mirror of https://github.com/abinit/abinit.git
392 lines
12 KiB
Mathematica
392 lines
12 KiB
Mathematica
(*
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Mathematica program to create code for the program metstr.f
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for the strain derivative of the nonlocal pseudopotential
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operator. The operator for angular momentum l has the form
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O_l = V_l(kp*kp) P_l(kp*kp, kp*k, k*k) V_l(k*k)
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where k and kp are the wavevectors of the input and output
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wavefunctions. and P_l are Legendre polynomials. The "*" sign
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represents a dot product. The V_l and d V_l/d(k*k) are multiplied
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in a separate routine and are not explicit in this code. The three
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sections of Mathematica code corresponding to iterm = 1, 2, 3 represent
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strain (s) derivatives of the 3 terms in the O_l product. (The angular
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momentum "l" is represented by "rank" following Abinit convention in
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the routine nonlop which calls metstr.)
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For the straight application of O_l to a wavefunction, the rank of
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the input k tensor equals the rank of the output kp tensor. This is
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also true for the strain derivative of P_l (iterm = 2). However,
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the strain derivatives of the V_l terms introduce two additional
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powers of k or kp, and thus couple to rank+2 tensors on either
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input or output.
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This version is modified to give contractions for internal strain, that
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is a 2nd derivative based on one cartesian strain derivative applied
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to the metric tensor and one derivative wrt a reduced atomic coordinate.
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The latter simply introduces a +I kpj or -I kj term in the polynomial.
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We will ignore the imaginary I and take care of that with the output
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of the code.
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*)
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MakeMetintstr[iterm_, outfile_] :=
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Module[{tnk,tnkp,idir,k,kp,dt,ks,kps,Plegendre,rank,
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rankin,rankout,limitin,limitout,poly,term,ii,jj},
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(* symmetric tensors of k and kp components, ranks 1 through 7
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as 2-dimensional Mathematica arrays tnk[[rank]][[element]] and tnkp
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number of elements is (rank+1)(rank+2)/2 *)
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tnk = {
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{1}, (* 0, 1 *)
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{k1, (* 1, 1 *)
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k2, (* 1, 2 *)
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k3}, (* 1, 3 *)
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{k1 k1, (* 2, 1 *)
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k2 k2, (* 2, 2 *)
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k3 k3, (* 2, 3 *)
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k3 k2, (* 2, 4 *)
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k3 k1, (* 2, 5 *)
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k2 k1}, (* 2, 6 *)
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{k1 k1 k1, (* 3, 1 *)
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k2 k2 k1, (* 3, 2 *)
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k3 k3 k1, (* 3, 3 *)
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k3 k2 k1, (* 3, 4 *)
