# 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.

## Detailed Description

## 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