Sparse Jacobian: Easy Driver
Keywords: sparse jacobian: easy driver Sparsejacobian syntax purpose f x p row col jac work color_method n_sweep vectorbase vectorset restrictions vectorsize uses forward example

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Sparse Jacobian: Easy Driver
Syntax
`jac = f.SparseJacobian(x)
jac = f.SparseJacobian(x, p)
n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work)
n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work)
`
Purpose
We use n for the domain size, and m for the range size of `f` . We use F : R n → R m do denote the AD function corresponding to `f` . The syntax above sets `jac` to the Jacobian jac = F ( 1 ) ( x ) This routine takes advantage of the sparsity of the Jacobian in order to reduce the amount of computation necessary. If `row` and `col` are present, it also takes advantage of the reduced set of elements of the Jacobian that need to be computed. One can use speed tests (e.g. speed_test ) to verify that results are computed faster than when using the routine Jacobian .
f
The object `f` has prototype `
ADFun<Base> f
` Note that the ADFun object `f` is not `const` (see Uses Forward below).
x
The argument `x` has prototype `
const VectorBase& x
` (see VectorBase below) and its size must be equal to `n` , the dimension of the domain space for `f` . It specifies that point at which to evaluate the Jacobian.
p
The argument `p` is optional and has prototype `
const VectorSet& p
` (see VectorSet below). If it has elements of type `bool`, its size is m * n . If it has elements of type `std::set<size_t>`, its size is m and all its set elements are between zero and n - 1 . It specifies a sparsity pattern for the Jacobian F ( 1 ) ( x ) . `
` If this sparsity pattern does not change between calls to `SparseJacobian` , it should be faster to calculate `p` once (using ForSparseJac or RevSparseJac ) and then pass `p` to `SparseJacobian` . Furthermore, if you specify `work` in the calling sequence, it is not necessary to keep the sparsity pattern; see the heading p under the `work` description. `
` In addition, if you specify `p` , CppAD will use the same type of sparsity representation (vectors of `bool` or vectors of `std::set<size_t>`) for its internal calculations. Otherwise, the representation for the internal calculations is unspecified.
row, col
The arguments `row` and `col` are optional and have prototype `
const VectorSize& row
const VectorSize& col
` (see VectorSize below). They specify which rows and columns of F ( 1 ) ( x ) are computes and in what order. Not all the non-zero entries in F ( 1 ) ( x ) need be computed, but all the entries specified by `row` and `col` must be possibly non-zero in the sparsity pattern. We use K to denote the value `jac.size()` which must also equal the size of `row` and `col` . Furthermore, for k = 0 , … , K -1 , it must hold that row [ k ] < m and col [ k ] < n .
jac
The result `jac` has prototype `
VectorBase& jac
` In the case where the arguments `row` and `col` are not present, the size of `jac` is m * n and for i = 0 , … , m -1 , j = 0 , … , n -1 , jac [ i * n + j ] = ∂ F i ∂ x j ( x ) `
` In the case where the arguments `row` and `col` are present, we use K to denote the size of `jac` . The input value of its elements does not matter. Upon return, for k = 0 , … , K - 1 , jac [ k ] = ∂ F i ∂ x j ( x ) , where i = row [ k ] and j = col [ k ]
work
If this argument is present, it has prototype `
sparse_jacobian_work& work
` This object can only be used with the routines `SparseJacobianForward` and `SparseJacobianReverse`. During its the first use, information is stored in `work` . This is used to reduce the work done by future calls to the same mode (forward or reverse), the same `f` , `p` , `row` , and `col` . If a future call is for a different mode, or any of these values have changed, you must first call `work.clear()` to inform CppAD that this information needs to be recomputed.
color_method
The coloring algorithm determines which columns (forward mode) or rows (reverse mode) can be computed during the same sweep. This field has prototype `

         std::string %work%.color_method

` and its default value (after a constructor or `clear()`) is `"cppad"`. If colpack_prefix is specified on the cmake command line, you can set this method to `"colpack"`. This value only matters on the first call to `sparse_jacobian` that follows the `work` constructor or a call to `work.clear()` .
p
If `work` is present, and it is not the first call after its construction or a clear, the sparsity pattern `p` is not used. This enables one to free the sparsity pattern and still compute corresponding sparse Jacobians.
n_sweep
The return value `n_sweep` has prototype `
size_t n_sweep
` If `SparseJacobianForward` (`SparseJacobianReverse`) is used, `n_sweep` is the number of first order forward (reverse) sweeps used to compute the requested Jacobian values. (This is also the number of colors determined by the coloring method mentioned above). This is proportional to the total work that `SparseJacobian` does, not counting the zero order forward sweep, or the work to combine multiple columns (rows) into a single sweep.
VectorBase
The type `VectorBase` must be a SimpleVector class with elements of type `Base` . The routine CheckSimpleVector will generate an error message if this is not the case.
VectorSet
The type `VectorSet` must be a SimpleVector class with elements of type `bool` or `std::set<size_t>`; see sparsity pattern for a discussion of the difference. The routine CheckSimpleVector will generate an error message if this is not the case.
Restrictions
If `VectorSet` has elements of `std::set<size_t>`, then `p[i]` must return a reference (not a copy) to the corresponding set. According to section 26.3.2.3 of the 1998 C++ standard, `std::valarray< std::set<size_t> >` does not satisfy this condition.
VectorSize
The type `VectorSize` must be a SimpleVector class with elements of type `size_t`. The routine CheckSimpleVector will generate an error message if this is not the case.
Uses Forward
After each call to Forward , the object `f` contains the corresponding Taylor coefficients . After a call to any of the sparse Jacobian routines, the zero order Taylor coefficients correspond to `f.Forward(0, x)` and the other coefficients are unspecified. After `SparseJacobian`, the previous calls to Forward are undefined.
Example
The routine sparse_jacobian.cpp is examples and tests of `sparse_jacobian`. It return `true`, if it succeeds and `false` otherwise.

Input File: cppad/local/sparse_jacobian.hpp