This section
describes and provides examples of two other useful gravlens
commands: findimg3
and findsrc.
Part I. findimg3 Command
The findimg3 command allows the user to obtain the image positions and magnifications produced by a number of various sources for a given lens model. This is extemely useful in obtaining the results of several different source positions for the same model. For example, we could find and compare the images produced by various source positions for the model used in Sections III and IV (a SIS lens with shear). We will make the same assumptions as those in Sections III and IV. Thus, the Einstein radius, or deflection angle, will be:
In this case we will use the sources positions:
We would establish the model using the same commands as those in Section III and IV as well; however, instead of using the findimg command, we use findimg3. The above source must be placed in a file which will be read by the findimg3 command. This input file will be set up to contain:
5
0.070 0.000
0.105 0.000
0.140 0.000
0.350 0.000
0.350 0.350
The first number indicates the number of source positions and the remaining lines provide the Cartesian coordinates for each.
The input file for the run will contain
startup 1 1
alpha 0.70 0 0 0 0 0.1 0 0 0 1
0 0 0 0 0 0 0 0 0 0
findimg3 <input file> <input file>
As before, we perform this run at the command prompt by entering:
> gravlens <file>
The results will be written to the output file specified in the findimg3 command. In this case it should contain:
7.000000e-002 0.000000e+000
# 5 images:
-2.020732e-005 -3.574718e-012 8.502403e-008
-3.500000e-001 5.313487e-001 -6.518694e+000
-6.998889e-001 -2.648949e-022 1.111464e+001
-3.500000e-001 -5.313487e-001 -6.518694e+000
8.554646e-001 -2.435950e-022 3.942950e+000
1.050000e-001 0.000000e+000
# 5 images:
-3.069898e-005 -4.044848e-014 8.942458e-008
-5.250000e-001 3.594529e-001 -1.424412e+001
-6.609935e-001 6.500279e-017 2.700747e+001
-5.250000e-001 -3.594529e-001 -1.424412e+001
8.943575e-001 1.998277e-014 3.500976e+000
1.400000e-001 0.000000e+000
# 3 images:
-4.167876e-005 -1.735578e-017 9.602622e-008
-6.220972e-001 1.914899e-022 -4.437312e+001
9.332500e-001 -4.139134e-024 3.174765e+000
3.500000e-001 0.000000e+000
# 3 images:
-1.334096e-004 1.608245e-015 2.423139e-007
-3.886888e-001 -5.015625e-020 -1.587069e+000
1.166600e+000 -2.726951e-014 2.222273e+000
3.500000e-001 3.500000e-001
# 3 images:
-2.003324e-004 -2.003554e-004 9.855972e-007
-1.378348e-001 -1.496193e-001 -4.043206e-001
1.048276e+000 6.555760e-001 2.228963e+000
Notice that as the source's distance from the lens increases, the number of images decreases. This is due to the fact that the source position is crossing the caustic that divides the areas of positions that produce differing amounts of images.
Part II. findsrc Commmand
The findsrc command essentially performs the reverse calculations of the above examples by finding the corresponding source and images produced given a certain image and model. This capability is very useful for more practical applications
For example, we can use this command to check the gravlens calculations from Section I and we setup the model using the same commands. However, rather than using the findimg command, we enter:
> findsrc -1.577168 -1.210594e-016
This should return:
findsrc results:
1.010001e+000 7.752510e-017 # source
# 2 images:
-1.577168e+000 -1.305127e-016 -5.914095e-001
2.587169e+000 1.985845e-016 1.591409e+000
This results different very slightly from the results obtained in Section I but this difference is very minute.
< SECTION
IVPart I. findimg3 Command
The findimg3 command allows the user to obtain the image positions and magnifications produced by a number of various sources for a given lens model. This is extemely useful in obtaining the results of several different source positions for the same model. For example, we could find and compare the images produced by various source positions for the model used in Sections III and IV (a SIS lens with shear). We will make the same assumptions as those in Sections III and IV. Thus, the Einstein radius, or deflection angle, will be:
In this case we will use the sources positions:
We would establish the model using the same commands as those in Section III and IV as well; however, instead of using the findimg command, we use findimg3. The above source must be placed in a file which will be read by the findimg3 command. This input file will be set up to contain:
5
0.070 0.000
0.105 0.000
0.140 0.000
0.350 0.000
0.350 0.350
The first number indicates the number of source positions and the remaining lines provide the Cartesian coordinates for each.
The input file for the run will contain
startup 1 1
alpha 0.70 0 0 0 0 0.1 0 0 0 1
0 0 0 0 0 0 0 0 0 0
findimg3 <input file> <input file>
As before, we perform this run at the command prompt by entering:
> gravlens <file>
The results will be written to the output file specified in the findimg3 command. In this case it should contain:
7.000000e-002 0.000000e+000
# 5 images:
-2.020732e-005 -3.574718e-012 8.502403e-008
-3.500000e-001 5.313487e-001 -6.518694e+000
-6.998889e-001 -2.648949e-022 1.111464e+001
-3.500000e-001 -5.313487e-001 -6.518694e+000
8.554646e-001 -2.435950e-022 3.942950e+000
1.050000e-001 0.000000e+000
# 5 images:
-3.069898e-005 -4.044848e-014 8.942458e-008
-5.250000e-001 3.594529e-001 -1.424412e+001
-6.609935e-001 6.500279e-017 2.700747e+001
-5.250000e-001 -3.594529e-001 -1.424412e+001
8.943575e-001 1.998277e-014 3.500976e+000
1.400000e-001 0.000000e+000
# 3 images:
-4.167876e-005 -1.735578e-017 9.602622e-008
-6.220972e-001 1.914899e-022 -4.437312e+001
9.332500e-001 -4.139134e-024 3.174765e+000
3.500000e-001 0.000000e+000
# 3 images:
-1.334096e-004 1.608245e-015 2.423139e-007
-3.886888e-001 -5.015625e-020 -1.587069e+000
1.166600e+000 -2.726951e-014 2.222273e+000
3.500000e-001 3.500000e-001
# 3 images:
-2.003324e-004 -2.003554e-004 9.855972e-007
-1.378348e-001 -1.496193e-001 -4.043206e-001
1.048276e+000 6.555760e-001 2.228963e+000
Notice that as the source's distance from the lens increases, the number of images decreases. This is due to the fact that the source position is crossing the caustic that divides the areas of positions that produce differing amounts of images.
Part II. findsrc Commmand
The findsrc command essentially performs the reverse calculations of the above examples by finding the corresponding source and images produced given a certain image and model. This capability is very useful for more practical applications
For example, we can use this command to check the gravlens calculations from Section I and we setup the model using the same commands. However, rather than using the findimg command, we enter:
> findsrc -1.577168 -1.210594e-016
This should return:
findsrc results:
1.010001e+000 7.752510e-017 # source
# 2 images:
-1.577168e+000 -1.305127e-016 -5.914095e-001
2.587169e+000 1.985845e-016 1.591409e+000
This results different very slightly from the results obtained in Section I but this difference is very minute.