> >]
beta = sqrt(numext::abs2(c0) + tailSqNorm);
```
Any idea why the `AutoDiffScalar` type here is taking a `CwiseBinaryOp` template parameter? And it looks like that binary op’s defined over vectors.
---
### Author:  [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)
#### Post date: [March 29, 2019, 7:52pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/7 "2019-03-29T19:52:51Z")
I think that is because the forward mode derivatives are being held in a vector (of `var` in this case).
---
### Author:  [@Bob\_Carpenter](https://discourse.mc-stan.org/u/Bob_Carpenter)
#### Post date: [March 29, 2019, 8:19pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/8 "2019-03-29T20:19:32Z")
It’d be interesting to see if it’s our `var` messing it up or if this would work with `double` in place of `stan::math::var`. It doesn’t look like a Stan problem. It looks like `sqrt` isn’t defined for this `AutodiffScalar` type.
---
### Author:  [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)
#### Post date: [March 29, 2019, 9:07pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/9 "2019-03-29T21:07:29Z")
This double-version compiles (and runs and does not crash)
```
// [[Rcpp::depends(BH)]]
// [[Rcpp::depends(RcppEigen)]]
// [[Rcpp::depends(StanHeaders)]]
#include
#include
#include
#include
#include
// [[Rcpp::export]]
Eigen::MatrixXd test_Jacobian(Eigen::MatrixXd A) {
typedef Eigen::AutoDiffScalar ADScalar;
typedef Eigen::Matrix ADMatrix;
ADMatrix A_(A.rows(), A.cols());
const int derivative_num = A.size();
int derivative_idx = 0;
for (int i = 0; i < A.size(); i++) {
A_(i).value() = A(i);
A_(i).derivatives() =
Eigen::VectorXd::Unit(derivative_num, derivative_idx);
derivative_idx++;
}
ADMatrix U = A_.fullPivHouseholderQr().matrixQ();
stan::math::matrix_d J(derivative_num, derivative_num);
int pos = 0;
for (int i = 0; i < A.rows(); i++) for (int j = 0; j < A.cols(); j++) {
J.col(pos++) = U(i, j).derivatives();
}
return J;
}
```
while the `var` version does not compile
```
// [[Rcpp::depends(BH)]]
// [[Rcpp::depends(RcppEigen)]]
// [[Rcpp::depends(StanHeaders)]]
#include
#include
#include
#include
#include
// [[Rcpp::export]]
std::vector test_Jacobian(Eigen::MatrixXd A) {
typedef Eigen::AutoDiffScalar ADScalar;
typedef Eigen::Matrix ADMatrix;
ADMatrix A_(A.rows(), A.cols());
std::vector theta;
std::vector gradient;
const int derivative_num = A.size();
int derivative_idx = 0;
for (int i = 0; i < A.size(); i++) {
theta.push_back(stan::math::to_var(A(i)));
A_(i).value() = theta.back();
A_(i).value() = A(i);
A_(i).derivatives() =
Eigen::VectorXd::Unit(derivative_num, derivative_idx);
derivative_idx++;
}
ADMatrix Q = A_.fullPivHouseholderQr().matrixQ();
stan::math::matrix_v J(derivative_num, derivative_num);
int pos = 0;
for (int i = 0; i < A.rows(); i++) for (int j = 0; j < A.cols(); j++) {
J.col(pos++) = Q(i, j).derivatives();
}
stan::math::var log_abs_det_J = stan::math::log_determinant(J);
log_abs_det_J.grad(theta, gradient);
return gradient;
}
```
due to the `sqrt` thing
```
In file included from /home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math.hpp:4:
In file included from /home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/rev/mat.hpp:11:
In file included from /home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/rev/mat/vectorize/apply_scalar_unary.hpp:4:
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/prim/mat/vectorize/apply_scalar_unary.hpp:39:37: error: implicit instantiation of undefined template
'Eigen::internal::traits, const Eigen::Matrix, const Eigen::Matrix > > >'
typedef typename Eigen::internal::traits::Scalar scalar_t;
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/prim/mat/fun/sqrt.hpp:31:17: note: in instantiation of template class
'stan::math::apply_scalar_unary, const
Eigen::Matrix, const Eigen::Matrix > > >' requested here
inline typename apply_scalar_unary::return_t sqrt(const T& x) {
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/Householder/Householder.h:88:12: note: while substituting deduced template arguments into function template 'sqrt'
[with T = Eigen::AutoDiffScalar, const Eigen::Matrix, const
Eigen::Matrix > >]
beta = sqrt(numext::abs2(c0) + tailSqNorm);
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/Householder/Householder.h:45:3: note: in instantiation of function template specialization
'Eigen::MatrixBase >, -1, -1, 0, -1, -1>, -1, 1, true>, -1, 1, false>
>::makeHouseholder >, -1, -1, 0, -1, -1>, -1, 1,
true>, -1, 1, false>, -1> >' requested here
makeHouseholder(essentialPart, tau, beta);
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/QR/FullPivHouseholderQR.h:521:30: note: in instantiation of member function
'Eigen::MatrixBase >, -1, -1, 0, -1, -1>, -1, 1, true>, -1, 1, false>
>::makeHouseholderInPlace' requested here
m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/QR/FullPivHouseholderQR.h:452:3: note: in instantiation of member function
'Eigen::FullPivHouseholderQR >, -1, -1, 0, -1, -1> >::computeInPlace' requested here
computeInPlace();
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/QR/FullPivHouseholderQR.h:136:7: note: in instantiation of function template specialization
'Eigen::FullPivHouseholderQR >, -1, -1, 0, -1, -1>
>::compute >, -1, -1, 0, -1, -1> >' requested here
compute(matrix.derived());
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/QR/FullPivHouseholderQR.h:671:10: note: in instantiation of function template specialization
'Eigen::FullPivHouseholderQR >, -1, -1, 0, -1, -1>
>::FullPivHouseholderQR >, -1, -1, 0, -1, -1> >' requested here
return FullPivHouseholderQR(eval());
^
testJ2.cpp:27:19: note: in instantiation of member function 'Eigen::MatrixBase >, -1, -1, 0, -1, -1>
>::fullPivHouseholderQr' requested here
ADMatrix Q = A_.fullPivHouseholderQr().matrixQ();
^
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/RcppEigen/include/Eigen/src/Core/util/ForwardDeclarations.h:17:29: note: template is declared here
template struct traits;
^
In file included from testJ2.cpp:4:
In file included from /home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math.hpp:4:
In file included from /home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/rev/mat.hpp:11:
In file included from /home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/rev/mat/vectorize/apply_scalar_unary.hpp:4:
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/prim/mat/vectorize/apply_scalar_unary.hpp:45:38: error: no member named 'RowsAtCompileTime' in
'Eigen::AutoDiffScalar, const Eigen::Matrix, const
Eigen::Matrix > >'
typedef Eigen::Matrix
~~~^
2 errors generated.
