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/petsc/src/ksp/pc/impls/sor/
H A Dsor.tex18 x_i^{n+1/2} = x_i^n + \omega A_{ii}^{-1}( b_i - \sum_{j < i} A_{ij} x_j^{n+1/2} - \sum_{j \ge i} A…
22 x_i^{n+1} = x_i^{n+1/2} + \omega A_{ii}^{-1}( b_i - \sum_{j \le i} A_{ij} x_j^{n+1/2} - \sum_{j > …
28 x_i^{1/2} = \omega A_{ii}^{-1}( b_i - \sum_{j < i} A_{ij} x_j^{1/2})
32 x_i = (1 - \omega) x_i^{1/2} + \omega A_{ii}^{-1}( b_i - \sum_{j < i} A_{ij} x_j^{1/2} - \sum_{j > …
90 x_i = \omega D_{ii}^{-1}(b_i - \sum_{j<i} A_{ij} x_j)
93 x_i = (D_{ii}/\omega)^{-1}(b_i - \sum_{j<i} A_{ij} x_j)
/petsc/src/mat/tests/output/
H A Dex120_3.out2 max|(x_j^T*x_i) - delta_ji|: 9.99201e-16
H A Dex120_1.out2 max|(x_j^T*x_i) - delta_ji|: 9.99201e-16
H A Dex120_2.out2 max|(x_j^T*x_i) - delta_ji|: 6.04172e-16
H A Dex120_4.out2 max|(x_j^T*x_i) - delta_ji|: 6.04172e-16
H A Dex116_2.out2 max|(x_j^T*x_i) - delta_ji|: 3.10862e-15
H A Dex116_1.out2 max|(x_j^T*x_i) - delta_ji|: 5.89658e-16
/petsc/src/ksp/ksp/utils/lmvm/
H A Dlmproducts.c187 Vec x_i_, x_i; in LMProductsUpdate_Internal() local
194 PetscCall(VecDuplicate(x_i_, &x_i)); in LMProductsUpdate_Internal()
195 PetscCall(VecCopy(x_i_, x_i)); in LMProductsUpdate_Internal()
218 PetscCall(VecDot(y_j, x_i, &dot_true)); in LMProductsUpdate_Internal()
231 PetscCall(VecDestroy(&x_i)); in LMProductsUpdate_Internal()
H A Dlmvmutils.c972 Vec x_i, op_x_i; in MatLMVMUpdateOpVecs() local
974 PetscCall(LMBasisGetVecRead(X, i, &x_i)); in MatLMVMUpdateOpVecs()
976 PetscCall(op(B, x_i, op_x_i)); in MatLMVMUpdateOpVecs()
978 PetscCall(LMBasisRestoreVecRead(X, i, &x_i)); in MatLMVMUpdateOpVecs()
/petsc/doc/manual/
H A Dtao.md1634 x(\mu) = (1+\mu) \frac{1}{N} \sum_{i=1}^N x_i - \mu x_{N+1},
1697 l_i & \text{if} \; x_i < l_i \\
1698 u_i & \text{if} \; x_i > u_i \\
1699 x_i & \text{otherwise}
1729 \text{lower bounded}: & \mathcal{L}(x) & = & \{ i \; : \; x_i \leq l_i + \epsilon \; \land \; g(x)_…
1730 \text{upper bounded}: & \mathcal{U}(x) & = & \{ i \; : \; x_i \geq u_i + \epsilon \; \land \; g(x)_…
2710 \phi(x_i - l_i, F_i(x)) & \text{if } -\infty < l_i < u_i = \infty, \\
2711 -\phi(u_i-x_i, -F_i(x)) & \text{if } -\infty = l_i < u_i < \infty, \\
2712 \phi(x_i - l_i, \phi(u_i - x_i, - F_i(x))) & \text{if } -\infty < l_i < u_i < \infty, \\
2714 l_i - x_i & \text{if } -\infty < l_i = u_i < \infty.
[all …]
H A Dvec.md695 …| ``VecAbs(Vec x);`` | :math:`x_i = |x_{i}|` …
697 …| ``VecReciprocal(Vec x);`` | :math:`x_i = 1/x_{i}` …
699 …| ``VecShift(Vec x, PetscScalar s);`` | :math:`x_i = s + x_{i}` …
701 …| ``VecSet(Vec x, PetscScalar alpha);`` | :math:`x_i = \alpha` …
H A Dts.md40 {u^n}_i = \xi_i(t_n) \doteq u(x_i,t_n),
/petsc/src/dm/impls/plex/
H A Dplexgeometry.c498 PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 0]); in DMPlexLocatePoint_Quad_2D_Linear_Internal() local
509 PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j); in DMPlexLocatePoint_Quad_2D_Linear_Internal()