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make correlation matrix forula easier on the numerics

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This commit is contained in:
Valentin Boettcher 2022-02-07 14:42:54 +01:00
parent f9cd4779f9
commit d0f297fabc
1 changed files with 267 additions and 119 deletions
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386
hopsflow/gaussflow_two.py
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@ -342,48 +342,77 @@ class CorrelationMatrix(Propagator):
# straight from mathematica
result[:, i, j] += (
G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* (
(
np.exp(-(s * G_e[n]) - t * α_e[l][g])
* α[l][g]
* (
-(
np.exp(t * G_e[m])
* (-1 + np.exp(s * (G_e[n] + α_e[l][g])))
* G_e[m]
)
+ (
np.exp(t * G_e[m])
- np.exp(t * α_e[l][g])
+ np.exp(s * (G_e[m] + G_e[n]) + t * α_e[l][g])
- np.exp(t * G_e[m] + s * (G_e[n] + α_e[l][g]))
)
* G_e[n]
+ np.exp(t * α_e[l][g])
* (-1 + np.exp(s * (G_e[m] + G_e[n])))
* α_e[l][g]
)
)
/ ((-G_e[m] + α_e[l][g]) * (G_e[n] + α_e[l][g]))
+ (
αc[l][g]
* (
(-np.exp(s * G_e[n]) + np.exp(s * αc_e[l][g])) * G_e[m]
- np.exp(s * G_e[n]) * G_e[n]
+ np.exp(s * (G_e[m] + G_e[n] + αc_e[l][g]))
* (G_e[n] - αc_e[l][g])
+ np.exp(s * αc_e[l][g]) * αc_e[l][g]
)
)
/ (
np.exp(s * (G_e[n] + αc_e[l][g]))
* (G_e[n] - αc_e[l][g])
* (G_e[m] + αc_e[l][g])
)
(
np.exp(s * G_e[m] - t * G_e[m])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* α[l][g]
)
) / (np.exp(t * G_e[m]) * (G_e[m] + G_e[n]))
/ ((G_e[m] + G_e[n]) * (G_e[n] + α_e[l][g]))
- (
np.exp(-(t * G_e[m]) - s * G_e[n])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* α[l][g]
)
/ ((G_e[m] + G_e[n]) * (G_e[n] + α_e[l][g]))
- (
np.exp(s * G_e[m] - t * G_e[m])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* α[l][g]
)
/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
+ (
np.exp(-(t * G_e[m]) - s * G_e[n])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* α[l][g]
)
/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
- (
np.exp(-(s * G_e[n]) - t * α_e[l][g])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* α[l][g]
)
/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
+ (
np.exp(s * α_e[l][g] - t * α_e[l][g])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* α[l][g]
)
/ ((G_e[m] - α_e[l][g]) * (G_e[n] + α_e[l][g]))
- (
np.exp(s * G_e[m] - t * G_e[m])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* αc[l][g]
)
/ ((G_e[m] + G_e[n]) * (G_e[n] - αc_e[l][g]))
+ (
np.exp(-(t * G_e[m]) - s * G_e[n])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* αc[l][g]
)
/ ((G_e[m] + G_e[n]) * (G_e[n] - αc_e[l][g]))
+ (
np.exp(s * G_e[m] - t * G_e[m])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* αc[l][g]
)
/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
- (
np.exp(-(t * G_e[m]) - s * αc_e[l][g])
* G[i, 1 + 2 * l, m]
* G[j, 1 + 2 * l, n]
* αc[l][g]
)
/ ((G_e[n] - αc_e[l][g]) * (G_e[m] + αc_e[l][g]))
)
return result
@ -443,84 +472,203 @@ class CorrelationMatrix(Propagator):
for l, r, m, n in iterate_ragged(len(α_e), len(α0d), G.shape[2], G.shape[2]):
for g in range(len(α_e[l])):
result += (
G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* (
(
α[l][g]
* (
-(
(
(G_e[m] + G_e[n])
* (G_e[m] + α0d_e[r])
* (G_e[n] + α_e[l][g])
)
/ np.exp(t * (α0d_e[r] + α_e[l][g]))
)
+ (
(G_e[m] + G_e[n])
* (G_e[m] + α0d_e[r])
* (α0d_e[r] + α_e[l][g])
)
/ np.exp(t * (G_e[n] + α_e[l][g]))
+ (
(G_e[m] + G_e[n])
* (G_e[n] + α_e[l][g])
* (α0d_e[r] + α_e[l][g])
)
/ np.exp(t * (G_e[m] + α0d_e[r]))
- (
(G_e[m] + α0d_e[r])
* (G_e[n] + α_e[l][g])
