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https://github.com/TREX-CoE/qmckl.git
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Added WB2 kernel back.
This commit is contained in:
Francois Coppens
parent
db13db8afa
commit
883416d84c
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@ -89,15 +89,15 @@ from applying the updates to the original matrix.
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| ~determinant~ | ~double~ | inout | Determinant of the Slater-matrix |
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*** Requirements
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* ~context~ is not ~QMCKL_NULL_CONTEXT~
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* ~LDS >= 2~
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* ~Dim >= 2~
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* ~N_updates >= 1~
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* ~Updates~ is allocated with $N_updates \times Dim$ elements
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* ~Updates_index~ is allocated with $N_updates$ elements
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* ~breakdown~ is a small number such that $0 < breakdown << 1$
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* ~Slater_inv~ is allocated with $Dim \times Dim$ elements
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* ~determinant > 0~
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- ~context~ is not ~QMCKL_NULL_CONTEXT~
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- ~LDS >= 2~
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- ~Dim >= 2~
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- ~N_updates >= 1~
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- ~Updates~ is allocated with $N_updates \times Dim$ elements
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- ~Updates_index~ is allocated with $N_updates$ elements
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- ~breakdown~ is a small number such that $0 < breakdown << 1$
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- ~Slater_inv~ is allocated with $Dim \times Dim$ elements
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- ~determinant > 0~
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*** Pedagogical kernel source (in Fortran)
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The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
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@ -251,7 +251,7 @@ integer function qmckl_sm_naive_doc_f(context, &
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end function qmckl_sm_naive_doc_f
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#+end_src
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**** C interface to the pedagogical kernel (not directly exposed)
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**** C interface (not directly exposed)
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The following Fortran function ~qmckl_sm_naive_doc~ makes sure
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that the pedagogical kernel ~qmckl_sm_naive_doc_f~, written in
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Fortran, can be called from C using the ~ISO_C_BINDING~. The Fortran function ~qmckl_sm_naive_doc~ will be exposed in the header file 'qmckl.h'
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@ -1418,6 +1418,382 @@ This function cannot be used by itself and is used in Sherman-Morrison with upda
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with Sherman-Morrison and update splitting. Please look at the performance reccomendations for those two kernels.
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* Woodbury 2x2
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** ~qmckl_woodbury_2x2~
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:PROPERTIES:
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:Name: qmckl_woodbury_2x2
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:CRetType: qmckl_exit_code
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:FRetType: qmckl_exit_code
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:END:
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*** Introduction
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The Woodbury 2x2 kernel. It is used to apply two rank-1 updates at once. The formula used in
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this algorithm is called the Woodbury Matrix Identity
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\[
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(S + U V)^{-1} = S^{-1} - C B^{-1} D
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\]
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where
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$S$ is the Slater-matrix
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$U$ and $V$ are the matrices containing the updates and the canonical basis matrix
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$S^{-1}$ is the inverse of the Slater-matrix
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$C:= S^{-1}U$, a Dim $\times 2$ matrix
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$B := 1 + VC$, the $2 \times 2$ matrix that is going to be inverted
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$D := VS^{-1}$, a $2 \times Dim$ matrix
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If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
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from applying the updates to the original matrix.
