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The Functions in QMGsurvey III
ATTENTION: This page is still under construction!
SeedRandom in advance recommended; Scans the chosen leaf via random curves.
Arguments
| Argument | Type | Description |
|---|---|---|
| X | MatConf(Dim,Nim) | a matrix configuration |
| x | Real(Dim) | an initial point in target space |
| delta | Real | a positive finite step length |
| nPrime | Int | the (positive) number of random curves |
| n | Int | the (positive) number of steps (initial point excluded) |
| m | Int | the (positive) number of intermediate steps (zero means no intermediate steps) |
| l | Int | a positive even integer, the effective dimension of the quantum manifold |
| leaf="TSleaf" | Str | the chosen leaf, can be "TSleaf", "QMleaf" or "GQMleaf". "TSleaf" is the hybrid leaf (using theta), "QMleaf" is the hybrid leaf using omega and "GQMleaf" is the hybrid leaf using omega and g |
cqmgScan is not parallelizable.
Output
The output is xsScan.
| Output | Type | Description |
|---|---|---|
| xsScan | Real(nPrime*n+1,Dim) | the points in the scan of the chosen leaf, xsScan(1) is the initial point x |
Description
cqmgScan constructs a scan of the chosen leaf through x. This is done via curves with random initial tangent vector and an initial point that is randomly chosen from the previously calculated points. Since random numbers are involved, it is recomended to seed a random state in advance to maintain reproducability. Compare to [1] section 3.3.
Example(s)
An example for the fuzzy sphere:
X=qmgXsu2[4];
l=2;
x={0,0,1};
delta={0.01};
nPrime=10;
n=1000;
m=3;
leaf="QMleaf";
SeedRandom[1];
cqmgScan[X,x,delta,nPrime,n,m,l,leaf]Constructs local coordinates for the chosen leaf.
Arguments
| Argument | Type | Description |
|---|---|---|
| X | MatConf(Dim,Nim) | a matrix configuration |
| x | Real(Dim) | an initial point in target space |
| delta | Real | a positive finite step length |
| n | Int | the (positive) number of steps (initial point excluded) |
| m | Int | the (positive) number of intermediate steps (zero means no intermediate steps) |
| l | Int | a positive even integer, the effective dimension of the quantum manifold |
| leaf="TSleaf" | Str | the chosen leaf, can be "TSleaf", "QMleaf" or "GQMleaf". "TSleaf" is the hybrid leaf (using theta), "QMleaf" is the hybrid leaf using omega and "GQMleaf" is the hybrid leaf using omega and g |
| calculateJaccobians=True | Bool | True: the Jaccobians are calculated; False: the Jaccobians are not calculated |
| epsilon=10^-8 | Real | the (positive) finite difference in the calculation of the Jaccobians |
cqmgCoordinates is not parallelizable.
Output
The output is {xssCoordinates,xssJaccobians} if calculateJaccobians=True; the output is {xssCoordinates} if calculateJaccobians=False.
| Output | Type | Description |
|---|---|---|
| xssCoordinates | Real(2*n+1,...l times...,2*n+1,Dim) | |
| xssJaccobians | Real(2*n+1,...l times...,2*n+1,l,Dim) |
Description
cqmgCoordinates
constructs a scan of the chosen leaf. This is done via curves with random initial tangent vector and an initial point that is randomly chosen from the previously calculated points. Since random numbers are involved, it is recomended to seed a random state in advance to maintain reproducability. Compare to [1] section 3.3.
Example(s)
An example for the fuzzy sphere:
X=qmgXsu2[4];
l=2;
x={0,0,1};
delta={0.01};
nPrime=10;
n=1000;
m=3;
leaf="QMleaf";
SeedRandom[1];
cqmgScan[X,x,delta,nPrime,n,m,l,leaf]For internal use; Initialzation function of cqmgPointInTileQ, cqmgPointsInTile, cqmgFindOptimalPointInTile and cqmgFilledTileQ; these perform important calculations in the context of tilings.
For internal use; Initialzation function of cqmgIntegrands; cqmgIntegrands calculates the integrands for integration over the chosen leaf.
Integrates over a given tile.
Integrates over a tiling.
Processes the output of cqmgIntegrateTiling in the context of quantization.
Preview of cqmgIntegrateTile; only calculates local coordinates.
Preview of cqmgIntegrateTiling; only calculates a covering with local coordinates.
Integrates custom functions over a tiling via the output of cqmgIntegrateTiling.
Initialization function of cqmgKaehlerCost; cqmgKaehlerCost calculates the Kähler cost for a given linear subspace of the tangent space.
Extraction function of cqmgKaehlerCost; cqmgKaehlerCost calculates the Kähler cost for a given linear subspace of the tangent space.
Simplified function built on cqmgKaehlerCost; calculates the Kähler cost for a given linear subspace of the tangent space.
Calculates the Kähler cost for the chosen leaf.
SeedRandom in advance recommended; calculates the Kähler cost for random subspaces.
Calculates the Poisson structure induced by omega in the form of theta for a given point.
SeedRandom in advance recommended; performs various checks that validate the quality of the semiclassical limit based on the output of cqmgIntegrateTiling.
SeedRandom in advance recommended; constructs a table with the most interesting output of cqmgQuantizationValidation.