribution */ Mat preallocator; PetscInt r, rstart, rend; PetscInt m, n, M, N; PetscCall(MatGetRowUpperTriangular(Y)); PetscCall(MatGetRowUpperTriangular(X)); PetscCall(MatGetSize(Y, &M, &N)); PetscCall(MatGetLocalSize(Y, &m, &n)); PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &preallocator)); PetscCall(MatSetType(preallocator, MATPREALLOCATOR)); PetscCall(MatSetLayouts(preallocator, Y->rmap, Y->cmap)); PetscCall(MatSetUp(preallocator)); PetscCall(MatGetOwnershipRange(preallocator, &rstart, &rend)); for (r = rstart; r < rend; ++r) { PetscInt ncols; const PetscInt *row; const PetscScalar *vals; PetscCall(MatGetRow(Y, r, &ncols, &row, &vals)); PetscCall(MatSetValues(preallocator, 1, &r, ncols, row, vals, INSERT_VALUES)); PetscCall(MatRestoreRow(Y, r, &ncols, &row, &vals)); PetscCall(MatGetRow(X, r, &ncols, &row, &vals)); PetscCall(MatSetValues(preallocator, 1, &r, ncols, row, vals, INSERT_VALUES)); PetscCall(MatRestoreRow(X, r, &ncols, &row, &vals)); } PetscCall(MatSetOption(preallocator, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE)); PetscCall(MatAssemblyBegin(preallocator, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(preallocator, MAT_FINAL_ASSEMBLY)); PetscCall(MatRestoreRowUpperTriangular(Y)); PetscCall(MatRestoreRowUpperTriangular(X)); PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), B)); PetscCall(MatSetType(*B, ((PetscObject)Y)->type_name)); PetscCall(MatSetLayouts(*B, Y->rmap, Y->cmap)); PetscCall(MatPreallocatorPreallocate(preallocator, PETSC_FALSE, *B)); PetscCall(MatDestroy(&preallocator)); } PetscFunctionReturn(0); } PetscErrorCode MatAXPY_Basic(Mat Y, PetscScalar a, Mat X, MatStructure str) { PetscBool isshell, isdense, isnest; PetscFunctionBegin; PetscCall(MatIsShell(Y, &isshell)); if (isshell) { /* MatShell has special support for AXPY */ PetscErrorCode (*f)(Mat, PetscScalar, Mat, MatStructure); PetscCall(MatGetOperation(Y, MATOP_AXPY, (void (**)(void)) & f)); if (f) { PetscCall((*f)(Y, a, X, str)); PetscFunctionReturn(0); } } /* no need to preallocate if Y is dense */ PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)Y, &isdense, MATSEQDENSE, MATMPIDENSE, "")); if (isdense) { PetscCall(PetscObjectTypeCompare((PetscObject)X, MATNEST, &isnest)); if (isnest) { PetscCall(MatAXPY_Dense_Nest(Y, a, X)); PetscFunctionReturn(0); } if (str == DIFFERENT_NONZERO_PATTERN || str == UNKNOWN_NONZERO_PATTERN) str = SUBSET_NONZERO_PATTERN; } if (str != DIFFERENT_NONZERO_PATTERN && str != UNKNOWN_NONZERO_PATTERN) { PetscInt i, start, end, j, ncols, m, n; const PetscInt *row; PetscScalar *val; const PetscScalar *vals; PetscCall(MatGetSize(X, &m, &n)); PetscCall(MatGetOwnershipRange(X, &start, &end)); PetscCall(MatGetRowUpperTriangular(X)); if (a == 1.0) { for (i = start; i < end; i++) { PetscCall(MatGetRow(X, i, &ncols, &row, &vals)); PetscCall(MatSetValues(Y, 1, &i, ncols, row, vals, ADD_VALUES)); PetscCall(MatRestoreRow(X, i, &ncols, &row, &vals)); } } else { PetscInt vs = 100; /* realloc if needed, as this function may be used in parallel */ PetscCall(PetscMalloc1(vs, &val)); for (i = start; i < end; i++) { PetscCall(MatGetRow(X, i, &ncols, &row, &vals)); if (vs < ncols) { vs = PetscMin(2 * ncols, n); PetscCall(PetscRealloc(vs * sizeof(*val), &val)); } for (j = 0; j < ncols; j++) val[j] = a * vals[j]; PetscCall(MatSetValues(Y, 