NAG Library Function Document

nag_pls_orth_scores_pred (g02ldc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     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:     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:     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:     xbar[ip] – 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:     ybar[my] – 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:     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:     xstd[ip] – 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:     ystd[my] – 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:   b[$\mathit{dim}$] – 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:   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:   n – IntegerInput

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

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

13:   mz – IntegerInput

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

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

14:   isz[mz] – 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:   z[$\mathit{dim}$] – 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:   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:   yhat[$\mathit{dim}$] – 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:   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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g02ldce.c)

9.2  Program Data

Program Data (g02ldce.d)

9.3  Program Results

Program Results (g02ldce.r)