NAG Library Routine Document

F08ZPF (ZGGGLM)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

On entry: $m$, the number of rows of the matrices $A$ and $B$.

Constraint: $\mathbf{M}\ge 0$.

2:     N – INTEGERInput

On entry: $n$, the number of columns of the matrix $A$.

Constraint: $0\le \mathbf{N}\le \mathbf{M}$.

3:     P – INTEGERInput

On entry: $p$, the number of columns of the matrix $B$.

Constraint: $\mathbf{P}\ge \mathbf{M}-\mathbf{N}$.

4:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the $m$ by $n$ matrix $A$.

On exit: A is overwritten.

5:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F08ZPF (ZGGGLM) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{M}\right)$.

6:     B(LDB,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{P}\right)$.

On entry: the $m$ by $p$ matrix $B$.

On exit: B is overwritten.

7:     LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F08ZPF (ZGGGLM) is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{M}\right)$.

8:     D(M) – COMPLEX (KIND=nag_wp) arrayInput/Output

On entry: the left-hand side vector $d$ of the GLM equation.

On exit: D is overwritten.

9:     X(N) – COMPLEX (KIND=nag_wp) arrayOutput

On exit: the solution vector $x$ of the GLM problem.

10:   Y(P) – COMPLEX (KIND=nag_wp) arrayOutput

On exit: the solution vector $y$ of the GLM problem.

11:   WORK($\max \left(1,\mathbf{LWORK}\right)$) – COMPLEX (KIND=nag_wp) arrayWorkspace

On exit: if $\mathbf{INFO}=\mathbf{0}$, the real part of $\mathbf{WORK}\left(1\right)$ contains the minimum value of LWORK required for optimal performance.

12:   LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F08ZPF (ZGGGLM) is called.

If $\mathbf{LWORK}=-1$, a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.

Suggested value: for optimal performance, $\mathbf{LWORK}\ge \mathbf{N}+\min \left(\mathbf{M},\mathbf{P}\right)+\max \left(\mathbf{M},\mathbf{P}\right)\times \mathit{nb}$, where $\mathit{nb}$ is the optimal block size.

Constraint: $\mathbf{LWORK}\ge \max \left(1,\mathbf{M}+\mathbf{N}+\mathbf{P}\right)$ or $\mathbf{LWORK}=-1$.

13:   INFO – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{INFO}=1$

The upper triangular factor $R$ associated with $A$ in the generalized $RQ$ factorization of the pair $\left(A,B\right)$ is singular, so that $\mathrm{rank}\left(A\right)<m$; the least squares solution could not be computed.

$\mathbf{INFO}=2$

The bottom $\left(N-M\right)$ by $\left(N-M\right)$ part of the upper trapezoidal factor $T$ associated with $B$ in the generalized $QR$ factorization of the pair $\left(A,B\right)$ is singular, so that $\mathrm{rank}\left(\begin{array}{cc}A& B\end{array}\right)<N$; the least squares solutions could not be computed.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f08zpfe.f90)

9.2  Program Data

Program Data (f08zpfe.d)

9.3  Program Results

Program Results (f08zpfe.r)