naginterfaces.library.blas.zrotgs

naginterfaces.library.blas.zrotgs(a, b)[source]

zrotgs generates a complex Givens plane rotation having real sine.

For full information please refer to the NAG Library document for f06cb

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06cbf.html

Parameters
acomplex

The value , the first element of the vector which determines the rotation.

bcomplex

The value , the second element of the vector which determines the rotation.

Returns
acomplex

The value .

bcomplex

The value , the tangent of the rotation.

ccomplex

The value , the cosine of the rotation.

sfloat

The value , the sine of the rotation.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

zrotgs generates a complex Givens plane rotation with parameters (complex) and (real), such that, given complex and :

If is real, then is also real. On exit, is overwritten by , the tangent of the rotation; and can be reconstructed from the single stored value , by a subsequent call to zcsgs().

If and , where is the machine precision, the function sets and .

If and , the function sets

Note that is always set to , unless overflow would occur, in which case the function returns the value of the complex expression

is the float value given by .