quadratic function
I have used both linear least squares and radial basis functions as a proxy equation, calculated from the results of computer simulations which are calculating some objective function value based on a number of varied input parameters. As an alternative option I want to add a quadratic function so if there are parameters/variables x,y,z then rather than just having a linear function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to have the option not to include all the different second order terms. Where should I start looking? Thanks Brennan
On Thu, Oct 28, 2010 at 06:38, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
I have used both linear least squares and radial basis functions as a proxy equation, calculated from the results of computer simulations which are calculating some objective function value based on a number of varied input parameters.
As an alternative option I want to add a quadratic function so if there are parameters/variables x,y,z then rather than just having a linear function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to have the option not to include all the different second order terms.
A = np.column_stack([ np.ones_like(x), x, y, z, x*x, y*y, z*z, x*y, y*z, x*z, ]) x, res, rank, s = np.linalg.lstsq(A, f) -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco
On 29/10/2010 2:34 a.m., Robert Kern wrote:
On Thu, Oct 28, 2010 at 06:38, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
I have used both linear least squares and radial basis functions as a proxy equation, calculated from the results of computer simulations which are calculating some objective function value based on a number of varied input parameters.
As an alternative option I want to add a quadratic function so if there are parameters/variables x,y,z then rather than just having a linear function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to have the option not to include all the different second order terms. A = np.column_stack([ np.ones_like(x), x, y, z, x*x, y*y, z*z, x*y, y*z, x*z, ]) x, res, rank, s = np.linalg.lstsq(A, f)
OK, so in other words, you can use linalg.lstsq for whatever higher order terms you want to include or exclude. Very nice. Thanks. On a related topic I also use the Rbf radial basis function as a proxy equation. I have one set of data that it fails to return an Rbf for and I've just realised that in my set of simulations that are used to build the proxy equation I have some duplicate equations. I'm wondering if Rbf doesn't like duplicate points? It obviously doesn't affect linalg.lstsq. Brennan
On Thu, Oct 28, 2010 at 12:33, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
On 29/10/2010 2:34 a.m., Robert Kern wrote:
On Thu, Oct 28, 2010 at 06:38, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
I have used both linear least squares and radial basis functions as a proxy equation, calculated from the results of computer simulations which are calculating some objective function value based on a number of varied input parameters.
As an alternative option I want to add a quadratic function so if there are parameters/variables x,y,z then rather than just having a linear function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to have the option not to include all the different second order terms. A = np.column_stack([ np.ones_like(x), x, y, z, x*x, y*y, z*z, x*y, y*z, x*z, ]) x, res, rank, s = np.linalg.lstsq(A, f)
OK, so in other words, you can use linalg.lstsq for whatever higher order terms you want to include or exclude. Very nice. Thanks.
Right. Just as long as the problem is linear in the coefficients, the design matrix can be derived however you like.
On a related topic I also use the Rbf radial basis function as a proxy equation. I have one set of data that it fails to return an Rbf for and I've just realised that in my set of simulations that are used to build the proxy equation I have some duplicate equations. I'm wondering if Rbf doesn't like duplicate points? It obviously doesn't affect linalg.lstsq.
Rbf doesn't like duplicate points. :-) -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco
On 29/10/2010 6:35 a.m., Robert Kern wrote:
On Thu, Oct 28, 2010 at 12:33, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
On 29/10/2010 2:34 a.m., Robert Kern wrote:
On Thu, Oct 28, 2010 at 06:38, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
I have used both linear least squares and radial basis functions as a proxy equation, calculated from the results of computer simulations which are calculating some objective function value based on a number of varied input parameters.
As an alternative option I want to add a quadratic function so if there are parameters/variables x,y,z then rather than just having a linear function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to have the option not to include all the different second order terms. A = np.column_stack([ np.ones_like(x), x, y, z, x*x, y*y, z*z, x*y, y*z, x*z, ]) x, res, rank, s = np.linalg.lstsq(A, f)
OK, so in other words, you can use linalg.lstsq for whatever higher order terms you want to include or exclude. Very nice. Thanks. Right. Just as long as the problem is linear in the coefficients, the design matrix can be derived however you like.
So I could optionally put log terms in if I thought it was linear in log(x) for example?
On a related topic I also use the Rbf radial basis function as a proxy equation. I have one set of data that it fails to return an Rbf for and I've just realised that in my set of simulations that are used to build the proxy equation I have some duplicate equations. I'm wondering if Rbf doesn't like duplicate points? It obviously doesn't affect linalg.lstsq. Rbf doesn't like duplicate points. :-) OK, fair enough, I just need to add a bit of housekeeping to remove duplicate simulations. Thanks for the confirmation.
On Thu, Oct 28, 2010 at 12:47, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
On 29/10/2010 6:35 a.m., Robert Kern wrote:
On Thu, Oct 28, 2010 at 12:33, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
On 29/10/2010 2:34 a.m., Robert Kern wrote:
On Thu, Oct 28, 2010 at 06:38, Brennan Williams <brennan.williams@visualreservoir.com> wrote:
I have used both linear least squares and radial basis functions as a proxy equation, calculated from the results of computer simulations which are calculating some objective function value based on a number of varied input parameters.
As an alternative option I want to add a quadratic function so if there are parameters/variables x,y,z then rather than just having a linear function f=a+bx+cy+dz I'll have f=a+bx+cx**2 + dxy + .... I'd like to have the option not to include all the different second order terms. A = np.column_stack([ np.ones_like(x), x, y, z, x*x, y*y, z*z, x*y, y*z, x*z, ]) x, res, rank, s = np.linalg.lstsq(A, f)
OK, so in other words, you can use linalg.lstsq for whatever higher order terms you want to include or exclude. Very nice. Thanks. Right. Just as long as the problem is linear in the coefficients, the design matrix can be derived however you like.
So I could optionally put log terms in if I thought it was linear in log(x) for example?
Yup! -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco
participants (2)
-
Brennan Williams -
Robert Kern