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Sherman-Morrison/independent_test_harness/sm.c
Francois Coppens f35ad6a777 Small bugfix in qmckl_slagel_splitting()
2022-07-21 08:16:25 +02:00

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#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <string.h>
#include "kernels.h"
extern uint64_t n_splits;
extern uint64_t block_fail;
extern uint64_t recursive_calls;
int min(int a, int b) {
return (a > b) ? b : a;
}
uint32_t qmckl_sherman_morrison(
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];
uint32_t l = 0;
// For each update
while (l < N_updates) {
// C = S^{-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: v_l^T * C
const int cui = Updates_index[l] - 1;
double den = 1.0 + C[cui];
if (fabs(den) < breakdown) {
return 1;
}
double iden = 1.0 / den;
// Update det(A)
if (!determinant)
*determinant *= den;
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t j = 0; j < LDS; j++) {
D[j] = Slater_inv[cui * LDS + j]; // selecting proper column of v_l^T * S_inv
}
// A^{-1} = A^{-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_woodbury_2(const uint64_t vLDS, const uint64_t vDim,
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;
/*
COMPUTE S^{-1}P - CB^{-1}D : Dim x LDS,
where S^{-1}P : Dim x LDS,
C := S^{-1}PP^TU : Dim x 2,
B := 1 + VC : 2 x 2,
D := VS^{-1}P : 2 x LDS,
P^TU : LDS x 2,
V : 2 x Dim
*/
const uint32_t row1 = (Updates_index[0] - 1);
const uint32_t row2 = (Updates_index[1] - 1);
// Compute C = (S^T)^{-1}U : Dim x 2
double __attribute__((aligned(8))) C[2 * Dim];
for (uint32_t i = 0; i < Dim; i++) {
C[i * 2] = 0;
C[i * 2 + 1] = 0;
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t k = 0; k < LDS; k++) {
C[i * 2] += Slater_inv[i * LDS + k] * Updates[k];
C[i * 2 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
}
}
// const double alpha = 1.0, beta = 0.0;
// const bool TransA = true, TransB = false;
// (void) cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
// Dim, 2, LDS, alpha, Slater_inv, LDS, Updates, LDS, beta,
// C, 2);
// (void) qmckl_dgemm(context, CblasNoTrans, CblasTrans,
// 2, Dim, LDS, alpha, Updates, LDS, Slater_inv, LDS, beta,
// C, 2);
// (void) qmckl_dgemm(context, TransA, TransB,
// 2, Dim, LDS, alpha, Updates, LDS, Slater_inv, LDS,
// beta, C, 2);
// Compute B = 1 + VC : 2 x 2
const double B0 = C[row1 * 2] + 1;
const double B1 = C[row1 * 2 + 1];
const double B2 = C[row2 * 2];
const double B3 = C[row2 * 2 + 1] + 1;
// Check if determinant of inverted matrix is not zero
double det = B0 * B3 - B1 * B2;
if (fabs(det) < breakdown) {
return 1;
}
// Update det(S) when passed
if (determinant != NULL)
*determinant *= det;
// Compute B^{-1} with explicit formula for 2 x 2 inversion
double __attribute__((aligned(8))) Binv[4], idet = 1.0 / det;
Binv[0] = idet * B3;
Binv[1] = -1.0 * idet * B1;
Binv[2] = -1.0 * idet * B2;
Binv[3] = idet * B0;
// tmp = B^{-1}D : 2 x LDS
double __attribute__((aligned(8))) tmp[2 * LDS];
double *__restrict r1dim = &(Slater_inv[row1 * LDS]);
double *__restrict r2dim = &(Slater_inv[row2 * LDS]);
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t j = 0; j < LDS; j++) {
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
tmp[LDS + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
}
// Compute (S^T)^{-1} - C * tmp : Dim x LDS
for (uint32_t i = 0; i < Dim; i++) {
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t j = 0; j < LDS; j++) {
