preconditioned inverse iteration
(mata, matm, pre, num=1, maxit=20, printrates=True, GramSchmidt=True)
| 73 | |
| 74 | |
| 75 | def PINVIT(mata, matm, pre, num=1, maxit=20, printrates=True, GramSchmidt=True): |
| 76 | """preconditioned inverse iteration""" |
| 77 | import scipy.linalg |
| 78 | |
| 79 | r = mata.CreateRowVector() |
| 80 | |
| 81 | uvecs = MultiVector(r, num) |
| 82 | vecs = MultiVector(r, 2*num) |
| 83 | # hv = MultiVector(r, 2*num) |
| 84 | |
| 85 | for v in vecs[0:num]: |
| 86 | v.SetRandom() |
| 87 | uvecs[:] = pre * vecs[0:num] |
| 88 | lams = Vector(num * [1]) |
| 89 | |
| 90 | for i in range(maxit): |
| 91 | vecs[0:num] = mata * uvecs - (matm * uvecs).Scale (lams) |
| 92 | vecs[num:2*num] = pre * vecs[0:num] |
| 93 | vecs[0:num] = uvecs |
| 94 | |
| 95 | vecs.Orthogonalize(matm) |
| 96 | |
| 97 | # hv[:] = mata * vecs |
| 98 | # asmall = InnerProduct (vecs, hv) |
| 99 | # hv[:] = matm * vecs |
| 100 | # msmall = InnerProduct (vecs, hv) |
| 101 | asmall = InnerProduct (vecs, mata * vecs) |
| 102 | msmall = InnerProduct (vecs, matm * vecs) |
| 103 | |
| 104 | ev,evec = scipy.linalg.eigh(a=asmall, b=msmall) |
| 105 | lams = Vector(ev[0:num]) |
| 106 | if printrates: |
| 107 | print (i, ":", list(lams)) |
| 108 | |
| 109 | uvecs[:] = vecs * Matrix(evec[:,0:num]) |
| 110 | return lams, uvecs |
| 111 | |
| 112 | |
| 113 | def LOBPCG(mata, matm, pre, num=1, maxit=20, initial=None, printrates=True, largest=False): |
nothing calls this directly
no test coverage detected