1, &i, ncols, row, val, ADD_VALUES)); PetscCall(MatRestoreRow(X, i, &ncols, &row, &vals)); } PetscCall(PetscFree(val)); } PetscCall(MatRestoreRowUpperTriangular(X)); PetscCall(MatAssemblyBegin(Y, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(Y, MAT_FINAL_ASSEMBLY)); } else { Mat B; PetscCall(MatAXPY_Basic_Preallocate(Y, X, &B)); PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str)); PetscCall(MatHeaderMerge(Y, &B)); } PetscFunctionReturn(0); } PetscErrorCode MatAXPY_BasicWithPreallocation(Mat B, Mat Y, PetscScalar a, Mat X, MatStructure str) { PetscInt i, start, end, j, ncols, m, n; const PetscInt *row; PetscScalar *val; const PetscScalar *vals; PetscFunctionBegin; PetscCall(MatGetSize(X, &m, &n)); PetscCall(MatGetOwnershipRange(X, &start, &end)); PetscCall(MatGetRowUpperTriangular(Y)); PetscCall(MatGetRowUpperTriangular(X)); if (a == 1.0) { for (i = start; i < end; i++) { PetscCall(MatGetRow(Y, i, &ncols, &row, &vals)); PetscCall(MatSetValues(B, 1, &i, ncols, row, vals, ADD_VALUES)); PetscCall(MatRestoreRow(Y, i, &ncols, &row, &vals)); PetscCall(MatGetRow(X, i, &ncols, &row, &vals)); PetscCall(MatSetValues(B, 1, &i, ncols, row, vals, ADD_VALUES)); PetscCall(MatRestoreRow(X, i, &ncols, &row, &vals)); } } else { PetscInt vs = 100; /* realloc if needed, as this function may be used in parallel */ PetscCall(PetscMalloc1(vs, &val)); for (i = start; i < end; i++) { PetscCall(MatGetRow(Y, i, &ncols, &row, &vals)); PetscCall(MatSetValues(B, 1, &i, ncols, row, vals, ADD_VALUES)); PetscCall(MatRestoreRow(Y, i, &ncols, &row, &vals)); PetscCall(MatGetRow(X, i, &ncols, &row, &vals)); if (vs < ncols) { vs = PetscMin(2 * ncols, n); PetscCall(PetscRealloc(vs * sizeof(*val), &val)); } for (j = 0; j < ncols; j++) val[j] = a * vals[j]; PetscCall(MatSetValues(B, 1, &i, ncols, row, val, ADD_VALUES)); PetscCall(MatRestoreRow(X, i, &ncols, &row, &vals)); } PetscCall(PetscFree(val)); } PetscCall(MatRestoreRowUpperTriangular(Y)); PetscCall(MatRestoreRowUpperTriangular(X)); PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); PetscFunctionReturn(0); } /*@ MatShift - Computes Y = Y + a I, where a is a PetscScalar and I is the identity matrix. Neighbor-wise Collective on Mat Input Parameters: + Y - the matrices - a - the PetscScalar Level: intermediate Notes: If Y is a rectangular matrix, the shift is done on the main diagonal Y_{ii} of the matrix (https://en.wikipedia.org/wiki/Main_diagonal) If the matrix Y is missing some diagonal entries this routine can be very slow. To make it fast one should initially fill the matrix so that all diagonal entries have a value (with a value of zero for those locations that would not have an entry). No operation is performed when a is zero. To form Y = Y + diag(V) use MatDiagonalSet() .seealso: `MatDiagonalSet()`, `MatScale()`, `MatDiagonalScale()` @*/ PetscErrorCode MatShift(Mat Y, PetscScalar a) { PetscFunctionBegin; PetscValidHeaderSpecific(Y, MAT_CLASSID, 1); PetscCheck(Y->assembled, PetscObjectComm((PetscObject)Y), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix"); PetscCheck(!Y->factortype, PetscObjectComm((PetscObject)Y), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix"); MatCheckPreallocated(Y, 1); if (a == 0.0) PetscFunctionReturn(0); if (Y->ops->shift) PetscUseTypeMethod(Y, shift, a); else