Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
sparsediag should always give you at least 10 digits of accuracy. What inaccuracy are you talking about?
On 12 Jun 2014, at 00:09, epquinn@pks.mpg.de wrote:
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
I am taking numerical derivatives (acknowledging that it's not generally the best idea), and the data exhibits some peaks that look spurious. When I try to resolve them the errors in the values for the ground state energy become significant. My idea was that if I could control the accuracy of the ground state energy values I could determine whether the peaks are indeed there.
Related to the 10 digits of accuracy, the error becomes very noticeable in the second derivative of the data already for a step size of 0.001.
Best, Eoin
sparsediag should always give you at least 10 digits of accuracy. What inaccuracy are you talking about?
On 12 Jun 2014, at 00:09, epquinn@pks.mpg.de wrote:
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
Often it is not a good idea evaluate numerical derivatives with a too small step size, due to it amplifies the error on incremental quotients. It is better to evaluate it for several bigger values and then extrapolate the limit.
Best,
M
2014-06-12 13:25 GMT-03:00 epquinn@pks.mpg.de:
I am taking numerical derivatives (acknowledging that it's not generally the best idea), and the data exhibits some peaks that look spurious. When I try to resolve them the errors in the values for the ground state energy become significant. My idea was that if I could control the accuracy of the ground state energy values I could determine whether the peaks are indeed there.
Related to the 10 digits of accuracy, the error becomes very noticeable in the second derivative of the data already for a step size of 0.001.
Best, Eoin
sparsediag should always give you at least 10 digits of accuracy. What inaccuracy are you talking about?
On 12 Jun 2014, at 00:09, epquinn@pks.mpg.de wrote:
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
If you want to take second derivatives with step sizes of 1e-3, then indeed you immediately lose 6 digits and it is not surprising that you get errors on the 3rd digit (which is the 9th in the total energy). Just increase the step size to 1e-2.
On 12 Jun 2014, at 09:25, epquinn@pks.mpg.de wrote:
I am taking numerical derivatives (acknowledging that it's not generally the best idea), and the data exhibits some peaks that look spurious. When I try to resolve them the errors in the values for the ground state energy become significant. My idea was that if I could control the accuracy of the ground state energy values I could determine whether the peaks are indeed there.
Related to the 10 digits of accuracy, the error becomes very noticeable in the second derivative of the data already for a step size of 0.001.
Best, Eoin
sparsediag should always give you at least 10 digits of accuracy. What inaccuracy are you talking about?
On 12 Jun 2014, at 00:09, epquinn@pks.mpg.de wrote:
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
OK, thanks for the replies.
With best regards, Eoin
If you want to take second derivatives with step sizes of 1e-3, then indeed you immediately lose 6 digits and it is not surprising that you get errors on the 3rd digit (which is the 9th in the total energy). Just increase the step size to 1e-2.
On 12 Jun 2014, at 09:25, epquinn@pks.mpg.de wrote:
I am taking numerical derivatives (acknowledging that it's not generally the best idea), and the data exhibits some peaks that look spurious. When I try to resolve them the errors in the values for the ground state energy become significant. My idea was that if I could control the accuracy of the ground state energy values I could determine whether the peaks are indeed there.
Related to the 10 digits of accuracy, the error becomes very noticeable in the second derivative of the data already for a step size of 0.001.
Best, Eoin
sparsediag should always give you at least 10 digits of accuracy. What inaccuracy are you talking about?
On 12 Jun 2014, at 00:09, epquinn@pks.mpg.de wrote:
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin
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