NAG CL Interface
g13ecc (kalman_​sqrt_​filt_​info_​var)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

On entry: the actual state dimension, $n$, i.e., the order of the matrices $S_i$ and $A_i^{-1}$.

Constraint: $\mathbf{n}\ge 1$.

2: $\mathbf{m}$ – Integer Input

On entry: the actual input dimension, $m$, i.e., the order of the matrix $Q_i^{-1/2}$.

Constraint: $\mathbf{m}\ge 1$.

3: $\mathbf{p}$ – Integer Input

On entry: the actual output dimension, $p$, i.e., the order of the matrix $R_{i+1}^{-1/2}$.

Constraint: $\mathbf{p}\ge 1$.

4: $\mathbf{inp\_ab}$ – Nag_ab_input Input

On entry: indicates how the matrix $B_i$ is to be passed to the function.

$\mathbf{inp\_ab}=\mathrm{Nag\_ab\_prod}$

Array b must contain the product $A_i^{-1}{B}_i$.

$\mathbf{inp\_ab}=\mathrm{Nag\_ab\_sep}$

Then array b must contain $B_i$.

5: $\mathbf{t}\left[\mathbf{n}\times \mathbf{tdt}\right]$ – double Input/Output

Note: the $(i,j)$th element of the matrix $T$ is stored in $\mathbf{t}\left[(i-1)\times \mathbf{tdt}+j-1\right]$.

On entry: the leading $n\times n$ upper triangular part of this array must contain $S_i^{-1}$ the square root of the inverse of the state covariance matrix $P_{i\mid i}$.

On exit: the leading $n\times n$ upper triangular part of this array contains $S_{i+1}^{-1}$, the square root of the inverse of the of the state covariance matrix $P_{i+1\mid i+1}$.

6: $\mathbf{tdt}$ – Integer Input

On entry: the stride separating matrix column elements in the array t.

Constraint: $\mathbf{tdt}\ge \mathbf{n}$.

7: $\mathbf{ainv}\left[\mathbf{n}\times \mathbf{tda}\right]$ – const double Input

Note: the $(i,j)$th element of the matrix is stored in $\mathbf{ainv}\left[(i-1)\times \mathbf{tda}+j-1\right]$.

On entry: the leading $n\times n$ part of this array must contain $A_i^{-1}$ the inverse of the state transition matrix.

8: $\mathbf{tda}$ – Integer Input

On entry: the stride separating matrix column elements in the array ainv.

Constraint: $\mathbf{tda}\ge \mathbf{n}$.

9: $\mathbf{b}\left[\mathbf{n}\times \mathbf{tdb}\right]$ – const double Input

Note: the $(i,j)$th element of the matrix $B$ is stored in $\mathbf{b}\left[(i-1)\times \mathbf{tdb}+j-1\right]$.

On entry: the leading $n\times m$ part of this array must contain $B_i$ (if $\mathbf{inp\_ab}=\mathrm{Nag\_ab\_sep}$) or its product with $A_i^{-1}$ (if $\mathbf{inp\_ab}=\mathrm{Nag\_ab\_prod}$).

10: $\mathbf{tdb}$ – Integer Input

On entry: the stride separating matrix column elements in the array b.

Constraint: $\mathbf{tdb}\ge \mathbf{m}$.

11: $\mathbf{rinv}\left[\mathbf{p}\times \mathbf{tdr}\right]$ – const double Input

Note: the $(i,j)$th element of the matrix is stored in $\mathbf{rinv}\left[(i-1)\times \mathbf{tdr}+j-1\right]$.

On entry: if the measurement noise covariance matrix is to be supplied separately from the output weight matrix, then the leading $p\times p$ upper triangular part of this array must contain $R_{i+1}^{-1/2}$, the right Cholesky factor of the inverse of the measurement noise covariance matrix. If this information is not to be input separately from the output weight matrix (see below) then the array rinv must be set to NULL.

12: $\mathbf{tdr}$ – Integer Input

On entry: the stride separating matrix column elements in the array rinv.

Constraint: $\mathbf{tdr}\ge \mathbf{p}$ if rinv is defined.

13: $\mathbf{c}\left[\mathbf{p}\times \mathbf{tdc}\right]$ – const double Input

Note: the $(i,j)$th element of the matrix $C$ is stored in $\mathbf{c}\left[(i-1)\times \mathbf{tdc}+j-1\right]$.

On entry: if the array rinv has been set to NULL then the leading $p\times n$ part of this array must contain $C_{i+1}$, the output weight matrix (or its product with $R_{i+1}^{-1/2}$) of the discrete system at instant $i+1$.

14: $\mathbf{tdc}$ – Integer Input

On entry: the stride separating matrix column elements in the array c.

Constraint: $\mathbf{tdc}\ge \mathbf{n}$.

15: $\mathbf{qinv}\left[\mathbf{m}\times \mathbf{tdq}\right]$ – const double Input

Note: the $(i,j)$th element of the matrix is stored in $\mathbf{qinv}\left[(i-1)\times \mathbf{tdq}+j-1\right]$.

On entry: the leading $m\times m$ upper triangular part of this array must contain $Q_i^{-1/2}$ the right Cholesky factor of the inverse of the process noise covariance matrix.

16: $\mathbf{tdq}$ – Integer Input

On entry: the stride separating matrix column elements in the array qinv.

Constraint: $\mathbf{tdq}\ge \mathbf{m}$.

17: $\mathbf{x}\left[\mathbf{n}\right]$ – double Input/Output

On entry: this array must contain the estimated state ${\hat{X}}_{i\mid i}$

On exit: the estimated state ${\hat{X}}_{i+1\mid i+1}$.

18: $\mathbf{rinvy}\left[\mathbf{p}\right]$ – const double Input

On entry: this array must contain $R_{i+1}^{-1/2}{Y}_{i+1}$, the product of the upper triangular matrix $R_{i+1}^{-1/2}$ and the measured output $Y_{i+1}$.

19: $\mathbf{z}\left[\mathbf{m}\right]$ – const double Input

On entry: this array must contain ${\overline{w}}_i$, the mean value of the state process noise.

20: $\mathbf{tol}$ – double Input

On entry: tol is used to test for near singularity of the matrix $S_{i+1}^{-1}$. If you set tol to be less than $n^2\times \epsilon$ then the tolerance is taken as $n^2\times \epsilon$, where $\epsilon$ is the machine precision.

21: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{tda}=⟨\mathit{\text{value}}⟩$ while $\mathbf{n}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tda}\ge \mathbf{n}$.

On entry, $\mathbf{tdb}=⟨\mathit{\text{value}}⟩$ while $\mathbf{m}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tdb}\ge \mathbf{m}$.

On entry, $\mathbf{tdc}=⟨\mathit{\text{value}}⟩$ while $\mathbf{n}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tdc}\ge \mathbf{n}$.

On entry, $\mathbf{tdq}=⟨\mathit{\text{value}}⟩$ while $\mathbf{m}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tdq}\ge \mathbf{m}$.

On entry, $\mathbf{tdr}=⟨\mathit{\text{value}}⟩$ while $\mathbf{p}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tdr}\ge \mathbf{p}$.

On entry, $\mathbf{tdt}=⟨\mathit{\text{value}}⟩$ while $\mathbf{n}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tdt}\ge \mathbf{n}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument inp_ab had an illegal value.

NE_INT_ARG_LT

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}\ge 1$.

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 1$.

On entry, $\mathbf{p}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{p}\ge 1$.

NE_MAT_SINGULAR

The matrix inverse(S) is singular.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results