# dlartg.f90 - Man Page

SRC/dlartg.f90

## Synopsis

### Functions/Subroutines

subroutine dlartg (f, g, c, s, r)
DLARTG generates a plane rotation with real cosine and real sine.

## Function/Subroutine Documentation

### subroutine dlartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)

DLARTG generates a plane rotation with real cosine and real sine.

Purpose:

``` DLARTG generates a plane rotation so that

[  C  S  ]  .  [ F ]  =  [ R ]
[ -S  C  ]     [ G ]     [ 0 ]

where C**2 + S**2 = 1.

The mathematical formulas used for C and S are
R = sign(F) * sqrt(F**2 + G**2)
C = F / R
S = G / R
Hence C >= 0. The algorithm used to compute these quantities
incorporates scaling to avoid overflow or underflow in computing the
square root of the sum of squares.

This version is discontinuous in R at F = 0 but it returns the same
C and S as ZLARTG for complex inputs (F,0) and (G,0).

This is a more accurate version of the BLAS1 routine DROTG,
with the following other differences:
F and G are unchanged on return.
If G=0, then C=1 and S=0.
If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
floating point operations (saves work in DBDSQR when
there are zeros on the diagonal).

Below, wp=>dp stands for double precision from LA_CONSTANTS module.```
Parameters

F

```          F is REAL(wp)
The first component of vector to be rotated.```

G

```          G is REAL(wp)
The second component of vector to be rotated.```

C

```          C is REAL(wp)
The cosine of the rotation.```

S

```          S is REAL(wp)
The sine of the rotation.```

R

```          R is REAL(wp)
The nonzero component of the rotated vector.```
Author

Edward Anderson, Lockheed Martin

Date

July 2016

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 110 of file dlartg.f90.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK