NAG Library Function Document

nag_pls_orth_scores_pred (g02ldc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 2.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{ip}$ – IntegerInput

On entry: the number of predictor variables in the fitted model. ip must take the same value as that supplied to nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc) to fit the model.

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

3:    $\mathbf{my}$ – IntegerInput

On entry: the number of response variables in the fitted model. my must take the same value as that supplied to nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc) to fit the model.

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

4:    $\mathbf{orig}$ – Nag_EstimatesOptionInput

On entry: indicates how parameter estimates are supplied.

$\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$

Parameter estimates are for the original data.

$\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$

Parameter estimates are for the centred, and possibly scaled, data.

Constraint: $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$ or $\mathrm{Nag\_EstimatesOrig}$.

5:    $\mathbf{xbar}\left[\mathbf{ip}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, xbar must contain mean values of predictor variables in the model; otherwise xbar is not referenced.

6:    $\mathbf{ybar}\left[\mathbf{my}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, ybar must contain the mean value of each response variable in the model; otherwise ybar is not referenced.

7:    $\mathbf{iscale}$ – Nag_ScalePredictorInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, iscale must take the value supplied to either nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc); otherwise iscale is not referenced.

Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, $\mathbf{iscale}=\mathrm{Nag\_PredNoScale}$, $\mathrm{Nag\_PredStdScale}$ or $\mathrm{Nag\_PredUserScale}$.

8:    $\mathbf{xstd}\left[\mathbf{ip}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$ and $\mathbf{iscale}\ne \mathrm{Nag\_PredNoScale}$, xstd must contain the scalings of predictor variables in the model as returned from either nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc); otherwise xstd is not referenced.

9:    $\mathbf{ystd}\left[\mathbf{my}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$ and $\mathbf{iscale}\ne \mathrm{Nag\_PredNoScale}$, ystd must contain the scalings of response variables as returned from either nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc); otherwise ystd is not referenced.

10:  $\mathbf{b}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array b must be at least

• $\max \left(1,\mathbf{pdb}\times \mathbf{my}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{ip}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$;
• $\max \left(1,1+\mathbf{ip}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$.

The $\left(i,j\right)$th element of the matrix $B$ is stored in

• $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, b must contain the parameter estimate for the centred, and possibly scaled, data as returned by nag_pls_orth_scores_fit (g02lcc); otherwise b must contain the parameter estimates for the original data as returned by nag_pls_orth_scores_fit (g02lcc).

11:  $\mathbf{pdb}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$,
  • if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, $\mathbf{pdb}\ge \mathbf{ip}$;
  • if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{pdb}\ge 1+\mathbf{ip}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \mathbf{my}$.

12:  $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of observations in the test data $Z$.

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

13:  $\mathbf{mz}$ – IntegerInput

On entry: the number of available predictor variables in the test data.

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

14:  $\mathbf{isz}\left[\mathbf{mz}\right]$ – const IntegerInput

On entry: indicates which predictor variables are to be included in the model. Predictor variables included from z must be in the same order as those included in the fitted model.

If $\mathbf{isz}\left[\mathit{j}-1\right]=1$, the $\mathit{j}$th predictor variable is included in the model, for $\mathit{j}=1,2,\dots ,\mathbf{mz}$, otherwise $\mathbf{isz}\left[j-1\right]=0$.

Constraints:

• $\mathbf{isz}\left[\mathit{j}-1\right]=0\text{ or }1$, for $\mathit{j}=1,2,\dots ,\mathbf{mz}$;
• ${\sum }_j\mathbf{isz}\left[j-1\right]=\mathbf{ip}$.

15:  $\mathbf{z}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array z must be at least

• $\max \left(1,\mathbf{pdz}\times \mathbf{mz}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdz}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

Where $\mathbf{Z}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{z}\left[\left(j-1\right)\times \mathbf{pdz}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{z}\left[\left(i-1\right)\times \mathbf{pdz}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: $\mathbf{Z}\left(\mathit{i},\mathit{j}\right)$ contains the $\mathit{i}$th observation on the $\mathit{j}$th available predictor variable, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ and $\mathit{j}=1,2,\dots ,\mathbf{mz}$.

16:  $\mathbf{pdz}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array z.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdz}\ge \mathbf{n}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdz}\ge \mathbf{mz}$.

17:  $\mathbf{yhat}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array yhat must be at least

• $\max \left(1,\mathbf{pdyhat}\times \mathbf{my}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdyhat}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

Where $\mathbf{YHAT}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{yhat}\left[\left(j-1\right)\times \mathbf{pdyhat}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{yhat}\left[\left(i-1\right)\times \mathbf{pdyhat}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: $\mathbf{YHAT}\left(i,j\right)$ contains the $i$th predicted value of the $j$th $y$-variable in the model.

18:  $\mathbf{pdyhat}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array yhat.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdyhat}\ge \mathbf{n}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdyhat}\ge \mathbf{my}$.

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

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_CHARACTER

On entry, $\mathbf{iscale}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, $\mathbf{iscale}=\mathrm{Nag\_PredNoScale}$, $\mathrm{Nag\_PredStdScale}$ or $\mathrm{Nag\_PredUserScale}$.

NE_INT

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

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

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

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

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

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

NE_INT_2

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

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}+1=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{pdb}\ge 1+\mathbf{ip}$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$, $\mathbf{pdb}\ge \mathbf{ip}$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \mathbf{my}$.

On entry, $\mathbf{pdyhat}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdyhat}\ge \mathbf{my}$.

On entry, $\mathbf{pdyhat}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdyhat}\ge \mathbf{n}$.

On entry, $\mathbf{pdz}=〈\mathit{\text{value}}〉$ and $\mathbf{mz}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdz}\ge \mathbf{mz}$.

On entry, $\mathbf{pdz}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdz}\ge \mathbf{n}$.

NE_INT_ARG_CONS

On entry, the number of elements of isz equal to $1$ is not ip.

NE_INT_ARRAY_VAL_1_OR_2

On entry, $\mathbf{isz}\left[j-1\right]=〈\mathit{\text{value}}〉$, $j=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{isz}\left[j-1\right]=0\text{ or }1$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g02ldce.c)

10.2  Program Data

Program Data (g02ldce.d)

10.3  Program Results

Program Results (g02ldce.r)