# lanv2 - Man Page

lanv2: 2x2 Schur factor

## Synopsis

### Functions

subroutine **dlanv2** (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)**DLANV2** computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

subroutine **slanv2** (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)**SLANV2** computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

## Detailed Description

## Function Documentation

### subroutine dlanv2 (double precision a, double precision b, double precision c, double precision d, double precision rt1r, double precision rt1i, double precision rt2r, double precision rt2i, double precision cs, double precision sn)

**DLANV2** computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

**Purpose:**

DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form: [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ] [ C D ] [ SN CS ] [ CC DD ] [-SN CS ] where either 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex conjugate eigenvalues.

**Parameters***A*A is DOUBLE PRECISION

*B*B is DOUBLE PRECISION

*C*C is DOUBLE PRECISION

*D*D is DOUBLE PRECISION On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form.

*RT1R*RT1R is DOUBLE PRECISION

*RT1I*RT1I is DOUBLE PRECISION

*RT2R*RT2R is DOUBLE PRECISION

*RT2I*RT2I is DOUBLE PRECISION The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0.

*CS*CS is DOUBLE PRECISION

*SN*SN is DOUBLE PRECISION Parameters of the rotation matrix.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Modified by V. Sima, Research Institute for Informatics, Bucharest, Romania, to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that abs(RT1R) >= abs(RT2R).

Definition at line **126** of file **dlanv2.f**.

### subroutine slanv2 (real a, real b, real c, real d, real rt1r, real rt1i, real rt2r, real rt2i, real cs, real sn)

**SLANV2** computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

**Purpose:**

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form: [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ] [ C D ] [ SN CS ] [ CC DD ] [-SN CS ] where either 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex conjugate eigenvalues.

**Parameters***A*A is REAL

*B*B is REAL

*C*C is REAL

*D*D is REAL On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form.

*RT1R*RT1R is REAL

*RT1I*RT1I is REAL

*RT2R*RT2R is REAL

*RT2I*RT2I is REAL The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0.

*CS*CS is REAL

*SN*SN is REAL Parameters of the rotation matrix.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Modified by V. Sima, Research Institute for Informatics, Bucharest, Romania, to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that abs(RT1R) >= abs(RT2R).

Definition at line **126** of file **slanv2.f**.

## Author

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