mirror of
https://github.com/TREX-CoE/Sherman-Morrison.git
synced 2024-08-25 06:31:44 +02:00
721 lines
25 KiB
C
721 lines
25 KiB
C
#include <math.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <string.h>
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#include "kernels.h"
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extern uint64_t n_splits;
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extern uint64_t block_fail;
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extern uint64_t recursive_calls;
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int min(int a, int b) {
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return (a > b) ? b : a;
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}
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uint32_t qmckl_sherman_morrison(
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const uint64_t vLDS, const uint64_t vDim, const uint64_t N_updates,
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const double *__restrict __attribute__((aligned(8))) Updates,
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const uint64_t *__restrict Updates_index, const double breakdown,
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double *__restrict __attribute__((aligned(8))) Slater_inv,
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double *__restrict determinant) {
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const uint32_t Dim = 21;
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const uint32_t LDS = 24;
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double __attribute__((aligned(8))) C[Dim];
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double __attribute__((aligned(8))) D[LDS];
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uint32_t l = 0;
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// For each update
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while (l < N_updates) {
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// C = S^{-1} x u_l
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for (uint32_t i = 0; i < Dim; i++) {
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C[i] = 0.0;
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j]; // regular mat-vec product, but actually working on S_inv^T * U_l.
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}
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}
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// Denominator: v_l^T * C
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const int cui = Updates_index[l] - 1;
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double den = 1.0 + C[cui];
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if (fabs(den) < breakdown) {
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return 1;
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}
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double iden = 1.0 / den;
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// Update det(A)
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if (!determinant)
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*determinant *= den;
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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D[j] = Slater_inv[cui * LDS + j]; // selecting proper column of v_l^T * S_inv
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}
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// A^{-1} = A^{-1} - C x D / den
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for (uint32_t i = 0; i < Dim; i++) {
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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const double update = C[i] * D[j] * iden;
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Slater_inv[i * LDS + j] -= update;
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}
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}
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l += 1;
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}
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return 0;
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}
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uint32_t qmckl_woodbury_2(const uint64_t vLDS, const uint64_t vDim,
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const double *__restrict __attribute__((aligned(8)))
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Updates,
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const uint64_t *__restrict Updates_index,
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const double breakdown,
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double *__restrict __attribute__((aligned(8)))
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Slater_inv,
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double *__restrict determinant) {
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const uint32_t Dim = 21;
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const uint32_t LDS = 24;
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/*
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COMPUTE S^{-1}P - CB^{-1}D : Dim x LDS,
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where S^{-1}P : Dim x LDS,
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C := S^{-1}PP^TU : Dim x 2,
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B := 1 + VC : 2 x 2,
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D := VS^{-1}P : 2 x LDS,
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P^TU : LDS x 2,
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V : 2 x Dim
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*/
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const uint32_t row1 = (Updates_index[0] - 1);
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const uint32_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 (uint32_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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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_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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// const double alpha = 1.0, beta = 0.0;
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// const bool TransA = true, TransB = false;
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// (void) cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
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// Dim, 2, LDS, alpha, Slater_inv, LDS, Updates, LDS, beta,
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// C, 2);
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// (void) qmckl_dgemm(context, CblasNoTrans, CblasTrans,
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// 2, Dim, LDS, alpha, Updates, LDS, Slater_inv, LDS, beta,
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// C, 2);
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// (void) qmckl_dgemm(context, TransA, TransB,
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// 2, Dim, LDS, alpha, Updates, LDS, Slater_inv, LDS,
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// beta, C, 2);
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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 1;
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}
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// Update det(S) when passed
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if (determinant != NULL)
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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 *__restrict r1dim = &(Slater_inv[row1 * LDS]);
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double *__restrict r2dim = &(Slater_inv[row2 * LDS]);
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_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 (uint32_t i = 0; i < Dim; i++) {