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k3 k1 k1, (* 3, 5 *)
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k2 k1 k1, (* 3, 6 *)
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k2 k2 k2, (* 3, 7 *)
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k3 k3 k2, (* 3, 8 *)
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k3 k2 k2, (* 3, 9 *)
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k3 k3 k3}, (* 3, 10*)
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{k1 k1 k1 k1, (* 4, 1 *)
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k2 k2 k1 k1, (* 4, 2 *)
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k3 k3 k1 k1, (* 4, 3 *)
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k3 k2 k1 k1, (* 4, 4 *)
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k3 k1 k1 k1, (* 4, 5 *)
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k2 k1 k1 k1, (* 4, 6 *)
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k2 k2 k2 k1, (* 4, 7 *)
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k3 k3 k2 k1, (* 4, 8 *)
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k3 k2 k2 k1, (* 4, 9 *)
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k3 k3 k3 k1, (* 4, 10 *)
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k2 k2 k2 k2, (* 4, 11 *)
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k3 k3 k2 k2, (* 4, 12 *)
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k3 k2 k2 k2, (* 4, 13 *)
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k3 k3 k3 k2, (* 4, 14 *)
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k3 k3 k3 k3}, (* 4, 15 *)
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{k1 k1 k1 k1 k1, (* 5, 1 *)
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k2 k2 k1 k1 k1, (* 5, 2 *)
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k3 k3 k1 k1 k1, (* 5, 3 *)
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k3 k2 k1 k1 k1, (* 5, 4 *)
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k3 k1 k1 k1 k1, (* 5, 5 *)
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k2 k1 k1 k1 k1, (* 5, 6 *)
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k2 k2 k2 k1 k1, (* 5, 7 *)
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k3 k3 k2 k1 k1, (* 5, 8 *)
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k3 k2 k2 k1 k1, (* 5, 9 *)
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k3 k3 k3 k1 k1, (* 5, 10 *)
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k2 k2 k2 k2 k1, (* 5, 11 *)
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k3 k3 k2 k2 k1, (* 5, 12 *)
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k3 k2 k2 k2 k1, (* 5, 13 *)
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k3 k3 k3 k2 k1, (* 5, 14 *)
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k3 k3 k3 k3 k1, (* 5, 15 *)
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k2 k2 k2 k2 k2, (* 5, 16 *)
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k3 k3 k2 k2 k2, (* 5, 17 *)
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k3 k2 k2 k2 k2, (* 5, 18 *)
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k3 k3 k3 k2 k2, (* 5, 19 *)
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k3 k3 k3 k3 k2, (* 5, 20 *)
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k3 k3 k3 k3 k3}, (* 5, 21 *)
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{k1 k1 k1 k1 k1 k1, (* 6, 1 *)
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k2 k2 k1 k1 k1 k1, (* 6, 2 *)
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k3 k3 k1 k1 k1 k1, (* 6, 3 *)
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k3 k2 k1 k1 k1 k1, (* 6, 4 *)
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k3 k1 k1 k1 k1 k1, (* 6, 5 *)
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k2 k1 k1 k1 k1 k1, (* 6, 6 *)
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k2 k2 k2 k1 k1 k1, (* 6, 7 *)
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k3 k3 k2 k1 k1 k1, (* 6, 8 *)
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k3 k2 k2 k1 k1 k1, (* 6, 9 *)
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k3 k3 k3 k1 k1 k1, (* 6, 10 *)
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k2 k2 k2 k2 k1 k1, (* 6, 11 *)
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k3 k3 k2 k2 k1 k1, (* 6, 12 *)
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k3 k2 k2 k2 k1 k1, (* 6, 13 *)
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k3 k3 k3 k2 k1 k1, (* 6, 14 *)
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k3 k3 k3 k3 k1 k1, (* 6, 15 *)
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k2 k2 k2 k2 k2 k1, (* 6, 16 *)
