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contruction of correlators and MPI parallelization.
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todo: writing into a file
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@simone-romiti
simone-romiti committed Jun 28, 2023
1 parent c10659c commit 1cfb721
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38 changes: 31 additions & 7 deletions doc/omeas_heavy_mesons.qmd
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Original file line number Diff line number Diff line change
Expand Up @@ -6,6 +6,8 @@ jupyter: python3
format-links: false # hide the existence of other formats
format:
html:
toc: true
toc-location: body
embed-resources: true # standalone html
html-math-method: mathjax # use the common latex commands
include-in-header: mathjax-config.html # equation numbering with sections
Expand Down Expand Up @@ -63,12 +65,12 @@ ${\bra{\Omega} \cdot \ket{\Omega} = \braket{\cdot}}$:
\begin{equation}
\begin{split}
{C}^{h_i, h_j}_{\Gamma_1, \Gamma_2}(t) &=
\eta_1 \frac{1}{V}
- \eta_1 \frac{1}{V}
\sum_{\vec{x}}
\mathcal{C}^{h_i, h_j}_{\Gamma_1, \Gamma_2}(t, \vec{x})
\\
&=
- \eta_{1} \eta_{2}
\eta_{1} \eta_{2}
\frac{1}{V}
\sum_{\vec{x}}
\braket{
Expand All @@ -82,7 +84,7 @@ ${\bra{\Omega} \cdot \ket{\Omega} = \braket{\cdot}}$:
where $h_i=c,s$, $\Gamma_i = 1, \gamma_5$.
The minus sign will vanish when doing the Wick contractions,
while
$\eta_{\mathbb{1}} = \pm 1$ and $\eta_{\gamma_5} = \pm i$
$\eta_{\mathbb{1}} = 1$ and $\eta_{\gamma_5} = -1$
are used just to compensate the sign change when daggering the spinor bilinears at the source:
<!-- -->
\begin{equation}
Expand Down Expand Up @@ -147,7 +149,7 @@ where ${\sigma_3 =
\end{bmatrix}
}$.
As a projector, it satisfies $P_i^2 = P_i$.
Moreover, $\sigma_3 = \sigma_3^\dagger$,
Moreover $\sigma_3 = \sigma_3^\dagger$,
hence $P_i^\dagger = P_i$.

- Obviously, $P_i$ commutes with the $\gamma$ matrices asthey act on different spaces.
Expand Down Expand Up @@ -190,7 +192,7 @@ If we now call $S = D^{-1}$ the inverse of the Dirac operator,
and use Wick's theorem:
<!-- -->
\begin{equation}
\braket{\psi_{a}(x) \bar{\psi}_{b}(0)} = S_{ab}(x|0) \, ,
\braket{\Psi_{a}(x) \bar{\Psi}_{b}(0)} = S_{ab}(x|0) \, ,
\end{equation}
<!-- -->
where $a$ and $b$ are a shortcut for the other indices of the spinor (spin, flavor, color, etc.),
Expand Down Expand Up @@ -261,14 +263,36 @@ Therefore, back to our correlators, we can write:
\\
\times
&
(\psi_{h}^{(\beta_2)})_{\substack{f_2 \\ \alpha_2}}(x)
(\eta_{h}^{(\beta_2)})^*_{\substack{f_3 \\ \alpha_3}}(0)
(\psi_{h}^{(\beta_2)})_{\substack{f_2 \\ \alpha_3}}(x)
(\eta_{h}^{(\beta_2)})^*_{\substack{f_3 \\ \alpha_4}}(0)
(P_j \tau_1)_{f_3 f_4} (\Gamma_2)_{\alpha_4 \alpha_1}
\, .
\end{split}
\end{equation}
<!-- -->

In terms of dot products (flavor and Dirac indices contracted):
<!-- -->
\begin{equation}
\begin{split}
\mathcal{C}^{h_i, h_j}_{\Gamma_1, \Gamma_2}(t, \vec{x})
=
\sum_{\beta_1, \beta_2}
&
\left[
(\eta_\ell^{(\beta_1)}(x))^{\dagger} (\tau_1 P_i) \Gamma_1 \psi_h^{(\beta_2)}(x)
\right]
\\
\times&
\left[
(\eta_h^{(\beta_2)}(0))^{\dagger} (P_j \tau_1) \Gamma_2 \psi_\ell^{(\beta_1)}(0)
\right]
\end{split}
\end{equation}
<!-- -->