make: *** [testJ2.o] Error 1
```
---
### Author:  [@Bob\_Carpenter](https://discourse.mc-stan.org/u/Bob_Carpenter)
#### Post date: [April 27, 2019, 4:18pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/10 "2019-04-27T16:18:50Z")
> [@bgoodri](#):
>
> due to the `sqrt` thing
It looks like you should be including our `sqrt` through `stan/math.hpp`.
What is `Eigen::AutoDiffScalar` and how doid that get involved here:
```no-highlight
/home/ben/R/x86_64-pc-linux-gnu-library/3.3/StanHeaders/include/stan/math/prim/mat/fun/sqrt.hpp:31:17: note: in instantiation of template class
'stan::math::apply_scalar_unary, const
Eigen::Matrix, const Eigen::Matrix > > >' requested here
inline typename apply_scalar_unary::return_t sqrt(const T& x) {
^
```
It looks like it’s trying to instantiate `sqrt(T)` with `T = Eigen::AutoDiffScalar>`.
To make this work, that’s going to have to be defined.
---
### Author:  [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)
#### Post date: [April 27, 2019, 4:50pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/11 "2019-04-27T16:50:19Z")
That may be true, but if we have to add a define `sqrt` and every function like it, then it just becomes yet another partially complete forward mode autodiff implementation. And it isn’t something we can expect users to do when they define external C++ functions.
But I don’t think it should be the case that
- Differentiating works if we `typedef Eigen::AutoDiffScalar ADScalar;`
- Differenatiating also works if we `typedef Eigen::AutoDiffScalar ADScalar;` as long as we only use `+`, `-`, `*`, and `/`
- But it does compile anymore if we use C++ math functions like `sqrt`
---
### Author:  [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)
#### Post date: [April 27, 2019, 5:46pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/12 "2019-04-27T17:46:24Z")
Moreover, I can get it to compile if I don’t `#include ` and instead `#include `
```
// [[Rcpp::depends(BH)]]
// [[Rcpp::depends(RcppEigen)]]
// [[Rcpp::depends(StanHeaders)]]
#include
#include
#include
#include
#include
// [[Rcpp::export]]
std::vector test_Jacobian(Eigen::MatrixXd A) {
typedef Eigen::Matrix vector_v;
typedef Eigen::Matrix
matrix_v;
typedef Eigen::AutoDiffScalar ADScalar;
typedef Eigen::Matrix ADMatrix;
ADMatrix A_(A.rows(), A.cols());
std::vector theta;
std::vector gradient;
const int derivative_num = A.size();
int derivative_idx = 0;
for (int i = 0; i < A.size(); i++) {
theta.push_back(stan::math::to_var(A(i)));
A_(i).value() = theta.back();
A_(i).value() = A(i);
A_(i).derivatives() =
Eigen::VectorXd::Unit(derivative_num, derivative_idx);
derivative_idx++;
}
ADMatrix Q = A_.householderQr().householderQ();
matrix_v J(derivative_num, derivative_num);
int pos = 0;
for (int i = 0; i < A.rows(); i++) for (int j = 0; j < A.cols(); j++) {
J.col(pos++) = Q(i, j).derivatives();
}
stan::math::var y = J(0, 0);
y.grad(theta, gradient);
return gradient;
}
```
---
### Author:  [@Bob\_Carpenter](https://discourse.mc-stan.org/u/Bob_Carpenter)
#### Post date: [April 29, 2019, 6:35pm UTC](https://discourse.mc-stan.org/t/am-i-leaking-eigen-autodiff/8103/13 "2019-04-29T18:35:15Z")
> [@bgoodri](#):
>
> I can get it to compile if I don’t `#include ` and instead `#include `
`rev/arr.hpp` is the header that doesn’t include Eigen. So it sounds like maybe there’s some kind of interference of definitions somewhere.