NAG Library Function Document

nag_regsn_mult_linear_tran_model (g02dkc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{ip}$ – IntegerInput

On entry: the number of terms in the linear model, $p$.

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

2:    $\mathbf{iconst}$ – IntegerInput

On entry: the number of constraints to be imposed on the arguments, $n_c$.

Constraint: $0<\mathbf{iconst}<\mathbf{ip}$.

3:    $\mathbf{p}\left[\mathbf{ip}\times \mathbf{ip}+2\times \mathbf{ip}\right]$ – const doubleInput

On entry: p as returned by nag_regsn_mult_linear (g02dac) and nag_regsn_mult_linear_upd_model (g02ddc).

4:    $\mathbf{c}\left[\mathbf{ip}\times \mathbf{tdc}\right]$ – const doubleInput

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

On entry: the iconst constraints stored by column, i.e., the $i$th constraint is stored in the $i$th column of c.

5:    $\mathbf{tdc}$ – IntegerInput

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

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

6:    $\mathbf{b}\left[\mathbf{ip}\right]$ – doubleInput/Output

On entry: the parameter estimates computed by using the singular value decomposition, ${\hat{\beta }}_{svd}$.

On exit: the parameter estimates of the arguments with the constraints imposed, ${\hat{\beta }}_c$.

7:    $\mathbf{rss}$ – doubleInput

On entry: the residual sum of squares as returned by nag_regsn_mult_linear (g02dac) or nag_regsn_mult_linear_upd_model (g02ddc).

Constraint: $\mathbf{rss}>0.0$.

8:    $\mathbf{df}$ – doubleInput

On entry: the degrees of freedom associated with the residual sum of squares as returned by nag_regsn_mult_linear (g02dac) or nag_regsn_mult_linear_upd_model (g02ddc).

Constraint: $\mathbf{df}>0.0$.

9:    $\mathbf{se}\left[\mathbf{ip}\right]$ – doubleOutput

On exit: the standard error of the parameter estimates in b.

10:  $\mathbf{cov}\left[\mathbf{ip}\times \left(\mathbf{ip}+1\right)/2\right]$ – doubleOutput

On exit: the upper triangular part of the variance-covariance matrix of the ip parameter estimates given in b. They are stored packed by column, i.e., the covariance between the parameter estimate given in $\mathbf{b}\left[\mathit{i}\right]$ and the parameter estimate given in $\mathbf{b}\left[\mathit{j}\right]$, $\mathit{j}\ge \mathit{i}$, is stored in $\mathbf{cov}\left[\mathit{j}\left(\mathit{j}+1\right)/2+\mathit{i}\right]$, for $\mathit{i}=0,1,\dots ,\mathbf{ip}-1$ and $\mathit{j}=\mathit{i},\dots ,\mathbf{ip}-1$.

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_GE

On entry, $\mathbf{iconst}=〈\mathit{\text{value}}〉$ while $\mathbf{ip}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{iconst}<\mathbf{ip}$.

NE_2_INT_ARG_LT

On entry, $\mathbf{tdc}=〈\mathit{\text{value}}〉$ while $\mathbf{iconst}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdc}\ge \mathbf{iconst}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LE

On entry, $\mathbf{iconst}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iconst}>0$.

NE_INT_ARG_LT

On entry, $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ip}\ge 1$.

NE_MAT_NOT_FULL_RANK

Matrix c does not give a model of full rank.

NE_REAL_ARG_LE

On entry, df must not be less than or equal to 0.0: $\mathbf{df}=〈\mathit{\text{value}}〉$.

On entry, rss must not be less than or equal to 0.0: $\mathbf{rss}=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g02dkce.c)

10.2

Program Data

Program Data (g02dkce.d)

10.3

Program Results

Program Results (g02dkce.r)