PetscCall(MatShift_Basic(Y, a)); PetscCall(PetscObjectStateIncrease((PetscObject)Y)); PetscFunctionReturn(0); } PetscErrorCode MatDiagonalSet_Default(Mat Y, Vec D, InsertMode is) { PetscInt i, start, end; const PetscScalar *v; PetscFunctionBegin; PetscCall(MatGetOwnershipRange(Y, &start, &end)); PetscCall(VecGetArrayRead(D, &v)); for (i = start; i < end; i++) PetscCall(MatSetValues(Y, 1, &i, 1, &i, v + i - start, is)); PetscCall(VecRestoreArrayRead(D, &v)); PetscCall(MatAssemblyBegin(Y, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(Y, MAT_FINAL_ASSEMBLY)); PetscFunctionReturn(0); } /*@ MatDiagonalSet - Computes Y = Y + D, where D is a diagonal matrix that is represented as a vector. Or Y[i,i] = D[i] if InsertMode is INSERT_VALUES. Neighbor-wise Collective on Mat Input Parameters: + Y - the input matrix . D - the diagonal matrix, represented as a vector - i - INSERT_VALUES or ADD_VALUES Note: If the matrix Y is missing some diagonal entries this routine can be very slow. To make it fast one should initially fill the matrix so that all diagonal entries have a value (with a value of zero for those locations that would not have an entry). Level: intermediate .seealso: `MatShift()`, `MatScale()`, `MatDiagonalScale()` @*/ PetscErrorCode MatDiagonalSet(Mat Y, Vec D, InsertMode is) { PetscInt matlocal, veclocal; PetscFunctionBegin; PetscValidHeaderSpecific(Y, MAT_CLASSID, 1); PetscValidHeaderSpecific(D, VEC_CLASSID, 2); PetscCall(MatGetLocalSize(Y, &matlocal, NULL)); PetscCall(VecGetLocalSize(D, &veclocal)); PetscCheck(matlocal == veclocal, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Number local rows of matrix %" PetscInt_FMT " does not match that of vector for diagonal %" PetscInt_FMT, matlocal, veclocal); if (Y->ops->diagonalset) PetscUseTypeMethod(Y, diagonalset, D, is); else PetscCall(MatDiagonalSet_Default(Y, D, is)); PetscCall(PetscObjectStateIncrease((PetscObject)Y)); PetscFunctionReturn(0); } /*@ MatAYPX - Computes Y = a*Y + X. Logically on Mat Input Parameters: + a - the PetscScalar multiplier . Y - the first matrix . X - the second matrix - str - either SAME_NONZERO_PATTERN, DIFFERENT_NONZERO_PATTERN, UNKNOWN_NONZERO_PATTERN, or SUBSET_NONZERO_PATTERN (nonzeros of X is a subset of Y's) Level: intermediate .seealso: `MatAXPY()` @*/ PetscErrorCode MatAYPX(Mat Y, PetscScalar a, Mat X, MatStructure str) { PetscFunctionBegin; PetscCall(MatScale(Y, a)); PetscCall(MatAXPY(Y, 1.0, X, str)); PetscFunctionReturn(0); } /*@ MatComputeOperator - Computes the explicit matrix Collective on Mat Input Parameters: + inmat - the matrix - mattype - the matrix type for the explicit operator Output Parameter: . mat - the explicit operator Note: This computation is done by applying the operators to columns of the identity matrix. This routine is costly in general, and is recommended for use only with relatively small systems. Currently, this routine uses a dense matrix format if mattype == NULL. Level: advanced @*/ PetscErrorCode MatComputeOperator(Mat inmat, MatType mattype, Mat *mat) { PetscFunctionBegin; PetscValidHeaderSpecific(inmat, MAT_CLASSID, 1); PetscValidPointer(mat, 3); PetscCall(MatConvert_Shell(inmat, mattype ? mattype : MATDENSE, MAT_INITIAL_MATRIX, mat)); PetscFunctionReturn(0); } /*@ MatComputeOperatorTranspose - Computes the explicit matrix representation of a give matrix that can