* (α0d_e[r] + α_e[l][g])
)
/ np.exp(t * (G_e[m] + G_e[n]))
+ (G_e[n] - α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[m] + G_e[n] + α0d_e[r] + α_e[l][g])
)
)
/ (
(G_e[m] + G_e[n])
* (G_e[n] - α0d_e[r])
* (G_e[m] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
* (α0d_e[r] + α_e[l][g])
)
+ αc[l][g]
* (
-(
1
/ (
np.exp(t * (G_e[m] + G_e[n]))
* (G_e[m] + G_e[n])
* (G_e[n] - α0d_e[r])
* (G_e[n] - αc_e[l][g])
)
)
+ 1
/ (
np.exp(t * (G_e[m] + α0d_e[r]))
* (G_e[n] - α0d_e[r])
* (G_e[m] + α0d_e[r])
* (α0d_e[r] - αc_e[l][g])
)
+ 1
/ (
(G_e[m] + G_e[n])
* (G_e[m] + α0d_e[r])
* (G_e[m] + αc_e[l][g])
)
+ 1
/ (
np.exp(t * (G_e[m] + αc_e[l][g]))
* (G_e[n] - αc_e[l][g])
* (G_e[m] + αc_e[l][g])
* (-α0d_e[r] + αc_e[l][g])
)
)
(G[2 * u, 1 + 2 * l, m] * G[2 * u, 1 + 2 * l, n] * α0d[r] * α[l][g])
/ ((G_e[m] + G_e[n]) * (G_e[m] + α0d_e[r]) * (G_e[n] + α_e[l][g]))
- (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ ((G_e[m] + G_e[n]) * (G_e[m] + α0d_e[r]) * (G_e[n] + α_e[l][g]))
- (
np.exp(-(t * G_e[m]) - t * G_e[n])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ ((G_e[m] + G_e[n]) * (-G_e[n] + α0d_e[r]) * (G_e[n] + α_e[l][g]))
+ (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ ((G_e[m] + G_e[n]) * (-G_e[n] + α0d_e[r]) * (G_e[n] + α_e[l][g]))
- (
G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(G_e[m] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
)
+ (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(G_e[m] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
)
+ (
np.exp(-(t * G_e[m]) - t * G_e[n])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(-G_e[n] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
)
- (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(-G_e[n] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
)
- (
np.exp(-(t * G_e[n]) - t * α_e[l][g])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(-G_e[n] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
)
+ (
np.exp(-(t * α0d_e[r]) - t * α_e[l][g])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(-G_e[n] + α0d_e[r])
* (G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
)
+ (
G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
* (α0d_e[r] + α_e[l][g])
)
- (
np.exp(-(t * α0d_e[r]) - t * α_e[l][g])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* α[l][g]
)
/ (
(G_e[m] - α_e[l][g])
* (G_e[n] + α_e[l][g])
* (α0d_e[r] + α_e[l][g])
)
- (
G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ ((G_e[m] + G_e[n]) * (G_e[m] + α0d_e[r]) * (G_e[n] - αc_e[l][g]))
+ (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ ((G_e[m] + G_e[n]) * (G_e[m] + α0d_e[r]) * (G_e[n] - αc_e[l][g]))
+ (
np.exp(-(t * G_e[m]) - t * G_e[n])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ ((G_e[m] + G_e[n]) * (-G_e[n] + α0d_e[r]) * (G_e[n] - αc_e[l][g]))
- (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ ((G_e[m] + G_e[n]) * (-G_e[n] + α0d_e[r]) * (G_e[n] - αc_e[l][g]))
+ (
G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ (
(G_e[m] + α0d_e[r])
* (G_e[n] - αc_e[l][g])
* (G_e[m] + αc_e[l][g])
)
- (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ (
(G_e[m] + α0d_e[r])
* (G_e[n] - αc_e[l][g])
* (G_e[m] + αc_e[l][g])
)
+ (
np.exp(-(t * G_e[m]) - t * α0d_e[r])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ (
(G_e[n] - αc_e[l][g])
* (α0d_e[r] - αc_e[l][g])
* (G_e[m] + αc_e[l][g])
)
- (
np.exp(-(t * G_e[m]) - t * αc_e[l][g])
* G[2 * u, 1 + 2 * l, m]
* G[2 * u, 1 + 2 * l, n]
* α0d[r]
* αc[l][g]
)
/ (
(G_e[n] - αc_e[l][g])
* (α0d_e[r] - αc_e[l][g])
* (G_e[m] + αc_e[l][g])
)
)