## Implementation

See comments in the code: `correlators.c`.
Expand Down
118 changes: 82 additions & 36 deletions meas/correlators.c
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Original file line number Diff line number Diff line change
Expand Up @@ -255,9 +255,9 @@ void light_correlators_measurement(const int traj, const int id, const int ieo)


// Function to allocate memory for a pointer of pointers for an array of d dimensions
void* allocateMultiDimensionalArray(int* sizes, int numDimensions, size_t elementSize) {
void* callocMultiDimensional(int* sizes, int numDimensions, size_t elementSize) {
if (numDimensions == 1) {
void* array = malloc(sizes[0] * sizeof(elementSize));
void* array = calloc(sizes[0], sizeof(elementSize));

if (array == NULL) {
printf("Memory allocation failed for dimension 0!");
Expand All @@ -267,15 +267,15 @@ void* allocateMultiDimensionalArray(int* sizes, int numDimensions, size_t elemen
return array;
}

void** pointerArray = (void**)malloc(sizes[0] * sizeof(void*));
void** pointerArray = (void**)calloc(sizes[0], sizeof(void*));

if (pointerArray == NULL) {
printf("Memory allocation failed for dimension %d!", numDimensions - 1);
return NULL;
}

for (int i = 0; i < sizes[0]; i++) {
pointerArray[i] = allocateMultiDimensionalArray(sizes + 1, numDimensions - 1);
pointerArray[i] = callocMultiDimensional(sizes + 1, numDimensions - 1);

if (pointerArray[i] == NULL) {
printf("Memory allocation failed for subarray %d in dimension %d!", i, numDimensions - 1);
Expand Down Expand Up @@ -345,13 +345,14 @@ void heavy_correlators_measurement(const int traj, const int id, const int ieo,
/* heavy-light correlator: dummy variables */

// the number of independent correlators is 16 = (2*2)_{h_1 h_2} * (2*2)_{Gamma_1 Gamma_2}
// h_i: c,s, Gamma = (1, gamma_5)
double *****C_hihj_Gamma1Gamma2 = (double *****) allocateMultiDimensionalArray({2,2,2,2,T}, 5, sizeof(double));
double *****res_hihj_Gamma1Gamma2 = (double *****) allocateMultiDimensionalArray({2,2,2,2,T}, 5, sizeof(double));
// h_i: c,s
// Gamma = 1, gamma_5
double *****C_hihj_Gamma1Gamma2 = (double *****) callocMultiDimensional({2,2,2,2,T}, 5, sizeof(double));
double ****res_hihj_Gamma1Gamma2 = (double ****) callocMultiDimensional({2,2,2,2}, 4, sizeof(double));
#ifdef TM_USE_MPI
double *****mpi_res_ij = (double *****) allocateMultiDimensionalArray({2,2,2,2,T}, 5, sizeof(double));
double ****mpi_res_hihj_Gamma1Gamma2 = (double ****) callocMultiDimensional({2,2,2,2}, 4, sizeof(double));
// send buffer for MPI_Gather
double *****sC_ij = (double *****) allocateMultiDimensionalArray({2,2,2,2,T}, 5, sizeof(double));
double *****sC_hihj_Gamma1Gamma2 = (double *****) callocMultiDimensional({2,2,2,2,T}, 5, sizeof(double));
#endif

FILE *ofs; // output file stream
Expand Down Expand Up @@ -438,18 +439,9 @@ void heavy_correlators_measurement(const int traj, const int id, const int ieo,
// psi = (psi[(s,p)][phi][beta][eo][f][x])[alpha][c] // last 3 indices are proper of the spinor struct
// Note: propagator in the sense that it is D^{-1}*source after the inversion