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k3 k3 k2 k2 k2 k1, (* 6, 17 *)
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k3 k2 k2 k2 k2 k1, (* 6, 18 *)
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k3 k3 k3 k2 k2 k1, (* 6, 19 *)
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k3 k3 k3 k3 k2 k1, (* 6, 20 *)
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k3 k3 k3 k3 k3 k1, (* 6, 21 *)
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k2 k2 k2 k2 k2 k2, (* 6, 22 *)
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k3 k3 k2 k2 k2 k2, (* 6, 23 *)
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k3 k2 k2 k2 k2 k2, (* 6, 24 *)
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k3 k3 k3 k2 k2 k2, (* 6, 25 *)
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k3 k3 k3 k3 k2 k2, (* 6, 26 *)
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k3 k3 k3 k3 k3 k2, (* 6, 27 *)
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k3 k3 k3 k3 k3 k3}, (* 6, 28 *)
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{k1 k1 k1 k1 k1 k1 k1, (* 7, 1 *)
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k2 k2 k1 k1 k1 k1 k1, (* 7, 2 *)
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k3 k3 k1 k1 k1 k1 k1, (* 7, 3 *)
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k3 k2 k1 k1 k1 k1 k1, (* 7, 4 *)
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k3 k1 k1 k1 k1 k1 k1, (* 7, 5 *)
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k2 k1 k1 k1 k1 k1 k1, (* 7, 6 *)
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k2 k2 k2 k1 k1 k1 k1, (* 7, 7 *)
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k3 k3 k2 k1 k1 k1 k1, (* 7, 8 *)
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k3 k2 k2 k1 k1 k1 k1, (* 7, 9 *)
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k3 k3 k3 k1 k1 k1 k1, (* 7, 10 *)
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k2 k2 k2 k2 k1 k1 k1, (* 7, 11 *)
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k3 k3 k2 k2 k1 k1 k1, (* 7, 12 *)
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k3 k2 k2 k2 k1 k1 k1, (* 7, 13 *)
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k3 k3 k3 k2 k1 k1 k1, (* 7, 14 *)
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k3 k3 k3 k3 k1 k1 k1, (* 7, 15 *)
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k2 k2 k2 k2 k2 k1 k1, (* 7, 16 *)
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k3 k3 k2 k2 k2 k1 k1, (* 7, 17 *)
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k3 k2 k2 k2 k2 k1 k1, (* 7, 18 *)
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k3 k3 k3 k2 k2 k1 k1, (* 7, 19 *)
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k3 k3 k3 k3 k2 k1 k1, (* 7, 20 *)
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k3 k3 k3 k3 k3 k1 k1, (* 7, 21 *)
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k2 k2 k2 k2 k2 k2 k1, (* 7, 22 *)
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k3 k3 k2 k2 k2 k2 k1, (* 7, 23 *)
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k3 k2 k2 k2 k2 k2 k1, (* 7, 24 *)
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k3 k3 k3 k2 k2 k2 k1, (* 7, 25 *)
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k3 k3 k3 k3 k2 k2 k1, (* 7, 26 *)
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k3 k3 k3 k3 k3 k2 k1, (* 7, 27 *)
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k3 k3 k3 k3 k3 k3 k1, (* 7, 28 *)
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k2 k2 k2 k2 k2 k2 k2, (* 7, 29 *)
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k3 k3 k2 k2 k2 k2 k2, (* 7, 30 *)
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k3 k2 k2 k2 k2 k2 k2, (* 7, 31 *)
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k3 k3 k3 k2 k2 k2 k2, (* 7, 32 *)
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k3 k3 k3 k3 k2 k2 k2, (* 7, 33 *)
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k3 k3 k3 k3 k3 k2 k2, (* 7, 34 *)
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k3 k3 k3 k3 k3 k3 k2, (* 7, 25 *)
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k3 k3 k3 k3 k3 k3 k3}};(* 7, 36 *)
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tnkp = {
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{1}, (* 0, 1 *)
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{kp1, (* 1, 1 *)
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kp2, (* 1, 2 *)
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kp3}, (* 1, 3 *)
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{kp1 kp1, (* 2, 1 *)
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kp2 kp2, (* 2, 2 *)