apply MatMultTranspose() Collective on Mat Input Parameters: + inmat - the matrix - mattype - the matrix type for the explicit operator Output Parameter: . mat - the explicit operator transposed Note: This computation is done by applying the transpose of the operator to columns of the identity matrix. This routine is costly in general, and is recommended for use only with relatively small systems. Currently, this routine uses a dense matrix format if mattype == NULL. Level: advanced @*/ PetscErrorCode MatComputeOperatorTranspose(Mat inmat, MatType mattype, Mat *mat) { Mat A; PetscFunctionBegin; PetscValidHeaderSpecific(inmat, MAT_CLASSID, 1); PetscValidPointer(mat, 3); PetscCall(MatCreateTranspose(inmat, &A)); PetscCall(MatConvert_Shell(A, mattype ? mattype : MATDENSE, MAT_INITIAL_MATRIX, mat)); PetscCall(MatDestroy(&A)); PetscFunctionReturn(0); } /*@ MatChop - Set all values in the matrix less than the tolerance to zero Input Parameters: + A - The matrix - tol - The zero tolerance Output Parameters: . A - The chopped matrix Level: intermediate .seealso: `MatCreate()`, `MatZeroEntries()` @*/ PetscErrorCode MatChop(Mat A, PetscReal tol) { Mat a; PetscScalar *newVals; PetscInt *newCols, rStart, rEnd, numRows, maxRows, r, colMax = 0; PetscBool flg; PetscFunctionBegin; PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)A, &flg, MATSEQDENSE, MATMPIDENSE, "")); if (flg) { PetscCall(MatDenseGetLocalMatrix(A, &a)); PetscCall(MatDenseGetLDA(a, &r)); PetscCall(MatGetSize(a, &rStart, &rEnd)); PetscCall(MatDenseGetArray(a, &newVals)); for (; colMax < rEnd; ++colMax) { for (maxRows = 0; maxRows < rStart; ++maxRows) newVals[maxRows + colMax * r] = PetscAbsScalar(newVals[maxRows + colMax * r]) < tol ? 0.0 : newVals[maxRows + colMax * r]; } PetscCall(MatDenseRestoreArray(a, &newVals)); } else { PetscCall(MatGetOwnershipRange(A, &rStart, &rEnd)); PetscCall(MatGetRowUpperTriangular(A)); for (r = rStart; r < rEnd; ++r) { PetscInt ncols; PetscCall(MatGetRow(A, r, &ncols, NULL, NULL)); colMax = PetscMax(colMax, ncols); PetscCall(MatRestoreRow(A, r, &ncols, NULL, NULL)); } numRows = rEnd - rStart; PetscCall(MPIU_Allreduce(&numRows, &maxRows, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)A))); PetscCall(PetscMalloc2(colMax, &newCols, colMax, &newVals)); PetscCall(MatGetOption(A, MAT_NO_OFF_PROC_ENTRIES, &flg)); /* cache user-defined value */ PetscCall(MatSetOption(A, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE)); /* short-circuit code in MatAssemblyBegin() and MatAssemblyEnd() */ /* that are potentially called many times depending on the distribution of A */ for (r = rStart; r < rStart + maxRows; ++r) { const PetscScalar *vals; const PetscInt *cols; PetscInt ncols, newcols, c; if (r < rEnd) { PetscCall(MatGetRow(A, r, &ncols, &cols, &vals)); for (c = 0; c < ncols; ++c) { newCols[c] = cols[c]; newVals[c] = PetscAbsScalar(vals[c]) < tol ? 0.0 : vals[c]; } newcols = ncols; PetscCall(MatRestoreRow(A, r, &ncols, &cols, &vals)); PetscCall(MatSetValues(A, 1, &r, newcols, newCols, newVals, INSERT_VALUES)); } PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); } PetscCall(MatRestoreRowUpperTriangular(A)); PetscCall(PetscFree2(newCols, newVals)); PetscCall(MatSetOption(A, MAT_NO_OFF_PROC_ENTRIES, flg)); /* reset option to its user-defined value */ } PetscFunctionReturn(0); }