After the previous post on TOTP tokens just now, let us get back to our discussion on CG method.
We were discussing the non-linear conjugate gradient method. CG could be used to find the minimum point of a quadratic form. It could also be used to minimize any continuous function for which the gradient can be computed. If we choose the residual as a negative gradient, we overcome the limitation that we cannot use a recursive formula for the residual. With the residual, we can use Gram Schmidt conjugation to find the search directions. This is the same as in the linear search. We find the step-length which is different from the linear case. This is difficult because we cannot do a line search. We have to approximate it by finding the minimum point of a quadratic form. We use the linear expression for the step length but we minimize the given function at the next step. Next to find the constants, we could use any method that finds the zero of the transpose of gradient at next step applied to the current search direction. Nonlinear CG can be preconditioned by choosing a pre-conditioner M that approximates the second derivative and has the property that M-inverse applied to residual is easy to compute. In the linear search, with the pre-conditioner, we could transform the quadratic form so that it is similar to a sphere. In a non-linear CG pre-conditioner performs this transformation for a region near the current position. We could use the diagonal as the pre-conditioner if the second derivative is too expensive to compute. However, this only works if we are close to the current position. Moreover, a pre-conditioner must be positive definite. Non-positive diagonal elements cannot be allowed. A conservative solution is to not pre-condition when the second derivative is not positive-definite.
#codingexercise
how do you minify and obfuscate the code with python ?
perhaps use pyminifier --obfuscate --pyz=/tmp/myprogram.pyz /tmp/program.py
or use BitBoost to fight reverse-engineering
Now with the previous code for TOTP tokens, we can have a script that can be distributed for each API caller to generate TOTP tokens for themselves.
#codingexercise
Convert hex to string:
'AD829C89031FD281'.decode('hex')
We were discussing the non-linear conjugate gradient method. CG could be used to find the minimum point of a quadratic form. It could also be used to minimize any continuous function for which the gradient can be computed. If we choose the residual as a negative gradient, we overcome the limitation that we cannot use a recursive formula for the residual. With the residual, we can use Gram Schmidt conjugation to find the search directions. This is the same as in the linear search. We find the step-length which is different from the linear case. This is difficult because we cannot do a line search. We have to approximate it by finding the minimum point of a quadratic form. We use the linear expression for the step length but we minimize the given function at the next step. Next to find the constants, we could use any method that finds the zero of the transpose of gradient at next step applied to the current search direction. Nonlinear CG can be preconditioned by choosing a pre-conditioner M that approximates the second derivative and has the property that M-inverse applied to residual is easy to compute. In the linear search, with the pre-conditioner, we could transform the quadratic form so that it is similar to a sphere. In a non-linear CG pre-conditioner performs this transformation for a region near the current position. We could use the diagonal as the pre-conditioner if the second derivative is too expensive to compute. However, this only works if we are close to the current position. Moreover, a pre-conditioner must be positive definite. Non-positive diagonal elements cannot be allowed. A conservative solution is to not pre-condition when the second derivative is not positive-definite.
#codingexercise
how do you minify and obfuscate the code with python ?
perhaps use pyminifier --obfuscate --pyz=/tmp/myprogram.pyz /tmp/program.py
or use BitBoost to fight reverse-engineering
Now with the previous code for TOTP tokens, we can have a script that can be distributed for each API caller to generate TOTP tokens for themselves.
#codingexercise
Convert hex to string:
'AD829C89031FD281'.decode('hex')
'\xad\x82\x9c\x89\x03\x1f\xd2\x81
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