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_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 0;
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}
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uint32_t qmckl_woodbury_3(const uint64_t vLDS, const uint64_t vDim,
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const double *__restrict __attribute__((aligned(8)))
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Updates,
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const uint64_t *__restrict Updates_index,
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const double breakdown,
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double *__restrict __attribute__((aligned(8)))
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Slater_inv,
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double *__restrict determinant) {
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const uint32_t Dim = 21;
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const uint32_t LDS = 24;
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/*
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COMPUTE (S^T)^{-1} - CB^{-1}D : Dim x LDS,
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where S^T : Dim x LDS,
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C := (S^T)^{-1}U : Dim x 3,
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B := 1 + VC : 3 x 3,
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D := V(S^T)^{-1} : 3 x LDS,
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U : LDS x 3,
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V : 3 x Dim
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*/
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const uint32_t row1 = (Updates_index[0] - 1);
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const uint32_t row2 = (Updates_index[1] - 1);
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const uint32_t row3 = (Updates_index[2] - 1);
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// Compute C = (S^T)^{-1}U : Dim x 3
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double __attribute__((aligned(8))) C[3 * Dim];
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for (uint32_t i = 0; i < Dim; i++) {
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C[i * 3] = 0;
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C[i * 3 + 1] = 0;
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C[i * 3 + 2] = 0;
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t k = 0; k < LDS; k++) {
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C[i * 3] += Slater_inv[i * LDS + k] * Updates[k];
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C[i * 3 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
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C[i * 3 + 2] += Slater_inv[i * LDS + k] * Updates[2 * LDS + k];
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}
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}
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// double alpha = 1.0, beta = 0.0;
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// cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
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// Dim, 3, LDS, alpha, Slater_inv, LDS, Updates, LDS, beta,
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// C, 3);
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// Compute B = 1 + VC : 3 x 3
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const double B0 = C[row1 * 3] + 1;
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const double B1 = C[row1 * 3 + 1];
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const double B2 = C[row1 * 3 + 2];
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const double B3 = C[row2 * 3];
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const double B4 = C[row2 * 3 + 1] + 1;
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const double B5 = C[row2 * 3 + 2];
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const double B6 = C[row3 * 3];
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const double B7 = C[row3 * 3 + 1];
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const double B8 = C[row3 * 3 + 2] + 1;
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// Check if determinant of B is not too close to zero
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double det;
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det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
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B2 * (B3 * B7 - B4 * B6);
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if (fabs(det) < breakdown) {
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return 1;
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}
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// Update det(Slater) if passed
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if (determinant != NULL)
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*determinant *= det;
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// Compute B^{-1} with explicit formula for 3 x 3 inversion
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double __attribute__((aligned(8))) Binv[9], idet = 1.0 / det;
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Binv[0] = (B4 * B8 - B7 * B5) * idet;
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Binv[1] = -(B1 * B8 - B7 * B2) * idet;
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Binv[2] = (B1 * B5 - B4 * B2) * idet;
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Binv[3] = -(B3 * B8 - B6 * B5) * idet;
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Binv[4] = (B0 * B8 - B6 * B2) * idet;
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Binv[5] = -(B0 * B5 - B3 * B2) * idet;
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Binv[6] = (B3 * B7 - B6 * B4) * idet;
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Binv[7] = -(B0 * B7 - B6 * B1) * idet;
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Binv[8] = (B0 * B4 - B3 * B1) * idet;
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// tmp = B^{-1}D : 3 x LDS
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double __attribute__((aligned(8))) tmp[3 * LDS];
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double *__restrict r1dim = &(Slater_inv[row1 * LDS]);
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double *__restrict r2dim = &(Slater_inv[row2 * LDS]);
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double *__restrict r3dim = &(Slater_inv[row3 * LDS]);
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
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tmp[LDS + j] = Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
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tmp[2 * LDS + j] = Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
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}
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// Compute (S^T)^{-1} - C * tmp : Dim x LDS
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for (uint32_t i = 0; i < Dim; i++) {
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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Slater_inv[i * LDS + j] -= C[i * 3] * tmp[j];
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Slater_inv[i * LDS + j] -= C[i * 3 + 1] * tmp[LDS + j];
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Slater_inv[i * LDS + j] -= C[i * 3 + 2] * tmp[2 * LDS + j];
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}
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}
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return 0;
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}
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/*
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COMPUTE S^{-1} - C B^{-1} D : Dim x LDS,
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where S^{-1} : Dim x LDS,