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kp3 kp3, (* 2, 3 *)
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kp3 kp2, (* 2, 4 *)
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kp3 kp1, (* 2, 5 *)
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kp2 kp1}, (* 2, 6 *)
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{kp1 kp1 kp1, (* 3, 1 *)
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kp2 kp2 kp1, (* 3, 2 *)
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kp3 kp3 kp1, (* 3, 3 *)
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kp3 kp2 kp1, (* 3, 4 *)
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kp3 kp1 kp1, (* 3, 5 *)
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kp2 kp1 kp1, (* 3, 6 *)
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kp2 kp2 kp2, (* 3, 7 *)
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kp3 kp3 kp2, (* 3, 8 *)
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kp3 kp2 kp2, (* 3, 9 *)
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kp3 kp3 kp3}, (* 3, 10*)
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{kp1 kp1 kp1 kp1, (* 4, 1 *)
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kp2 kp2 kp1 kp1, (* 4, 2 *)
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kp3 kp3 kp1 kp1, (* 4, 3 *)
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kp3 kp2 kp1 kp1, (* 4, 4 *)
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kp3 kp1 kp1 kp1, (* 4, 5 *)
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kp2 kp1 kp1 kp1, (* 4, 6 *)
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kp2 kp2 kp2 kp1, (* 4, 7 *)
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kp3 kp3 kp2 kp1, (* 4, 8 *)
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kp3 kp2 kp2 kp1, (* 4, 9 *)
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kp3 kp3 kp3 kp1, (* 4, 10 *)
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kp2 kp2 kp2 kp2, (* 4, 11 *)
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kp3 kp3 kp2 kp2, (* 4, 12 *)
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kp3 kp2 kp2 kp2, (* 4, 13 *)
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kp3 kp3 kp3 kp2, (* 4, 14 *)
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kp3 kp3 kp3 kp3}, (* 4, 15 *)
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{kp1 kp1 kp1 kp1 kp1, (* 5, 1 *)
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kp2 kp2 kp1 kp1 kp1, (* 5, 2 *)
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kp3 kp3 kp1 kp1 kp1, (* 5, 3 *)
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kp3 kp2 kp1 kp1 kp1, (* 5, 4 *)
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kp3 kp1 kp1 kp1 kp1, (* 5, 5 *)
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kp2 kp1 kp1 kp1 kp1, (* 5, 6 *)
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kp2 kp2 kp2 kp1 kp1, (* 5, 7 *)
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kp3 kp3 kp2 kp1 kp1, (* 5, 8 *)
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kp3 kp2 kp2 kp1 kp1, (* 5, 9 *)
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kp3 kp3 kp3 kp1 kp1, (* 5, 10 *)
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kp2 kp2 kp2 kp2 kp1, (* 5, 11 *)
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kp3 kp3 kp2 kp2 kp1, (* 5, 12 *)
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kp3 kp2 kp2 kp2 kp1, (* 5, 13 *)
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kp3 kp3 kp3 kp2 kp1, (* 5, 14 *)
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kp3 kp3 kp3 kp3 kp1, (* 5, 15 *)
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kp2 kp2 kp2 kp2 kp2, (* 5, 16 *)
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kp3 kp3 kp2 kp2 kp2, (* 5, 17 *)
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kp3 kp2 kp2 kp2 kp2, (* 5, 18 *)
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kp3 kp3 kp3 kp2 kp2, (* 5, 19 *)
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kp3 kp3 kp3 kp3 kp2, (* 5, 20 *)
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kp3 kp3 kp3 kp3 kp3}, (* 5, 21 *)
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{kp1 kp1 kp1 kp1 kp1 kp1, (* 6, 1 *)
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kp2 kp2 kp1 kp1 kp1 kp1, (* 6, 2 *)
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kp3 kp3 kp1 kp1 kp1 kp1, (* 6, 3 *)
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kp3 kp2 kp1 kp1 kp1 kp1, (* 6, 4 *)
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kp3 kp1 kp1 kp1 kp1 kp1, (* 6, 5 *)