Slater_inv[i * LDS + j] -= C[i * 2] * tmp[j];
Slater_inv[i * LDS + j] -= C[i * 2 + 1] * tmp[LDS + j];
}
}
return 0;
}
uint32_t qmckl_woodbury_3(const uint64_t vLDS, const uint64_t vDim,
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;
/*
COMPUTE (S^T)^{-1} - CB^{-1}D : Dim x LDS,
where S^T : Dim x LDS,
C := (S^T)^{-1}U : Dim x 3,
B := 1 + VC : 3 x 3,
D := V(S^T)^{-1} : 3 x LDS,
U : LDS x 3,
V : 3 x Dim
*/
const uint32_t row1 = (Updates_index[0] - 1);
const uint32_t row2 = (Updates_index[1] - 1);
const uint32_t row3 = (Updates_index[2] - 1);
// Compute C = (S^T)^{-1}U : Dim x 3
double __attribute__((aligned(8))) C[3 * Dim];
for (uint32_t i = 0; i < Dim; i++) {
C[i * 3] = 0;
C[i * 3 + 1] = 0;
C[i * 3 + 2] = 0;
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t k = 0; k < LDS; k++) {
C[i * 3] += Slater_inv[i * LDS + k] * Updates[k];
C[i * 3 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
C[i * 3 + 2] += Slater_inv[i * LDS + k] * Updates[2 * LDS + k];
}
}
// double alpha = 1.0, beta = 0.0;
// cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
// Dim, 3, LDS, alpha, Slater_inv, LDS, Updates, LDS, beta,
// C, 3);
// Compute B = 1 + VC : 3 x 3
const double B0 = C[row1 * 3] + 1;
const double B1 = C[row1 * 3 + 1];
const double B2 = C[row1 * 3 + 2];
const double B3 = C[row2 * 3];
const double B4 = C[row2 * 3 + 1] + 1;
const double B5 = C[row2 * 3 + 2];
const double B6 = C[row3 * 3];
const double B7 = C[row3 * 3 + 1];
const double B8 = C[row3 * 3 + 2] + 1;
// Check if determinant of B is not too close to zero
double det;
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
B2 * (B3 * B7 - B4 * B6);
if (fabs(det) < breakdown) {
return 1;
}
// Update det(Slater) if passed
if (determinant != NULL)
*determinant *= det;
// Compute B^{-1} with explicit formula for 3 x 3 inversion
double __attribute__((aligned(8))) Binv[9], idet = 1.0 / det;
Binv[0] = (B4 * B8 - B7 * B5) * idet;
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
Binv[2] = (B1 * B5 - B4 * B2) * idet;
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
Binv[4] = (B0 * B8 - B6 * B2) * idet;
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
Binv[6] = (B3 * B7 - B6 * B4) * idet;
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
Binv[8] = (B0 * B4 - B3 * B1) * idet;
// tmp = B^{-1}D : 3 x LDS
double __attribute__((aligned(8))) tmp[3 * LDS];
double *__restrict r1dim = &(Slater_inv[row1 * LDS]);
double *__restrict r2dim = &(Slater_inv[row2 * LDS]);
double *__restrict r3dim = &(Slater_inv[row3 * LDS]);
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t j = 0; j < LDS; j++) {
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
tmp[LDS + j] = Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
tmp[2 * LDS + j] = Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
}
// Compute (S^T)^{-1} - C * tmp : Dim x LDS
for (uint32_t i = 0; i < Dim; i++) {
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t j = 0; j < LDS; j++) {
Slater_inv[i * LDS + j] -= C[i * 3] * tmp[j];
Slater_inv[i * LDS + j] -= C[i * 3 + 1] * tmp[LDS + j];
Slater_inv[i * LDS + j] -= C[i * 3 + 2] * tmp[2 * LDS + j];
}
}
return 0;
}
/*
COMPUTE S^{-1} - C B^{-1} D : Dim x LDS,
where S^{-1} : Dim x LDS,
C := S^{-1} U : Dim x K, dgemm
B := 1 + V C : K x K, copy
D := V S^{-1} : K x LDS, copy
U : LDS x K,
V : K x Dim
tmp := B^{-1} D : K x LDS, dgemm