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C := S^{-1} U : Dim x K, dgemm
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B := 1 + V C : K x K, copy
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D := V S^{-1} : K x LDS, copy
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U : LDS x K,
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V : K x Dim
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tmp := B^{-1} D : K x LDS, dgemm
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S = S - C tmp : Dim x LDS, dgemm
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*/
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uint32_t qmckl_woodbury_k(const uint64_t vLDS,
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const uint64_t vDim,
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const uint64_t N_updates,
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const double *__restrict __attribute__((aligned(8))) Updates,
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const uint64_t *__restrict Updates_index,
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const double breakdown,
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double *__restrict __attribute__((aligned(8))) Slater_inv,
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double *__restrict determinant) {
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const uint32_t Dim = 21;
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const uint32_t LDS = 24;
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// Compute C = S^{-1} U : Dim x K : standard dgemm
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double C[Dim * N_updates];
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double alpha = 1.0, beta = 0.0;
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cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
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Dim, N_updates, LDS,
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alpha, Slater_inv, LDS, Updates, LDS,
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beta, C, N_updates);
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// Construct B = 1 + V C : K x K : selecting and copying row from C into B. Can maybe be off-loaded to GPU by splitting in N_updates tiles of N_updates strides, using PARALLEL and SIMD
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// Construct D = V S^{-1} : K x LDS
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double B[N_updates * N_updates], D[N_updates * LDS];
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for (uint32_t i = 0; i < N_updates; i++) {
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const uint32_t row = Updates_index[i] - 1;
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for (uint32_t j = 0; j < N_updates ; j++) B[i * N_updates + j] = C[row * N_updates + j] + (i == j);
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for (uint32_t j = 0; j < LDS; j++) D[i * LDS + j] = Slater_inv[row * LDS + j];
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}
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// Compute determinant by LU decomposition
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int ipiv[N_updates];
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lapack_int ret;
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ret = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, N_updates, N_updates, B, N_updates, ipiv);
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if (ret != 0) return ret;
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double det = 1.0;
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int j = 0;
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for (uint32_t i = 0; i < N_updates; i++) {
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j += min(abs(ipiv[i] - i), 1);
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det *= B[(N_updates + 1) * i];
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}
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if (j & 1 == 0) det = -det; // multiply det with -1 if j is even
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// Check if determinant of B is not too close to zero
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if (fabs(det) < breakdown) {
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return 1;
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}
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// Update det(Slater) if passed
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if (determinant) *determinant *= det;
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// Compute B^{-1} with explicit formula for K x K inversion
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ret = LAPACKE_dgetri(LAPACK_ROW_MAJOR, N_updates, B, N_updates, ipiv);
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if (ret != 0) return ret;
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// tmp = B^{-1} D : KxLDS = KxK X KxLDS : standard dgemm
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double tmp[N_updates * LDS];
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cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
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N_updates, LDS, N_updates,
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alpha, B, N_updates, D, LDS,
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beta, tmp, LDS);
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// Compute S^{-1} - C * tmp : Dim x LDS : standard dgemm
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alpha = -1.0, beta = 1.0;
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cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
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Dim, LDS, N_updates,
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alpha, C, N_updates, tmp, LDS,
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beta, Slater_inv, LDS);
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return 0;
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}
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uint32_t qmckl_slagel_splitting(
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const uint64_t vLDS, const uint64_t vDim, uint64_t N_updates,
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const double *__restrict __attribute__((aligned(8))) Updates,
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const uint64_t *__restrict Updates_index, const double breakdown,
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double *__restrict __attribute__((aligned(8))) Slater_inv,
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double *__restrict __attribute__((aligned(8))) later_updates,
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uint64_t *__restrict later_index, uint64_t *__restrict later,
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double *__restrict determinant) {
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const uint32_t LDS = 24;
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const uint32_t Dim = 21;
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double __attribute__((aligned(8))) C[LDS];
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double __attribute__((aligned(8))) D[LDS];
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uint32_t l = 0;
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// For each update
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while (l < N_updates) {
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// C = S^{-1} x U_l
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for (uint32_t i = 0; i < Dim; i++) {
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C[i] = 0.0;
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j]; // regular mat-vec product, but actually working on S_inv^T * U_l.