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kp2 kp1 kp1 kp1 kp1 kp1, (* 6, 6 *)
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kp2 kp2 kp2 kp1 kp1 kp1, (* 6, 7 *)
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kp3 kp3 kp2 kp1 kp1 kp1, (* 6, 8 *)
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kp3 kp2 kp2 kp1 kp1 kp1, (* 6, 9 *)
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kp3 kp3 kp3 kp1 kp1 kp1, (* 6, 10 *)
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kp2 kp2 kp2 kp2 kp1 kp1, (* 6, 11 *)
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kp3 kp3 kp2 kp2 kp1 kp1, (* 6, 12 *)
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kp3 kp2 kp2 kp2 kp1 kp1, (* 6, 13 *)
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kp3 kp3 kp3 kp2 kp1 kp1, (* 6, 14 *)
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kp3 kp3 kp3 kp3 kp1 kp1, (* 6, 15 *)
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kp2 kp2 kp2 kp2 kp2 kp1, (* 6, 16 *)
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kp3 kp3 kp2 kp2 kp2 kp1, (* 6, 17 *)
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kp3 kp2 kp2 kp2 kp2 kp1, (* 6, 18 *)
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kp3 kp3 kp3 kp2 kp2 kp1, (* 6, 19 *)
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kp3 kp3 kp3 kp3 kp2 kp1, (* 6, 20 *)
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kp3 kp3 kp3 kp3 kp3 kp1, (* 6, 21 *)
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kp2 kp2 kp2 kp2 kp2 kp2, (* 6, 22 *)
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kp3 kp3 kp2 kp2 kp2 kp2, (* 6, 23 *)
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kp3 kp2 kp2 kp2 kp2 kp2, (* 6, 24 *)
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kp3 kp3 kp3 kp2 kp2 kp2, (* 6, 25 *)
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kp3 kp3 kp3 kp3 kp2 kp2, (* 6, 26 *)
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kp3 kp3 kp3 kp3 kp3 kp2, (* 6, 27 *)
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kp3 kp3 kp3 kp3 kp3 kp3}, (* 6, 28 *)
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{kp1 kp1 kp1 kp1 kp1 kp1 kp1, (* 7, 1 *)
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kp2 kp2 kp1 kp1 kp1 kp1 kp1, (* 7, 2 *)
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kp3 kp3 kp1 kp1 kp1 kp1 kp1, (* 7, 3 *)
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kp3 kp2 kp1 kp1 kp1 kp1 kp1, (* 7, 4 *)
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kp3 kp1 kp1 kp1 kp1 kp1 kp1, (* 7, 5 *)
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kp2 kp1 kp1 kp1 kp1 kp1 kp1, (* 7, 6 *)
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kp2 kp2 kp2 kp1 kp1 kp1 kp1, (* 7, 7 *)
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kp3 kp3 kp2 kp1 kp1 kp1 kp1, (* 7, 8 *)
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kp3 kp2 kp2 kp1 kp1 kp1 kp1, (* 7, 9 *)
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kp3 kp3 kp3 kp1 kp1 kp1 kp1, (* 7, 10 *)
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kp2 kp2 kp2 kp2 kp1 kp1 kp1, (* 7, 11 *)
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kp3 kp3 kp2 kp2 kp1 kp1 kp1, (* 7, 12 *)
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kp3 kp2 kp2 kp2 kp1 kp1 kp1, (* 7, 13 *)
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kp3 kp3 kp3 kp2 kp1 kp1 kp1, (* 7, 14 *)
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kp3 kp3 kp3 kp3 kp1 kp1 kp1, (* 7, 15 *)
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kp2 kp2 kp2 kp2 kp2 kp1 kp1, (* 7, 16 *)
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kp3 kp3 kp2 kp2 kp2 kp1 kp1, (* 7, 17 *)
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kp3 kp2 kp2 kp2 kp2 kp1 kp1, (* 7, 18 *)
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kp3 kp3 kp3 kp2 kp2 kp1 kp1, (* 7, 19 *)
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kp3 kp3 kp3 kp3 kp2 kp1 kp1, (* 7, 20 *)
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kp3 kp3 kp3 kp3 kp3 kp1 kp1, (* 7, 21 *)
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kp2 kp2 kp2 kp2 kp2 kp2 kp1, (* 7, 22 *)
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kp3 kp3 kp2 kp2 kp2 kp2 kp1, (* 7, 23 *)
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kp3 kp2 kp2 kp2 kp2 kp2 kp1, (* 7, 24 *)
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kp3 kp3 kp3 kp2 kp2 kp2 kp1, (* 7, 25 *)
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kp3 kp3 kp3 kp3 kp2 kp2 kp1, (* 7, 26 *)
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kp3 kp3 kp3 kp3 kp3 kp2 kp1, (* 7, 27 *)
