Green's Functions #13

CarlosMejZ · 2023-06-02T15:59:11Z

These are the basic functionalities to compute one-body Green's functions for a selected CI wave function, as described in Phys. Rev. B 100, 125165 (2019) and J. Chem. Phys. 154, 121101 (2021). It implements both a continuous fraction based Lanczos and band Lanczos method. The console output needs to be adapted to match the one used in the rest of the code, and unit testing is required (so far, only a small example testing is possible within the standalone_driver.cxx test code).

…e doxygen docu.

wavefunction91

Initial round of comments - I can get things to compile locally. I'll fix CI this evening

include/macis/gf/bandlan.hpp

include/macis/gf/inn_prods.hpp

include/macis/gf/lanczos.hpp

src/macis/gf/bandlan.cxx

src/macis/gf/eigsolver.cxx

src/macis/gf/gf.cxx

wavefunction91 · 2023-06-02T19:04:15Z

@CarlosMejZ Do you have any ideas on how you might want to unit test this code? Are there exact results we can compare to / things we could reliably reproduce?

…Band Lanczos routines to use matrices which are guaranteed contiguous in memory.

src/macis/gf/bandlan.cxx

wavefunction91 · 2023-06-05T15:27:51Z

src/macis/gf/bandlan.cxx

-  delete[] WORK;
-  delete[] E;
+  D.resize(N);
+  lapack::heev_2stage(JOBZ, UPLO, N, A.data(), LDA, D.data());


Good call on the 2stage, but that' actually isn't faster for all general cases. Brings up an interesting point about how to select the algorithm though... Might be good to have a switch. I'll give it some thought.

include/macis/gf/eigsolver.hpp

include/macis/gf/gf.hpp

wavefunction91 · 2023-06-05T15:33:39Z

include/macis/gf/inn_prods.hpp

@@ -32,14 +32,7 @@ namespace macis {
 */
 inline double MyInnProd(const std::vector<double>& vecR,


At some point it might make sense to just remove these functions entirely since all overloads call the same blaspp function. Not a high-priority now, but something to keep in mind.

Would you rather have the full, lengthy blaspp call everytime, or a single wrapper to make it a little easier to read?

Globally, yes, but having local (e.g. lambda) aliases would be fine.

Ok, I can make local aliases.

wavefunction91 · 2023-06-05T15:36:09Z

src/macis/gf/bandlan.cxx

@@ -293,57 +159,42 @@ bool GetEigsysBand(std::vector<std::vector<double> > &mat, int nSupDiag,
  eigvals.clear();


This is a good piece of functionality. It might make sense to wrap it up into a nice LAPACK-style function for use elsewhere.

… all matrices to avoid using vector<vector> data types.

wavefunction91 · 2023-06-15T19:05:11Z

include/macis/gf/bandlan.hpp

-        // temp[coeff] -= bandH[it - 1][jt - 1] * qs[band_indx_j][coeff];
-        temp[coeff] -= bandH[it - 1][jt - 1] * qs[N * band_indx_j + coeff];
+        temp[coeff] -=
+            bandH[(it - 1) * nLanIts + jt - 1] * qs[N * band_indx_j + coeff];


Is there a reason you chose (what looks like to me) row-major for bandH?

Probably just the similarity with how I was linearizing qs (where each vector is stored contiguously). In the case of bandH, since it's a Hermitian matrix, it does not really matter. But I can change it if you prefer to have all matrices in column-major.

All depends on what is the most efficient storage scheme - i.e. which scheme will most likely give you the most opportunities for contiguous data access. It doesn't look like it particularly matters here.

However, it looks like this operation can be made a bit more efficient - correct me if I'm wrong, but your computing something that looks like

temp(:) -= alpha * qs(:,band_idx_j)

where alpha = bandH(it-1, jt-1). That's an axpy. Looks like it can be replaced on line 207 too

Good catch!

wavefunction91 · 2023-06-16T22:20:49Z

include/macis/gf/bandlan.hpp

-        // temp[coeff] -= bandH[it - 1][jt - 1] * qs[band_indx_j][coeff];
-        temp[coeff] -= bandH[it - 1][jt - 1] * qs[N * band_indx_j + coeff];
+        temp[coeff] -=
+            bandH[(it - 1) * nLanIts + jt - 1] * qs[N * band_indx_j + coeff];


All depends on what is the most efficient storage scheme - i.e. which scheme will most likely give you the most opportunities for contiguous data access. It doesn't look like it particularly matters here.