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}
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}
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// Denominator
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const int cui = Updates_index[l] - 1;
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double den = 1.0 + C[cui];
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// printf("test breakdown = %f, den = %f, C[cui] = %f, cui = %d\n", breakdown, fabs(den), C[cui], cui);
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if (fabs(den) < breakdown) { // Here is decided to split the update, or not.
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// printf("Split! breakdown = %f\n", breakdown);
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n_splits += 1;
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// U_l = U_l / 2: split the update in 2 equal halves and save the second halve
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// in later_updates
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t i = 0; i < LDS; i++) {
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later_updates[*later * LDS + i] = Updates[l * LDS + i] / 2.0;
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C[i] /= 2.0;
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}
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later_index[*later] = Updates_index[l];
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(*later)++;
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den = 1.0 + C[cui];
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} // From here onwards we continue with applying the first halve of the update to Slater_inv
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double iden = 1.0 / den;
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if (!determinant) *determinant *= den;
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// D = v^T x S^{-1} : 1 x LDS
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#pragma ivdep
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#pragma vector aligned, novecremainder
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for (uint32_t j = 0; j < LDS; j++) {
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D[j] = Slater_inv[cui * LDS + j];
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}
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// S^{-1} = S^{-1} - C x D / den
|
|
for (uint32_t i = 0; i < Dim; i++) {
|
|
#pragma ivdep
|
|
#pragma vector aligned, novecremainder
|
|
for (uint32_t j = 0; j < LDS; j++) {
|
|
const double update = C[i] * D[j] * iden;
|
|
Slater_inv[i * LDS + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
uint32_t qmckl_sherman_morrison_splitting(
|
|
const uint64_t vLDS, const uint64_t vDim, const uint64_t N_updates,
|
|
const double *__restrict __attribute__((aligned(8))) Updates,
|
|
const uint64_t *__restrict Updates_index, const double breakdown,
|
|
double *__restrict __attribute__((aligned(8))) Slater_inv,
|
|
double *__restrict determinant) {
|
|
|
|
const uint32_t Dim = 21;
|
|
const uint32_t LDS = 24;
|
|
|
|
double __attribute__((aligned(8))) later_updates[LDS * N_updates];
|
|
uint64_t later_index[N_updates];
|
|
uint64_t later = 0;
|
|
uint32_t rc;
|
|
|
|
