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Added Woodbury 3x3 kernel template generator.
This commit is contained in:
Francois Coppens
parent
549413abca
commit
6c0430a509
@ -921,14 +921,14 @@ assert(rc == QMCKL_SUCCESS);
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*** C source
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#+begin_src c :tangle (eval c) :comments org
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qmckl_exit_code qmckl_woodbury_3x3(const qmckl_context context,
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qmckl_exit_code qmckl_woodbury_3x3_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* Updates,
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const uint64_t* Updates_index,
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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* Slater_inv,
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double* determinant) {
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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 3
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B := 1 + V * C, 3 x 3
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@ -938,7 +938,7 @@ qmckl_exit_code qmckl_woodbury_3x3(const qmckl_context context,
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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_3x3",
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"qmckl_woodbury_3x3_hpc",
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NULL);
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}
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@ -1026,6 +1026,190 @@ qmckl_exit_code qmckl_woodbury_3x3(const qmckl_context context,
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}
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#+end_src
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#+NAME:woodbury_3x3_kernel_template
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#+begin_src c
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qmckl_exit_code qmckl_woodbury_3x3_{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 3
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B := 1 + V * C, 3 x 3
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D := V * S^{-1}, 3 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_3x3_{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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const uint64_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 (uint64_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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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 * 3] += Slater_inv[i * D{Dim}_P + k] * Updates[k];
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C[i * 3 + 1] += Slater_inv[i * D{Dim}_P + k] * Updates[D{Dim}_P + k];
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C[i * 3 + 2] += Slater_inv[i * D{Dim}_P + k] * Updates[2 * D{Dim}_P + k];
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}
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}
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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 QMCKL_FAILURE;
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}
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// Update det(Slater) if passed
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if (determinant)
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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 D{Dim}_P
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double __attribute__((aligned(8))) tmp[3 * 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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double* r3dim = &(Slater_inv[row3 * 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] + Binv[2] * r3dim[j];
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tmp[D{Dim}_P + j] =
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Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
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tmp[2 * D{Dim}_P + j] =
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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 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 * 3] * tmp[j];
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Slater_inv[i * D{Dim}_P + j] -= C[i * 3 + 1] * tmp[D{Dim}_P + j];
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Slater_inv[i * D{Dim}_P + j] -= C[i * 3 + 2] * tmp[2 * 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_3x3_kernel_generator
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#+begin_src python :noweb yes :exports none
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text="""
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<<woodbury_3x3_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 '\n'.join(result)
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#+end_src
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#+NAME:woodbury_3x3_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_3x3_{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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"""
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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 '\n'.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_3x3_kernel_generator()>>
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qmckl_exit_code qmckl_woodbury_3x3(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_3x3",
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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_3x3_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_3x3_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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*** Performance...
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This function is most efficient when used in cases where there are only 3 rank-1 updates and
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