However, it looks like this operation can be made a bit more efficient - correct me if I'm wrong, but your computing something that looks like

temp(:) -= alpha * qs(:,band_idx_j)

where alpha = bandH(it-1, jt-1). That's an axpy. Looks like it can be replaced on line 207 too

wavefunction91 · 2023-06-16T22:21:54Z

include/macis/gf/bandlan.hpp

+ * @date 25/04/2022
+ */
+template <class Cont, class Functor>
+void MyBandLan(const Functor &H, std::vector<Cont> &qs,


Naming conventions of My<Func> should get swapped out for something more meaningful. I think BandLan works fine here.

wavefunction91 · 2023-06-16T22:23:38Z

include/macis/gf/bandlan.hpp

+                  << std::endl;
+      } else {
+#pragma omp parallel for
+        for(size_t coeff = 0; coeff < temp.size(); coeff++)


This is an axpy with alpha = 1.0/bandH(it-1,jt-1) and beta = 0

wavefunction91 · 2023-06-16T22:24:18Z

include/macis/gf/bandlan.hpp

+        bandH.resize(nLanIts * nLanIts);
+        break;
+#pragma omp parallel for
+        for(size_t coeff = 0; coeff < temp.size(); coeff++)


I'd either use scal with alpha=0 or a memset here since it's contiguous

wavefunction91 · 2023-06-16T22:26:22Z

include/macis/gf/bandlan.hpp

+
+  for(int it = 1; it <= nLanIts; it++) {
+    int band_indx_i =
+        true_indx[it];  // TO WHAT ELEMENT OF THE VECTOR SET DO WE APPLY THIS


Can you explain this indirection here? Generally we want to avoid things like this (to e.g. allow for better usage of Level-3 BLAS when possible), but if its completely necessary, it's fine.

You mean the use of the effective index true_indx? (I'm afraid I don't know what you mean by indirection)

This is what I came up with to apply the matvecs in the right order to the right vector, since in band Lanczos, unlike in the regular one, at every iteration you act on a different vector in your set of nbands. Why is this a problem for BLAS? Shouldn't it be fine as long as you pass the right memory sector to act on?

I guess that a way to avoid this true_indx variable could be to turn the for loop over it into two, one external loop going over nLanIts // nbands and one internal loop going over nbands. I think that should be completely equivalent, and then the index in the internal loop would be essentially iterating over which vector in the basis to act on with the Hamiltonian. Do you think this would make the code better?

…ze the evaluation of G[w] for each frequency in the single band case. Removed MyInnProd header, substituted by lambdas for blas::dot.

…d core space determinants into the ASCI ranking (to allow for them to be substituted).

…y models. Test case added.

…ator

… be used in GF calculation.

…ackpp was not returning the right eigenvectors, but the eigenvectors to an intermediat tridiagonal matrix.

…mespace this is.

CarlosMejZ added 2 commits June 2, 2023 16:01

Added GF functionalities. TODO: Fix the outputs to console, polish th…

e95c43f

…e doxygen docu.

Filling in the doxygen docu for the GF-relevant routines.

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CarlosMejZ added the enhancement New feature or request label Jun 2, 2023

CarlosMejZ requested a review from wavefunction91 June 2, 2023 15:59

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Applied review comments from pull request, started reformulating the …

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…Band Lanczos routines to use matrices which are guaranteed contiguous in memory.

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… all matrices to avoid using vector<vector> data types.

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CarlosMejZ and others added 3 commits June 21, 2023 10:08

Cleaned GF routines from omp pragmas, only one remaining to paralleli…

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…ze the evaluation of G[w] for each frequency in the single band case. Removed MyInnProd header, substituted by lambdas for blas::dot.

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BUG FIXED: Passing wrong vector length to Band Lanczos. Also, include…

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…d core space determinants into the ASCI ranking (to allow for them to be substituted).

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Fixed Bug in GF calculation: Call to band diagonalization through Lap…

ff65ee7

…ackpp was not returning the right eigenvectors, but the eigenvectors to an intermediat tridiagonal matrix.

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Added functionalities to specify GF frequency grid.

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Green's Functions #13

Green's Functions #13

CarlosMejZ commented Jun 2, 2023

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CarlosMejZ Jun 19, 2023 •

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		@@ -32,14 +32,7 @@ namespace macis {
		*/
		inline double MyInnProd(const std::vector<double>& vecR,

		@@ -293,57 +159,42 @@ bool GetEigsysBand(std::vector<std::vector<double> > &mat, int nSupDiag,
		eigvals.clear();

Green's Functions #13

Are you sure you want to change the base?

Green's Functions #13

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CarlosMejZ Jun 19, 2023 • edited Loading

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