NAG Library Routine Document

F06SMF (ZGERU)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

On entry: $m$, the number of rows of the matrix $A$.

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

2:     N – INTEGERInput

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

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

3:     ALPHA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

4:     X($*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the dimension of the array X must be at least $\max \left(1,1+\left(\mathbf{M}-1\right)\times \left|\mathbf{INCX}\right|\right)$.

On entry: the $m$ element vector $x$.

If $\mathbf{INCX}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{X}\left(1+\left(\mathit{i}–1\right)\times \mathbf{INCX}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{M}$.

If $\mathbf{INCX}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{X}\left(1–\left(\mathbf{M}–\mathit{i}\right)\times \mathbf{INCX}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{M}$.

Intermediate elements of X are not referenced.

5:     INCX – INTEGERInput

On entry: the increment in the subscripts of X between successive elements of $x$.

Constraint: $\mathbf{INCX}\ne 0$.

6:     Y($*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the dimension of the array Y must be at least $\max \left(1,1+\left(\mathbf{N}-1\right)\times \left|\mathbf{INCY}\right|\right)$.

On entry: the $n$-element vector $y$.

If $\mathbf{INCY}>0$, $y_{\mathit{i}}$ must be stored in $\mathbf{Y}\left(1+\left(\mathit{i}-1\right)\times \mathbf{INCY}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

If $\mathbf{INCY}<0$, $y_{\mathit{i}}$ must be stored in $\mathbf{Y}\left(1-\left(\mathbf{N}-\mathit{i}\right)\times \mathbf{INCY}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

Intermediate elements of Y are not referenced.

7:     INCY – INTEGERInput

On entry: the increment in the subscripts of Y between successive elements of $y$.

Constraint: $\mathbf{INCY}\ne 0$.

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

Note: the second dimension of the array A must be at least $\mathbf{N}$.

On entry: the $m$ by $n$ matrix $A$.

On exit: the updated matrix $A$.

9:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06SMF (ZGERU) is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example