// unnecessary: // init_spinor_field(VOLUMEPLUSRAND / 2, 1); // initialize g_spinor_field so that I can copy it
spinor ******arr_eo_spinor = (spinor ******)callocMultiDimensional({2,2,4,2,2,VOLUME/2}, 6, sizeof(spinor));

spinor ******arr_eo_spinor = (spinor ******)allocateMultiDimensionalArray({2,2,4,2,2,VOLUME/2}, 6, sizeof(spinor));
// spinor ******h_arr_eo_spinor = (spinor ******)allocateMultiDimensionalArray({2,2,4,2,2,VOLUME/2}, 6, sizeof(spinor));

// (no even-odd): source+propagator, doublet, spin dilution index, even-odd, flavor, position (+ Dirac, color)
// (psi[phi][beta][f][x])[alpha][c] // last 3 indices are proper of the spinor struct
spinor ****arr_spinor = (spinor ****) allocateMultiDimensionalArray({2,4,2,VOLUME}, 4, sizeof(spinor));
// spinor ****h_propagator = (spinor ****) allocateMultiDimensionalArray({2,4,2,VOLUME/2}, 4, sizeof(spinor));

/* initalize the random sources: one source for each Dirc index beta=src_d --> spin dilution
*/
/* initalize the random sources: one source for each Dirac index beta=src_d --> spin dilution */
for (size_t i_phi = 0; i_phi < 2; i_phi++) { // doublet: light or heavy
for (size_t src_d = 0; src_d < 4; src_d++) { // spin dilution index
for (size_t i_f = 0; i_f < 2; i_f++) { // flavor index of the doublet
Expand Down Expand Up @@ -553,6 +545,10 @@ void heavy_correlators_measurement(const int traj, const int id, const int ieo,
}
}

// (no even-odd): source+propagator, doublet, spin dilution index, even-odd, flavor, position (+ Dirac, color)
// (psi[i_sp][phi][beta][f][x])[alpha][c] // last 3 indices are proper of the spinor struct
spinor *****arr_spinor = (spinor *****) callocMultiDimensional({2,2,4,2,VOLUME}, 5, sizeof(spinor));

// now we switch from even-odd representation to standard
for (size_t i_sp = 0; i_sp < 2; i_sp++) { // source or sink
for (size_t i_phi = 0; i_phi < 2; i_phi++) { // doublet index
Expand All @@ -575,23 +571,45 @@ void heavy_correlators_measurement(const int traj, const int id, const int ieo,
/* now we sum only over local space for every t */
for (t = 0; t < T; t++) {
j = g_ipt[t][0][0][0];

// dummy variables
res = 0.;
respa = 0.;
resp4 = 0.;

for (i = j; i < j + LX * LY * LZ; i++) {
res += _spinor_prod_re(l_propagator[0][0][i], l_propagator[0][0][i]);
_gamma0(phi, l_propagator[0][0][i]);
respa += _spinor_prod_re(l_propagator[0][0][i], phi);
_gamma5(phi, phi);
resp4 += _spinor_prod_im(l_propagator[0][0][i], phi);

for (size_t beta1 = 0; beta1 < 4; beta1++) {
for (size_t beta2 = 0; beta2 < 4; beta2++) {
for (size_t i = 0; i < 2; i++) {
for (size_t j = 0; j < 2; j++) {
for (size_t i_Gamma1 = 0; i_Gamma1 < 2; i_Gamma1++) {
for (size_t i_Gamma2 = 0; i_Gamma2 < 2; i_Gamma2++) {
res_hihj_Gamma1Gamma2 += _spinor_scalar_prod(); // COMPLETE HERE
// light correlators
for (size_t beta = 0; beta < 4; beta++) { // spin dilution
res += _spinor_prod_re(arr_spinor[1][0][beta][0][i], arr_spinor[1][0][beta][0][i]);
_gamma0(phi, arr_spinor[1][0][beta][0][i]);
respa += _spinor_prod_re(arr_spinor[1][0][beta][0][i], phi);
_gamma5(phi, phi);
resp4 += _spinor_prod_im(arr_spinor[1][0][beta][0][i], phi);
}

for (size_t i_f = 0; i_f < 2; i_f++) {
for (size_t j_f = 0; j_f < 2; j_f++) {
for (size_t i_Gamma1 = 0; i_Gamma1 < 2; i_Gamma1++) {
for (size_t i_Gamma2 = 0; i_Gamma2 < 2; i_Gamma2++) {
for (size_t beta1 = 0; beta1 < 4; beta1++) {
for (size_t beta2 = 0; beta2 < 4; beta2++) {
double dum1, dum2 = 0.0, 0.0; // dummy variables

