Matrix Calculus
MatrixCalculus provides matrix calculus for everyone. It is an online tool that computes vector and matrix derivatives (matrix calculus).
derivative of
w.r.t.
\({}\)
where
- {{v.name}} is a
Export functions as
Common subexpressions
{{ctrl.service.error.msg}}
0.5*x'*A*x
A*exp(x)
sin(x)'*y
(y.*v)'*x
a^b
norm2(A*x-y)^2
sum(log(exp(-y.*(X*w)) + vector(1)))
tr(A*X'*B*X*C)
log(det(inv(X)))
- +
- addition
- -
- subtraction
- *
- multiplication
- /
- division
- ^
- power
- .*
- element-wise multiplication
- ./
- element-wise division
- .^
- element-wise power
- sin()
- element-wise sin
- cos()
- element-wise cos
- tan()
- element-wise tan
- arcsin()
- element-wise arcsin
- arccos()
- element-wise arccos
- arctan()
- element-wise arctan
- log()
- element-wise natural log
- exp()
- element-wise exp
- tanh()
- element-wise tanh
- abs()
- element-wise absolute value
- sign()
- element-wise sign
- relu()
- element-wise relu
- sum()
- sum of all entries
- norm1()
- element-wise 1-norm
- norm2()
- Frobenius norm
- tr()
- trace
- det()
- determinant
- inv()
- inverse
- sum()
- sum of all entries
- norm1()
- 1-norm
- norm2()
- Euclidean norm
- vector()
- constant vector
- matrix()
- constant matrix
Only scalars, vectors, and matrices are displayed as output. If the derivative is a higher order tensor it will be computed but it cannot be displayed in matrix notation. Sometimes higher order tensors are represented using Kronecker products. However, this can be ambiguous in some cases. Here, only in unambiguous cases the result is displayed using Kronecker products. The python code still works on the true higher order tensors.
If you are interested in solving optimization problems easily, you can check out the online tool geno-project.org.
Last updated February 2022.
Due to numerous requests, we have updated the layout convention! We use mixed layout now. For more details, please see the documentation.