---
name: "lartgs"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/lartgs"
---

# lartgs(3)

lartgs: generate plane rotation for bidiag SVD

## NAME

lartgs - lartgs: generate plane rotation for bidiag SVD

## SYNOPSIS

### Functions

subroutine **dlartgs** (x, y, sigma, cs, sn)\
 **DLARTGS** generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.  subroutine **slartgs** (x, y, sigma, cs, sn)\
 **SLARTGS** generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

## Detailed Description

## Function Documentation

### subroutine dlartgs (double precision x, double precision y, double precision sigma, double precision cs, double precision sn)

**DLARTGS** generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

**Purpose:**

```
!>
!> DLARTGS generates a plane rotation designed to introduce a bulge in
!> Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
!> problem. X and Y are the top-row entries, and SIGMA is the shift.
!> The computed CS and SN define a plane rotation satisfying
!>
!>    [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],
!>    [ -SN  CS  ]     [    X * Y    ]     [ 0 ]
!>
!> with R nonnegative.  If X^2 - SIGMA and X * Y are 0, then the
!> rotation is by PI/2.
!>
```

**Parameters**

*X*

```
!>          X is DOUBLE PRECISION
!>          The (1,1) entry of an upper bidiagonal matrix.
!>
```

*Y*

```
!>          Y is DOUBLE PRECISION
!>          The (1,2) entry of an upper bidiagonal matrix.
!>
```

*SIGMA*

```
!>          SIGMA is DOUBLE PRECISION
!>          The shift.
!>
```

*CS*

```
!>          CS is DOUBLE PRECISION
!>          The cosine of the rotation.
!>
```

*SN*

```
!>          SN is DOUBLE PRECISION
!>          The sine of the rotation.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **89** of file **dlartgs.f**.

### subroutine slartgs (real x, real y, real sigma, real cs, real sn)

**SLARTGS** generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

**Purpose:**

```
!>
!> SLARTGS generates a plane rotation designed to introduce a bulge in
!> Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
!> problem. X and Y are the top-row entries, and SIGMA is the shift.
!> The computed CS and SN define a plane rotation satisfying
!>
!>    [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],
!>    [ -SN  CS  ]     [    X * Y    ]     [ 0 ]
!>
!> with R nonnegative.  If X^2 - SIGMA and X * Y are 0, then the
!> rotation is by PI/2.
!>
```

**Parameters**

*X*

```
!>          X is REAL
!>          The (1,1) entry of an upper bidiagonal matrix.
!>
```

*Y*

```
!>          Y is REAL
!>          The (1,2) entry of an upper bidiagonal matrix.
!>
```

*SIGMA*

```
!>          SIGMA is REAL
!>          The shift.
!>
```

*CS*

```
!>          CS is REAL
!>          The cosine of the rotation.
!>
```

*SN*

```
!>          SN is REAL
!>          The sine of the rotation.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **89** of file **slartgs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.