# drotg.f90 - Man Page

BLAS/SRC/drotg.f90

## Synopsis

### Functions/Subroutines

subroutine drotg (a, b, c, s)
DROTG

## Function/Subroutine Documentation

### subroutine drotg (real(wp) a, real(wp) b, real(wp) c, real(wp) s)

DROTG

Purpose:

``` DROTG constructs a plane rotation
[  c  s ] [ a ] = [ r ]
[ -s  c ] [ b ]   [ 0 ]
satisfying c**2 + s**2 = 1.

The computation uses the formulas
sigma = sgn(a)    if |a| >  |b|
= sgn(b)    if |b| >= |a|
r = sigma*sqrt( a**2 + b**2 )
c = 1; s = 0      if r = 0
c = a/r; s = b/r  if r != 0
The subroutine also computes
z = s    if |a| > |b|,
= 1/c  if |b| >= |a| and c != 0
= 1    if c = 0
This allows c and s to be reconstructed from z as follows:
If z = 1, set c = 0, s = 1.
If |z| < 1, set c = sqrt(1 - z**2) and s = z.
If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).```

lartg:          generate plane rotation, more accurate than BLAS rot,

lartgp:         generate plane rotation, more accurate than BLAS rot

Parameters

A

```          A is DOUBLE PRECISION
On entry, the scalar a.
On exit, the scalar r.```

B

```          B is DOUBLE PRECISION
On entry, the scalar b.
On exit, the scalar z.```

C

```          C is DOUBLE PRECISION
The scalar c.```

S

```          S is DOUBLE PRECISION
The scalar s.```
Author

Edward Anderson, Lockheed Martin

Contributors:

Weslley Pereira, University of Colorado Denver, USA

Further Details:

```  Anderson E. (2017)
Algorithm 978: Safe Scaling in the Level 1 BLAS
ACM Trans Math Softw 44:1--28
https://doi.org/10.1145/3061665```

Definition at line 91 of file drotg.f90.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page drotg(3) is an alias of drotg.f90(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK