Hello, I am not sure what do you mean by "differentiate a matrix wrt to a vector", is it a sort of gradient? In any case, if you could express your aim through the standard partial derivatives of functions (which GiNaC can do) you will succeed. Best wishes, Vladimir -- Vladimir V. Kisil http://www.maths.leeds.ac.uk/~kisilv/ Book: Geometry of Mobius Maps https://doi.org/10.1142/p835 Soft: Geometry of cycles http://moebinv.sourceforge.net/ Jupyter notebooks: https://github.com/vvkisil/MoebInv-notebooks
On Wed, 3 Mar 2021 14:42:30 +0200, Orxan Shibliyev <orxan.shibli@gmail.com> said:
OSh> Suppose, I have a 5x5 matrix and I want to differentiate the OSh> matrix wrt to a 5x1 matrix in order to obtain a 3D matrix or OSh> tensor. In the following code, A.diff(uL); cannot compile. Is OSh> it possible to differentiate a matrix with symbolic elements OSh> wrt to a vector which also contains symbols? OSh> #include <iostream> #include <ginac/ginac.h> using namespace OSh> std; using namespace GiNaC; OSh> int main() { const int DIM = 5; OSh> symbol g("g"); OSh> symbol uL1("uL1"); symbol uL2("uL2"); symbol uL3("uL3"); OSh> symbol uL4("uL4"); symbol uL5("uL5"); OSh> matrix uL = { {uL1}, {uL2}, {uL3}, {uL4}, {uL5} }; OSh> auto qL = matrix(DIM, 1); OSh> qL(0,0) = sqrt(uL1); qL(1,0) = uL2 / qL(0,0); qL(2,0) = uL3 OSh> / qL(0,0); qL(3,0) = uL4 / qL(0,0); qL(4,0) = (uL5 + (g - 1) * OSh> (uL5 - 0.5 * (pow(uL2,2) + pow(uL3,2) + pow(uL4,2)) / uL1)) / OSh> uL1; OSh> symbol uR1("uR1"); symbol uR2("uR2"); symbol uR3("uR3"); OSh> symbol uR4("uR4"); symbol uR5("uR5"); OSh> matrix uR = { {uR1}, {uR2}, {uR3}, {uR4}, {uR5} }; OSh> auto qR = matrix(DIM, 1); OSh> qR(0,0) = sqrt(uR1); qR(1,0) = uR2 / qR(0,0); qR(2,0) = uR3 OSh> / qR(0,0); qR(3,0) = uR4 / qR(0,0); qR(4,0) = (uR5 + (g - 1) * OSh> (uR5 - 0.5 * (pow(uR2,2) + pow(uR3,2) + pow(uR4,2)) / uR1)) / OSh> uR1; OSh> auto q = qL.add(qR); q.mul_scalar(0.5); OSh> matrix B = { {2*q(0,0), 0, 0, 0, 0}, {q(1,0), q(0,0), 0, 0, OSh> 0}, {q(1,0), q(0,0), 0, 0, 0}, {q(2,0), 0, q(0,0), 0, 0}, OSh> {q(3,0), 0, 0, q(0,0), 0}, {q(4,0)/g, (g-1)*q(1,0)/g, OSh> (g-1)*q(2,0)/g, (g-1)*q(3,0)/g, q(0,0)/g} }; OSh> matrix C = { {q(1,0), q(0,0), 0, 0, 0}, {(g-1)*q(4,0)/g, OSh> (g+1)*q(1,0)/g, (1-g)*q(2,0)/g, (1-g)*q(3,0)/g, OSh> (g-1)*q(0,0)/g}, {0, q(2,0), q(1,0), 0, 0}, {0, q(3,0), 0, OSh> q(1,0), 0}, {0, q(4,0), 0, 0, q(1,0)} }; OSh> auto A = B.mul(C.inverse()); OSh> A.diff(uL); OSh> return 0; } OSh> ---------------------------------------------------- OSh> Alternatives: OSh> ---------------------------------------------------- OSh> _______________________________________________ GiNaC-list OSh> mailing list GiNaC-list@ginac.de OSh> https://www.ginac.de/mailman/listinfo/ginac-list