rc = qmckl_slagel_splitting(LDS, Dim, N_updates, Updates, Updates_index,
|
|
breakdown, Slater_inv, later_updates, later_index,
|
|
&later, determinant);
|
|
// if (rc != 0) printf("Something when catastrophically wrong in QMCKL_SLAGEL_SPLITTING\n");
|
|
|
|
if (later > 0) {
|
|
recursive_calls++;
|
|
// printf("Later > 0\n");
|
|
rc = qmckl_sherman_morrison_splitting(LDS, Dim, later, later_updates,
|
|
later_index, breakdown, Slater_inv,
|
|
determinant);
|
|
// if (rc != 0) printf("Something when catastrophically wrong in QMCKL_SHERMAN_MORRISON_SPLITTING\n");
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
uint32_t qmckl_sherman_morrison_smw32s(
|
|
const uint64_t vLDS, const uint64_t vDim, const uint64_t N_updates,
|
|
const double *__restrict __attribute__((aligned(8))) Updates,
|
|
const uint64_t *__restrict Updates_index, const double breakdown,
|
|
double *__restrict __attribute__((aligned(8))) Slater_inv,
|
|
double *__restrict determinant) {
|
|
|
|
const uint32_t Dim = 21;
|
|
const uint32_t LDS = 24;
|
|
|
|
double __attribute__((aligned(8))) later_updates[LDS * N_updates];
|
|
uint64_t later_index[N_updates];
|
|
uint64_t later = 0;
|
|
uint32_t rc;
|
|
|
|
if (N_updates == 4) { // Special case for 4 rank-1 updates: 2+2
|
|
rc = qmckl_woodbury_2(LDS, Dim, Updates, Updates_index,
|
|
breakdown, Slater_inv, determinant);
|
|
if (rc != 0) { // Send the entire block to slagel_splitting
|
|
block_fail += 1;
|
|
uint64_t l = 0;
|
|
rc = qmckl_slagel_splitting(LDS, Dim, 2, Updates,
|
|
Updates_index, breakdown, Slater_inv,
|
|
later_updates + (LDS * later),
|
|
later_index + later, &l, determinant);
|
|
later += l;
|
|
}
|
|
rc = qmckl_woodbury_2(LDS, Dim, &Updates[2*LDS], &Updates_index[2],
|
|
breakdown, Slater_inv, determinant);
|
|
if (rc != 0) { // Send the entire block to slagel_splitting
|
|
block_fail += 1;
|
|
uint64_t l = 0;
|
|
rc = qmckl_slagel_splitting(LDS, Dim, 2, &Updates[2*LDS],
|
|
&Updates_index[2], breakdown, Slater_inv,
|
|
later_updates + (LDS * later),
|
|
later_index + later, &l, determinant);
|
|
later += l;
|
|
}
|
|
if (later > 0) {
|
|
recursive_calls++;
|
|
rc = qmckl_sherman_morrison_splitting(LDS, Dim, later, later_updates,
|
|
later_index, breakdown, Slater_inv,
|
|
determinant);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
// if (N_updates == 6) { // Special case for 6 rank-1 updates: 2+2+2
|
|
// rc = qmckl_woodbury_2(LDS, Dim, Updates, Updates_index,
|
|
// breakdown, Slater_inv, determinant);
|
|
// if (rc != 0) { // Send the entire block to slagel_splitting
|
|
// block_fail += 1;
|
|
// uint64_t l = 0;
|
|
// rc = qmckl_slagel_splitting(LDS, Dim, 2, Updates,
|
|
// Updates_index, breakdown, Slater_inv,
|
|
// later_updates + (LDS * later),
|
|
// later_index + later, &l, determinant);
|
|
// later += l;
|
|
// }
|
|
// rc = qmckl_woodbury_2(LDS, Dim, &Updates[2*LDS], &Updates_index[2],
|
|
// breakdown, Slater_inv, determinant);
|
|
// if (rc != 0) { // Send the entire block to slagel_splitting
|
|
// block_fail += 1;
|
|
// uint64_t l = 0;
|
|
// rc = qmckl_slagel_splitting(LDS, Dim, 2, &Updates[2*LDS],
|
|
// &Updates_index[2], breakdown, Slater_inv,
|
|
// later_updates + (LDS * later),
|
|
// later_index + later, &l, determinant);
|
|
// later += l;
|
|
// }
|
|
// rc = qmckl_woodbury_2(LDS, Dim, &Updates[4*LDS], &Updates_index[4],