// 1st contribution
phi = arr_spinor[1][1][beta_2][i_f][i];
if (Gamma_1 == 1) { // Gamma_1 = 1
_gamma5(phi, phi);
}
_spinor_scalar_prod(dum1, arr_spinor[0][0][beta_1][1 - i_f][i], phi);

// 2nd contribution
phi = arr_spinor[1][0][beta_1][1 - i_f][i];
if (Gamma_2 == 1) { // Gamma_1 = gamma_5
_gamma5(phi, phi);
}
_spinor_scalar_prod(dum2, arr_spinor[0][1][beta_2][i_f][i], phi);

res_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2] += dum1 * dum2;
}
}
}
Expand Down Expand Up @@ -621,14 +639,42 @@ void heavy_correlators_measurement(const int traj, const int id, const int ieo,
Cp4[t] = +resp4 / (g_nproc_x * LX) / (g_nproc_y * LY) / (g_nproc_z * LZ) / 2. /
optr1->kappa / optr1->kappa;
#endif

for (size_t i_f = 0; i_f < 2; i_f++) {
for (size_t j_f = 0; j_f < 2; j_f++) {
for (size_t i_Gamma1 = 0; i_Gamma1 < 2; i_Gamma1++) {
for (size_t i_Gamma2 = 0; i_Gamma2 < 2; i_Gamma2++) {
#if defined TM_USE_MPI
MPI_Reduce(&res_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2], &mpi_res_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2], 1, MPI_DOUBLE, MPI_SUM, 0, g_mpi_time_slices);
res_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2] = mpi_res_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2];
C_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2][t] = -eta_Gamma[i_Gamma1]*res / (g_nproc_x * LX) / (g_nproc_y * LY) / (g_nproc_z * LZ);
#else
C_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2][t] = -eta_Gamma[i_Gamma1]*res / (g_nproc_x * LX) / (g_nproc_y * LY) / (g_nproc_z * LZ);
#endif
}
}
}
}
}

#ifdef TM_USE_MPI
/* some gymnastics needed in case of parallelisation */
if (g_mpi_time_rank == 0) {
// light correlators
MPI_Gather(sCpp, T, MPI_DOUBLE, Cpp, T, MPI_DOUBLE, 0, g_mpi_SV_slices);
MPI_Gather(sCpa, T, MPI_DOUBLE, Cpa, T, MPI_DOUBLE, 0, g_mpi_SV_slices);
MPI_Gather(sCp4, T, MPI_DOUBLE, Cp4, T, MPI_DOUBLE, 0, g_mpi_SV_slices);

// heavy mesons
for (size_t i_f = 0; i_f < 2; i_f++) {
for (size_t j_f = 0; j_f < 2; j_f++) {
for (size_t i_Gamma1 = 0; i_Gamma1 < 2; i_Gamma1++) {
for (size_t i_Gamma2 = 0; i_Gamma2 < 2; i_Gamma2++) {
MPI_Gather(sC_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2], T, MPI_DOUBLE, C_hihj_Gamma1Gamma2[i_f][j_f][beta_1][beta_2], T, MPI_DOUBLE, 0, g_mpi_SV_slices);
}
}
}
}
}
#endif

Expand Down Expand Up @@ -671,17 +717,17 @@ void heavy_correlators_measurement(const int traj, const int id, const int ieo,
free(Cpp);
free(Cpa);
free(Cp4);
free(C_ij);
free(C_hihj_Gamma1Gamma2);
}
free(sCpp);
free(sCpa);
free(sCp4);
free(sC_ij);
free(sC_hihj_Gamma1Gamma2);
#else
free(Cpp);
free(Cpa);
free(Cp4);
free(C_ij);
free(C_hihj_Gamma1Gamma2);
#endif
} // for(max_time_slices)
} // for(max_samples)
Expand Down

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