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*** API
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#+NAME: qmckl_woodbury_2x2_args
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| Variable | Type | In/Out | Description |
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|-----------------+-------------------+-------+-------------------------------------------------|
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| ~context~ | ~qmckl_context~ | in | Global state |
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| ~LDS~ | ~uint64_t~ | in | Leading dimension of Slater_inv |
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| ~Dim~ | ~uint64_t~ | in | Dimension of Slater_inv |
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| ~Updates~ | ~double[2*Dim]~ | in | Array containing the updates |
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| ~Updates_index~ | ~uint64_t[2]~ | in | Array containing the rank-1 updates |
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| ~breakdown~ | ~double~ | in | Break-down parameter on which to fail or not |
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| ~Slater_inv~ | ~double[LDS*Dim]~ | inout | Array containing the inverse of a Slater-matrix |
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| ~determinant~ | ~double~ | inout | Determinant of Slater-matrix |
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*** Requirements
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- ~context~ is not ~qmckl_null_context~
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- ~LDS >= 2~
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- ~Dim >= 2~
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- ~Updates~ is allocated with $2 \times Dim$ elements
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- ~Updates_index~ is allocated with $2$ elements
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- ~breakdown~ is a small number such that $0 < breakdown << 1$
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- ~Slater_inv~ is allocated with $Dim \times Dim$ elements
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*** Pedagogical kernel source (in Fortran)
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**** C interface (not directly exposed)
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*** C headers (exposed in qmckl.h)
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#+CALL: generate_c_header(table=qmckl_woodbury_2x2_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src c :tangle (eval h_func) :comments org
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qmckl_exit_code qmckl_woodbury_2x2 (
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const qmckl_context context,
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const uint64_t LDS,
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const uint64_t Dim,
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const double* Updates,
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const uint64_t* Updates_index,
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const double breakdown,
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double* Slater_inv,
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double* determinant );
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#+end_src
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*** C sources
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#+begin_src c :tangle (eval c) :comments org
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qmckl_exit_code qmckl_woodbury_2x2_hpc(const qmckl_context context,
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const uint64_t LDS,
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const uint64_t Dim,
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const double* __restrict Updates,
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const uint64_t* __restrict Updates_index,
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const double breakdown,
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double* __restrict Slater_inv,
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double* __restrict determinant) {
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/*
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C := S^{-1} * U, dim x 2
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B := 1 + V * C, 2 x 2
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D := V * S^{-1}, 2 x dim
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*/
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if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
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return qmckl_failwith(context,
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QMCKL_NULL_CONTEXT,
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"qmckl_woodbury_2x2_hpc",
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NULL);
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}
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const uint64_t row1 = (Updates_index[0] - 1);
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const uint64_t row2 = (Updates_index[1] - 1);
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// Compute C = (S^T)^{-1}U : Dim x 2
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double __attribute__((aligned(8))) C[2 * Dim];
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for (uint64_t i = 0; i < Dim; i++) {
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C[i * 2] = 0;
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C[i * 2 + 1] = 0;
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IVDEP
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ALIGNED
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for (uint64_t k = 0; k < LDS; k++) {
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C[i * 2] += Slater_inv[i * LDS + k] * Updates[k];
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C[i * 2 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
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}
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}
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// Compute B = 1 + VC : 2 x 2
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const double B0 = C[row1 * 2] + 1;
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const double B1 = C[row1 * 2 + 1];
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const double B2 = C[row2 * 2];
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const double B3 = C[row2 * 2 + 1] + 1;
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// Check if determinant of inverted matrix is not zero
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double det = B0 * B3 - B1 * B2;
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if (fabs(det) < breakdown) {
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return QMCKL_FAILURE;
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}
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// Update det(S) when passed
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if (determinant)
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*determinant *= det;
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// Compute B^{-1} with explicit formula for 2 x 2 inversion
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double __attribute__((aligned(8))) Binv[4], idet = 1.0 / det;
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Binv[0] = idet * B3;
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Binv[1] = -1.0 * idet * B1;
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Binv[2] = -1.0 * idet * B2;
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Binv[3] = idet * B0;
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// tmp = B^{-1}D : 2 x LDS
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double __attribute__((aligned(8))) tmp[2 * LDS];
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double* r1dim = &(Slater_inv[row1 * LDS]);
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double* r2dim = &(Slater_inv[row2 * LDS]);
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IVDEP
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ALIGNED
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for (uint64_t j = 0; j < LDS; j++) {
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tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
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tmp[LDS + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
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}
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// Compute (S^T)^{-1} - C * tmp : Dim x LDS
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for (uint64_t i = 0; i < Dim; i++) {
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IVDEP
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ALIGNED
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for (uint64_t j = 0; j < LDS; j++) {
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Slater_inv[i * LDS + j] -= C[i * 2] * tmp[j];
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Slater_inv[i * LDS + j] -= C[i * 2 + 1] * tmp[LDS + j];
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}
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}
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return QMCKL_SUCCESS;
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}
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#+end_src
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#+NAME:woodbury_2x2_kernel_template
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#+begin_src c
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static inline qmckl_exit_code qmckl_woodbury_2x2_{Dim}(
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const qmckl_context context,
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const double* __restrict Updates,
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const uint64_t* __restrict Updates_index,
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const double breakdown,
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double* __restrict Slater_inv,
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double* __restrict determinant) {
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/*
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C := S^{-1} * U, dim x 2
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B := 1 + V * C, 2 x 2
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D := V * S^{-1}, 2 x dim
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*/
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if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
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return qmckl_failwith(context,
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QMCKL_NULL_CONTEXT,
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"qmckl_woodbury_2x2_{Dim}",
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NULL);
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}
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const uint64_t row1 = (Updates_index[0] - 1);
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const uint64_t row2 = (Updates_index[1] - 1);
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// Compute C = (S^T)^{-1}U : {Dim} x 2
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double __attribute__((aligned(8))) C[2 * {Dim}];
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for (uint64_t i = 0; i < {Dim}; i++) {
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C[i * 2] = 0;
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C[i * 2 + 1] = 0;
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IVDEP
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ALIGNED
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for (uint64_t k = 0; k < D{Dim}_P; k++) {
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C[i * 2] += Slater_inv[i * D{Dim}_P + k] * Updates[k];
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C[i * 2 + 1] += Slater_inv[i * D{Dim}_P + k] * Updates[D{Dim}_P + k];
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}
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}
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// Compute B = 1 + VC : 2 x 2
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const double B0 = C[row1 * 2] + 1;
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const double B1 = C[row1 * 2 + 1];
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const double B2 = C[row2 * 2];
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const double B3 = C[row2 * 2 + 1] + 1;
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// Check if determinant of inverted matrix is not zero
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double det = B0 * B3 - B1 * B2;
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if (fabs(det) < breakdown) {
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return QMCKL_FAILURE;
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}
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// Update det(S) when passed
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if (determinant)
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*determinant *= det;
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// Compute B^{-1} with explicit formula for 2 x 2 inversion
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double __attribute__((aligned(8))) Binv[4], idet = 1.0 / det;
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Binv[0] = idet * B3;
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Binv[1] = -1.0 * idet * B1;
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Binv[2] = -1.0 * idet * B2;
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Binv[3] = idet * B0;
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// tmp = B^{-1}D : 2 x D{Dim}_P
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double __attribute__((aligned(8))) tmp[2 * D{Dim}_P];
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double* r1dim = &(Slater_inv[row1 * D{Dim}_P]);
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double* r2dim = &(Slater_inv[row2 * D{Dim}_P]);
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IVDEP
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ALIGNED
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for (uint64_t j = 0; j < D{Dim}_P; j++) {
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tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
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tmp[D{Dim}_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
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}
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// Compute (S^T)^{-1} - C * tmp : {Dim} x D{Dim}_P
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for (uint64_t i = 0; i < {Dim}; i++) {
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IVDEP
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ALIGNED
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for (uint64_t j = 0; j < D{Dim}_P; j++) {
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Slater_inv[i * D{Dim}_P + j] -= C[i * 2] * tmp[j];
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Slater_inv[i * D{Dim}_P + j] -= C[i * 2 + 1] * tmp[D{Dim}_P + j];
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}
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}
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return QMCKL_SUCCESS;
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}
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#+end_src
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#+NAME:woodbury_2x2_kernel_generator
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#+begin_src python :noweb yes :exports none
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text="""
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<<woodbury_2x2_kernel_template>>
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"""
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result = []
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for Dim in <<kernel_generator_range>>:
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Dim=str(Dim)
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result.append(text.replace("{Dim}",Dim) )
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return ''.join(result)
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#+end_src
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#+NAME:woodbury_2x2_switch-case_generator
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#+begin_src python :noweb yes :exports none
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text="""
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case {Dim}:
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return qmckl_woodbury_2x2_{Dim}(context,
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Updates,
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Updates_index,
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breakdown,
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Slater_inv,
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determinant);"""
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result = []
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for Dim in <<kernel_generator_range>>:
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Dim=str(Dim)
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result.append(text.replace("{Dim}",Dim) )
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return ''.join(result)
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#+end_src
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#+begin_src c :tangle (eval c) :comments org :noweb yes
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<<woodbury_2x2_kernel_generator()>>
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qmckl_exit_code qmckl_woodbury_2x2(const qmckl_context context,
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const uint64_t LDS,
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const uint64_t Dim,
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const double* Updates,
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const uint64_t* Updates_index,
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const double breakdown,
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double* Slater_inv,
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double* determinant) {
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if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
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return qmckl_failwith(context,
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QMCKL_NULL_CONTEXT,
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"qmckl_woodbury_2x2",
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NULL);
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}
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if (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // Most cases
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switch (Dim) {
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<<woodbury_2x2_switch-case_generator()>>
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}
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}
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else { // When SIMD_LENGTH > 1, called with LDS == Dim AND Dim != (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH)
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return qmckl_woodbury_2x2_hpc(context,
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LDS,
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Dim,
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Updates,
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Updates_index,
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breakdown,
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Slater_inv,
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determinant);
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}
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return QMCKL_FAILURE;
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}
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#+end_src
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*** Fortran interfaces (exposed in qmckl_f.F90)
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:PROPERTIES:
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:Name: qmckl_woodbury_2x2
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:CRetType: qmckl_exit_code
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:FRetType: qmckl_exit_code
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:END:
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#+CALL: generate_f_interface(table=qmckl_woodbury_2x2_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
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interface
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integer(c_int32_t) function qmckl_woodbury_2x2 &
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(context, LDS, Dim, Updates, Updates_index, breakdown, Slater_inv, determinant) &
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bind(C)
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use, intrinsic :: iso_c_binding
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import
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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integer (c_int64_t) , intent(in) , value :: LDS
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integer (c_int64_t) , intent(in) , value :: Dim
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real (c_double ) , intent(in) :: Updates(2*Dim)
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integer (c_int64_t) , intent(in) :: Updates_index(2)
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real (c_double ) , intent(in) , value :: breakdown
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real (c_double ) , intent(inout) :: Slater_inv(LDS*Dim)
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real (c_double ) , intent(inout) :: determinant
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end function qmckl_woodbury_2x2
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end interface
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#+end_src
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*** Performance
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This function is most efficient when used in cases where there are only 2 rank-1 updates and
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it is sure they will not result in a singular matrix.
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*** Tests
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#+begin_src c :tangle (eval c_test)
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assert(Updates2 != NULL);
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assert(Updates_index2 != NULL);
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assert(Slater_inv2 != NULL);
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det = -1.4432116661319376e-11;
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rc = qmckl_woodbury_2x2(context, LDS, Dim, Updates2, Updates_index2, breakdown, Slater_inv2, &det);
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assert(fabs(det-2.367058141251457e-10) < 1e-15);
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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res[i * Dim + j] = 0;
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for (unsigned int k = 0; k < Dim; k++) {
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res[i * Dim + j] += Slater2[i * Dim + k] * Slater_inv2[k * LDS + j];
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}
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}
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}
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rc = QMCKL_SUCCESS;
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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if (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
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rc = QMCKL_FAILURE;
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}
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if (i != j && fabs(res[i * Dim + j]) > tolerance) {
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rc = QMCKL_FAILURE;
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}
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}
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}
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assert(rc == QMCKL_SUCCESS);
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#+end_src
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* Sherman-Morrison with Slagel Splitting
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** ~qmckl_sm_splitting~
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:PROPERTIES:
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Reference in New Issue
Block a user