|
|
// breakdown, Slater_inv, determinant);
|
|
// if (rc != 0) { // Send the entire block to slagel_splitting
|
|
// block_fail += 1;
|
|
// uint64_t l = 0;
|
|
// rc = qmckl_slagel_splitting(LDS, Dim, 2, &Updates[4*LDS],
|
|
// &Updates_index[4], breakdown, Slater_inv,
|
|
// later_updates + (LDS * later),
|
|
// later_index + later, &l, determinant);
|
|
// later += l;
|
|
// }
|
|
// if (later > 0) {
|
|
// recursive_calls++;
|
|
// rc = qmckl_sherman_morrison_splitting(LDS, Dim, later, later_updates,
|
|
// later_index, breakdown, Slater_inv,
|
|
// determinant);
|
|
// }
|
|
// return 0;
|
|
// }
|
|
|
|
// And for the other cases != 4, 6
|
|
// Apply first 3*n_of_3blocks updates in n_of_3blocks blocks of 3 updates with
|
|
// Woodbury 3x3 kernel
|
|
uint32_t n_of_3blocks = N_updates / 3;
|
|
uint32_t remainder = N_updates % 3;
|
|
uint32_t length_3block = 3 * LDS;
|
|
|
|
if (n_of_3blocks > 0) {
|
|
for (uint32_t i = 0; i < n_of_3blocks; i++) {
|
|
const double *Updates_3block = &Updates[i * length_3block];
|
|
const uint64_t *Updates_index_3block = &Updates_index[i * 3];
|
|
rc = qmckl_woodbury_3(LDS, Dim, Updates_3block, Updates_index_3block,
|
|
breakdown, Slater_inv, determinant);
|
|
if (rc != 0) { // Send the entire block to slagel_splitting
|
|
// printf("QMCKL_WOODBURY_3 failed. Sending to QMCKL_SLAGEL_SPLITTING\n");
|
|
block_fail += 1;
|
|
uint64_t l = 0;
|
|
rc = qmckl_slagel_splitting(LDS, Dim, 3, Updates_3block,
|
|
Updates_index_3block, breakdown, Slater_inv,
|
|
later_updates + (LDS * later),
|
|
later_index + later, &l, determinant);
|
|
// if (rc != 0) printf("Something when catastrophically wrong in QMCKL_SLAGEL_SPLITTING\n");
|
|
later += l;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Apply last remaining block of 2 updates with Woodbury 2x2 kernel
|
|
if (remainder == 2) {
|
|
const double *Updates_2block = &Updates[n_of_3blocks * length_3block];
|
|
const uint64_t *Updates_index_2block = &Updates_index[3 * n_of_3blocks];
|
|
rc = qmckl_woodbury_2(LDS, Dim, Updates_2block, Updates_index_2block,
|
|
breakdown, Slater_inv, determinant);
|
|
if (rc != 0) { // Send the entire block to slagel_splitting
|
|
// printf("QMCKL_WOODBURY_2 failed. Sending to QMCKL_SLAGEL_SPLITTING\n");
|
|
block_fail += 1;
|
|
uint64_t l = 0;
|
|
rc = qmckl_slagel_splitting(LDS, Dim, 2, Updates_2block,
|
|
Updates_index_2block, breakdown, Slater_inv,
|
|
later_updates + (LDS * later),
|
|
later_index + later, &l, determinant);
|
|
// if (rc != 0) printf("Something when catastrophically wrong in QMCKL_SLAGEL_SPLITTING\n");
|
|
later += l;
|
|
}
|
|
}
|
|
|
|
// Apply last remaining update with slagel_splitting
|
|
if (remainder == 1) {
|
|
// // printf("Sending single update to QMCKL_SLAGEL_SPLITTING\n");
|
|
const double *Updates_1block = &Updates[n_of_3blocks * length_3block];
|
|
const uint64_t *Updates_index_1block = &Updates_index[3 * n_of_3blocks];
|
|
uint64_t l = 0;
|
|
rc = qmckl_slagel_splitting(LDS, Dim, 1, Updates_1block,
|
|
Updates_index_1block, breakdown, Slater_inv,
|
|
later_updates + (LDS * later),
|
|
later_index + later, &l, determinant);
|
|
// if (rc != 0) printf("Something when catastrophically wrong in QMCKL_SLAGEL_SPLITTING\n");
|
|
later += l;
|
|
}
|
|
|
|
if (later > 0) {
|
|
recursive_calls++;