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kp3 kp3 kp3 kp3 kp3 kp3 kp1, (* 7, 28 *)
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kp2 kp2 kp2 kp2 kp2 kp2 kp2, (* 7, 29 *)
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kp3 kp3 kp2 kp2 kp2 kp2 kp2, (* 7, 30 *)
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kp3 kp2 kp2 kp2 kp2 kp2 kp2, (* 7, 31 *)
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kp3 kp3 kp3 kp2 kp2 kp2 kp2, (* 7, 32 *)
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kp3 kp3 kp3 kp3 kp2 kp2 kp2, (* 7, 33 *)
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kp3 kp3 kp3 kp3 kp3 kp2 kp2, (* 7, 34 *)
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kp3 kp3 kp3 kp3 kp3 kp3 kp2, (* 7, 25 *)
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kp3 kp3 kp3 kp3 kp3 kp3 kp3}};(* 7, 36 *) ;
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(* quantities needed to set up wavevector polynomials
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k = input wavefunction wavevector
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kp = output wavefunction wavevector
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m = the metric tensor gmet *)
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k = {k1, k2, k3};
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kp = {kp1, kp2, kp3};
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(* symmetry of metric tensor is built in here
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only symmetric strains are to be permitted so derivatives will
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retain this symmetry *)
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m = {{m11[s], m12[s], m13[s]}, {m12[s], m22[s], m23[s]},
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{m13[s], m23[s], m33[s]}};
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dt = kp.m.k;
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ks = k.m.k;
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kps = kp.m.kp;
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(* The Legendre polynomials P_l are modified so that each term is
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of of order k^l * kp^l. We only treat l = 0, 1, 2, and 3. *)
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Plegendre={1, dt, 1.5 dt^2 - 0.5 kps ks, 2.5 dt^3 - 1.5 kps dt ks};
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Do[
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rankinarr = {rank ,rank+1,rank ,rank+1,rank+2,rank+3};
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rankoutarr = {rank+3,rank+2,rank+1,rank ,rank+1,rank };
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rankin = rankinarr[[iterm]];
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rankout = rankoutarr[[iterm]];
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Write[outfile,TextForm["elseif(rank=="],FortranForm[rank],
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TextForm[") then#"]];
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limitin = (rankin+1)(rankin+2)/2;
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limitout = (rankout+1)(rankout+2)/2;
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Write[outfile,TextForm["ntnin="],FortranForm[limitin],TextForm["#"]];
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Write[outfile,TextForm["ntnout="],FortranForm[limitout],TextForm["#"]];
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Write[outfile,TextForm["allocate(cm(3,"],FortranForm[limitin],
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TextForm[","],FortranForm[limitout],TextForm[")#"]];
|
|
Write[outfile,TextForm["cm(:,:,:)=0.#"]];
|
|
|
|
Do[
|
|
|
|
poly = {kp[[idir]] D[kps,s] Plegendre[[rank+1]],
|
|
k[[idir]] D[kps,s] Plegendre[[rank+1]],
|
|
kp[[idir]] D[Plegendre[[rank+1]],s],
|
|
k[[idir]] D[Plegendre[[rank+1]],s],
|
|
kp[[idir]] D[ks, s] Plegendre[[rank+1]],
|
|
k[[idir]] D[ks, s] Plegendre[[rank+1]]};
|
|
|
|
(* this is the only real computational step -- extracting the tensor
|
|
components *)
|
|
|
|
Do[term = Simplify[
|
|
Coefficient[poly[[iterm]], (tnkp[[rankout+1]][[jj]] *
|
|
tnk[[rankin+1]][[ii]])]];
|
|
|
|
Write[outfile,
|
|
TextForm["cm("],
|
|
FortranForm[idir],
|
|
TextForm[","],
|
|
FortranForm[ii],
|
|
TextForm[","],
|
|
FortranForm[jj],
|
|
TextForm[")="],
|
|
FortranForm[term],
|
|
TextForm["#"]],
|
|
|
|
{jj,1,limitout}, {ii,1,limitin}],
|
|
|
|
{idir,1,3}],
|
|
|
|
{rank,0,3}];
|
|
|
|
(* {rank,1,3}]; *)
|
|
(*HACK: drop rank = 0 for term 6; result is zero and causes trouble *)
|
|
|
|
Close[outfile];
|
|
|
|
]
|