S = S - C tmp : Dim x LDS, dgemm
*/
uint32_t qmckl_woodbury_k(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;
// Compute C = S^{-1} U : Dim x K : standard dgemm
double C[Dim * N_updates];
double alpha = 1.0, beta = 0.0;
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
Dim, N_updates, LDS,
alpha, Slater_inv, LDS, Updates, LDS,
beta, C, N_updates);
// 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
// Construct D = V S^{-1} : K x LDS
double B[N_updates * N_updates], D[N_updates * LDS];
for (uint32_t i = 0; i < N_updates; i++) {
const uint32_t row = Updates_index[i] - 1;
for (uint32_t j = 0; j < N_updates ; j++) B[i * N_updates + j] = C[row * N_updates + j] + (i == j);
for (uint32_t j = 0; j < LDS; j++) D[i * LDS + j] = Slater_inv[row * LDS + j];
}
// Compute determinant by LU decomposition
int ipiv[N_updates];
lapack_int ret;
ret = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, N_updates, N_updates, B, N_updates, ipiv);
if (ret != 0) return ret;
double det = 1.0;
int j = 0;
for (uint32_t i = 0; i < N_updates; i++) {
j += min(abs(ipiv[i] - i), 1);
det *= B[(N_updates + 1) * i];
}
if (j & 1 == 0) det = -det; // multiply det with -1 if j is even
// Check if determinant of B is not too close to zero
if (fabs(det) < breakdown) {
return 1;
}
// Update det(Slater) if passed
if (determinant) *determinant *= det;
// Compute B^{-1} with explicit formula for K x K inversion
ret = LAPACKE_dgetri(LAPACK_ROW_MAJOR, N_updates, B, N_updates, ipiv);
if (ret != 0) return ret;
// tmp = B^{-1} D : KxLDS = KxK X KxLDS : standard dgemm
double tmp[N_updates * LDS];
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
N_updates, LDS, N_updates,
alpha, B, N_updates, D, LDS,
beta, tmp, LDS);
// Compute S^{-1} - C * tmp : Dim x LDS : standard dgemm
alpha = -1.0, beta = 1.0;
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
Dim, LDS, N_updates,
alpha, C, N_updates, tmp, LDS,
beta, Slater_inv, LDS);
return 0;
}
uint32_t qmckl_slagel_splitting(
const uint64_t vLDS, const uint64_t vDim, 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 __attribute__((aligned(8))) later_updates,
uint64_t *__restrict later_index, uint64_t *__restrict later,
double *__restrict determinant) {
const uint32_t LDS = 24;
const uint32_t Dim = 21;
double __attribute__((aligned(8))) C[LDS];
double __attribute__((aligned(8))) D[LDS];
uint32_t l = 0;
// For each update
while (l < N_updates) {
// C = S^{-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];
// printf("test breakdown = %f, den = %f, C[cui] = %f, cui = %d\n", breakdown, fabs(den), C[cui], cui);
if (fabs(den) < breakdown) { // Here is decided to split the update, or not.
// printf("Split! breakdown = %f\n", breakdown);
n_splits += 1;
// U_l = U_l / 2: split the update in 2 equal halves and save the second halve
// in later_updates
#pragma ivdep
#pragma vector aligned, novecremainder
for (uint32_t i = 0; i < LDS; i++) {
later_updates[*later * LDS + i] = Updates[l * LDS + i] / 2.0;
C[i] /= 2.0;
}
later_index[*later] = Updates_index[l];
(*later)++;
den = 1.0 + C[cui];
} // From here onwards we continue with applying the first halve of the update to Slater_inv
double iden = 1.0 / den;
if (!determinant) *determinant *= den;
// D = v^T x S^{-1} : 1 x LDS
#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;
}
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;
}
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