|
|
// printf("Sending remaining updates to QMCKL_SHERMAN_MORRISON_SPLITTING\n");
|
|
rc = qmckl_sherman_morrison_splitting(LDS, Dim, later, later_updates,
|
|
later_index, breakdown, Slater_inv,
|
|
determinant);
|
|
// if (rc != 0) printf("Something when catastrophically wrong in QMCKL_SHERMAN_MORRISON_SPLITTING\n");
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
// Sherman Morrison, leaving zero denominators for later
|
|
uint32_t qmckl_sherman_morrison_later(
|
|
const uint64_t vLDS, const uint64_t vDim, const uint64_t N_updates,
|
|
const double *__restrict __attribute__((aligned(8))) Updates,
|
|
const uint64_t *__restrict Updates_index, const double breakdown,
|
|
double *__restrict __attribute__((aligned(8))) Slater_inv,
|
|
double *__restrict determinant) {
|
|
|
|
const uint32_t Dim = 21;
|
|
const uint32_t LDS = 24;
|
|
|
|
double __attribute__((aligned(8))) C[Dim];
|
|
double __attribute__((aligned(8))) D[LDS];
|
|
|
|
double __attribute__((aligned(8))) later_updates[LDS * N_updates];
|
|
uint64_t later_index[N_updates];
|
|
uint64_t later = 0;
|
|
|
|
uint32_t l = 0;
|
|
// For each update
|
|
while (l < N_updates) {
|
|
|
|
// C = A^{-1} x U_l
|
|
for (uint32_t i = 0; i < Dim; i++) {
|
|
C[i] = 0.0;
|
|
#pragma ivdep
|
|
#pragma vector aligned, novecremainder
|
|
for (uint32_t j = 0; j < LDS; j++) {
|
|
C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j]; // regular mat-vec product, but actually working on S_inv^T * U_l.
|
|
}
|
|
}
|
|
|
|
// Denominator
|
|
const int cui = Updates_index[l] - 1;
|
|
double den = 1.0 + C[cui];
|
|
if (fabs(den) < breakdown) {
|
|
#pragma ivdep
|
|
#pragma vector aligned, novecremainder
|
|
// for (uint32_t i = 0; i < Dim; i++) {
|
|
for (uint32_t i = 0; i < LDS; i++) {
|
|
later_updates[later * LDS + i] = Updates[l * LDS + i];
|
|
}
|
|
later_index[later] = Updates_index[l];
|
|
later++;
|
|
l += 1;
|
|
continue;
|
|
}
|
|
double iden = 1.0 / den;
|
|
|
|
if (!determinant) *determinant *= den;
|
|
|
|
// D = v^T x A^{-1}
|
|
#pragma ivdep
|
|
#pragma vector aligned, novecremainder
|
|
for (uint32_t j = 0; j < LDS; j++) {
|
|
D[j] = Slater_inv[cui * LDS + j];
|
|
}
|
|
|
|
// S^{-1} = S^{-1} - C x D / den
|
|
for (uint32_t i = 0; i < Dim; i++) {
|
|
#pragma ivdep
|
|
#pragma vector aligned, novecremainder
|
|
for (uint32_t j = 0; j < LDS; j++) {
|
|
const double update = C[i] * D[j] * iden;
|
|
Slater_inv[i * LDS + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
if (later == N_updates) { // If all the updates have failed, exit early with an error
|
|
return 1;
|
|
}
|
|
else if (later > 0) { // If some have failed, make a recursive call
|
|
recursive_calls++;
|
|
(void) qmckl_sherman_morrison_later(LDS, Dim, later, later_updates,
|
|
later_index, breakdown, Slater_inv, determinant);
|
|
}
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
// Inplace inverse n x n matrix A.
|
|
// returns:
|
|
// ret = 0 on success
|
|
// ret < 0 illegal argument value
|
|
// ret > 0 singular matrix
|
|
lapack_int inverse(double *a, uint64_t m, uint64_t n) {
|
|
int ipiv[m + 1];
|
|
lapack_int ret;
|
|
ret = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, m, n, a, n, ipiv);
|
|
if (ret != 0) return ret;
|
|
ret = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
|
|
return ret;
|
|
}
|