void	f06smf_ (const Integer m, const Integer n, const Complex alpha, const Complex x[], const Integer incx, const Complex y[], const Integer incy, Complex a[], const Integer lda)

The routine may be called by the names f06smf, nagf_blas_zgeru or its BLAS name zgeru.

3 Description

f06smf performs the rank-1 update operation

A \leftarrow α x y^{T} + A,

where

A

is an

m \times n

complex matrix,

x

is an

m

element complex vector,

y

is an

n

-element complex vector, and

α

is a complex scalar.

4 References

None.

5 Arguments

1: $m$ – Integer Input: On entry: $m$ , the number of rows of the matrix $A$ .

Constraint: $m \geq 0$ .
2: $n$ – Integer Input: On entry: $n$ , the number of columns of the matrix $A$ .

Constraint: $n \geq 0$ .
3: $alpha$ – Complex (Kind=nag_wp) Input: On entry: the scalar $α$ .
4: $x (*)$ – Complex (Kind=nag_wp) array Input: Note: the dimension of the array x must be at least $\max (1, 1 + (m - 1) \times | incx |)$ .

On entry: the $m$ element vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x (1 + (i - 1) \times incx)$ , for $i = 1, 2, \dots, m$ .

If $incx < 0$ , $x_{i}$ must be stored in $x (1 - (m - i) \times incx)$ , for $i = 1, 2, \dots, m$ .

Intermediate elements of X are not referenced.
5: $incx$ – Integer Input: On entry: the increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx \neq 0$ .
6: $y (*)$ – Complex (Kind=nag_wp) array Input: Note: the dimension of the array y must be at least $\max (1, 1 + (n - 1) \times | incy |)$ .

On entry: the $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y (1 + (i - 1) \times incy)$ , for $i = 1, 2, \dots, n$ .

If $incy < 0$ , $y_{i}$ must be stored in $y (1 - (n - i) \times incy)$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of y are not referenced.
7: $incy$ – Integer Input: On entry: the increment in the subscripts of y between successive elements of $y$ .

Constraint: $incy \neq 0$ .
8: $a (lda, *)$ – Complex (Kind=nag_wp) array Input/Output: Note: the second dimension of the array a must be at least $n$ .

On entry: the $m \times n$ matrix $A$ .

On exit: the updated matrix $A$ .
9: $lda$ – Integer Input: On entry: the first dimension of the array a as declared in the (sub)program from which f06smf is called.

Constraint: $lda \geq \max (1, m)$ .