# las2 - Man Page

las2: 2x2 triangular SVD

## Synopsis

### Functions

subroutine dlas2 (f, g, h, ssmin, ssmax)
DLAS2 computes singular values of a 2-by-2 triangular matrix.
subroutine slas2 (f, g, h, ssmin, ssmax)
SLAS2 computes singular values of a 2-by-2 triangular matrix.

## Function Documentation

### subroutine dlas2 (double precision f, double precision g, double precision h, double precision ssmin, double precision ssmax)

DLAS2 computes singular values of a 2-by-2 triangular matrix.

Purpose:

``` DLAS2  computes the singular values of the 2-by-2 matrix
[  F   G  ]
[  0   H  ].
On return, SSMIN is the smaller singular value and SSMAX is the
larger singular value.```
Parameters

F

```          F is DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.```

G

```          G is DOUBLE PRECISION
The (1,2) element of the 2-by-2 matrix.```

H

```          H is DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.```

SSMIN

```          SSMIN is DOUBLE PRECISION
The smaller singular value.```

SSMAX

```          SSMAX is DOUBLE PRECISION
The larger singular value.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

```  Barring over/underflow, all output quantities are correct to within
a few units in the last place (ulps), even in the absence of a guard
digit in addition/subtraction.

In IEEE arithmetic, the code works correctly if one matrix element is
infinite.

Overflow will not occur unless the largest singular value itself
overflows, or is within a few ulps of overflow.

Underflow is harmless if underflow is gradual. Otherwise, results
may correspond to a matrix modified by perturbations of size near
the underflow threshold.```

Definition at line 104 of file dlas2.f.

### subroutine slas2 (real f, real g, real h, real ssmin, real ssmax)

SLAS2 computes singular values of a 2-by-2 triangular matrix.

Purpose:

``` SLAS2  computes the singular values of the 2-by-2 matrix
[  F   G  ]
[  0   H  ].
On return, SSMIN is the smaller singular value and SSMAX is the
larger singular value.```
Parameters

F

```          F is REAL
The (1,1) element of the 2-by-2 matrix.```

G

```          G is REAL
The (1,2) element of the 2-by-2 matrix.```

H

```          H is REAL
The (2,2) element of the 2-by-2 matrix.```

SSMIN

```          SSMIN is REAL
The smaller singular value.```

SSMAX

```          SSMAX is REAL
The larger singular value.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

```  Barring over/underflow, all output quantities are correct to within
a few units in the last place (ulps), even in the absence of a guard
digit in addition/subtraction.

In IEEE arithmetic, the code works correctly if one matrix element is
infinite.

Overflow will not occur unless the largest singular value itself
overflows, or is within a few ulps of overflow.

Underflow is harmless if underflow is gradual. Otherwise, results
may correspond to a matrix modified by perturbations of size near
the underflow threshold.```

Definition at line 104 of file slas2.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK