# lags2 - Man Page

lags2: 2x2 orthogonal factor, step in tgsja

## Synopsis

### Functions

subroutine clags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
CLAGS2
subroutine dlags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.
subroutine slags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.
subroutine zlags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
ZLAGS2

## Function Documentation

### subroutine clags2 (logical upper, real a1, complex a2, real a3, real b1, complex b2, real b3, real csu, complex snu, real csv, complex snv, real csq, complex snq)

CLAGS2

Purpose:

``` CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
that if ( UPPER ) then

U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
( 0  A3 )     ( x  x  )
and
V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
( 0  B3 )     ( x  x  )

or if ( .NOT.UPPER ) then

U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
( A2 A3 )     ( 0  x  )
and
V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
( B2 B3 )     ( 0  x  )
where

U = (   CSU    SNU ), V = (  CSV    SNV ),
( -SNU**H  CSU )      ( -SNV**H CSV )

Q = (   CSQ    SNQ )
( -SNQ**H  CSQ )

The rows of the transformed A and B are parallel. Moreover, if the
input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
of A is not zero. If the input matrices A and B are both not zero,
then the transformed (2,2) element of B is not zero, except when the
first rows of input A and B are parallel and the second rows are
zero.```
Parameters

UPPER

```          UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.```

A1

`          A1 is REAL`

A2

`          A2 is COMPLEX`

A3

```          A3 is REAL
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.```

B1

`          B1 is REAL`

B2

`          B2 is COMPLEX`

B3

```          B3 is REAL
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.```

CSU

`          CSU is REAL`

SNU

```          SNU is COMPLEX
The desired unitary matrix U.```

CSV

`          CSV is REAL`

SNV

```          SNV is COMPLEX
The desired unitary matrix V.```

CSQ

`          CSQ is REAL`

SNQ

```          SNQ is COMPLEX
The desired unitary matrix Q.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 156 of file clags2.f.

### subroutine dlags2 (logical upper, double precision a1, double precision a2, double precision a3, double precision b1, double precision b2, double precision b3, double precision csu, double precision snu, double precision csv, double precision snv, double precision csq, double precision snq)

DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.

Purpose:

``` DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
that if ( UPPER ) then

U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
( 0  A3 )     ( x  x  )
and
V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
( 0  B3 )     ( x  x  )

or if ( .NOT.UPPER ) then

U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
( A2 A3 )     ( 0  x  )
and
V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
( B2 B3 )     ( 0  x  )

The rows of the transformed A and B are parallel, where

U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )

Z**T denotes the transpose of Z.```
Parameters

UPPER

```          UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.```

A1

`          A1 is DOUBLE PRECISION`

A2

`          A2 is DOUBLE PRECISION`

A3

```          A3 is DOUBLE PRECISION
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.```

B1

`          B1 is DOUBLE PRECISION`

B2

`          B2 is DOUBLE PRECISION`

B3

```          B3 is DOUBLE PRECISION
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.```

CSU

`          CSU is DOUBLE PRECISION`

SNU

```          SNU is DOUBLE PRECISION
The desired orthogonal matrix U.```

CSV

`          CSV is DOUBLE PRECISION`

SNV

```          SNV is DOUBLE PRECISION
The desired orthogonal matrix V.```

CSQ

`          CSQ is DOUBLE PRECISION`

SNQ

```          SNQ is DOUBLE PRECISION
The desired orthogonal matrix Q.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 150 of file dlags2.f.

### subroutine slags2 (logical upper, real a1, real a2, real a3, real b1, real b2, real b3, real csu, real snu, real csv, real snv, real csq, real snq)

SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.

Purpose:

``` SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
that if ( UPPER ) then

U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
( 0  A3 )     ( x  x  )
and
V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
( 0  B3 )     ( x  x  )

or if ( .NOT.UPPER ) then

U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
( A2 A3 )     ( 0  x  )
and
V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
( B2 B3 )     ( 0  x  )

The rows of the transformed A and B are parallel, where

U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )

Z**T denotes the transpose of Z.```
Parameters

UPPER

```          UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.```

A1

`          A1 is REAL`

A2

`          A2 is REAL`

A3

```          A3 is REAL
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.```

B1

`          B1 is REAL`

B2

`          B2 is REAL`

B3

```          B3 is REAL
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.```

CSU

`          CSU is REAL`

SNU

```          SNU is REAL
The desired orthogonal matrix U.```

CSV

`          CSV is REAL`

SNV

```          SNV is REAL
The desired orthogonal matrix V.```

CSQ

`          CSQ is REAL`

SNQ

```          SNQ is REAL
The desired orthogonal matrix Q.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 150 of file slags2.f.

### subroutine zlags2 (logical upper, double precision a1, complex*16 a2, double precision a3, double precision b1, complex*16 b2, double precision b3, double precision csu, complex*16 snu, double precision csv, complex*16 snv, double precision csq, complex*16 snq)

ZLAGS2

Purpose:

``` ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
that if ( UPPER ) then

U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
( 0  A3 )     ( x  x  )
and
V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
( 0  B3 )     ( x  x  )

or if ( .NOT.UPPER ) then

U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
( A2 A3 )     ( 0  x  )
and
V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
( B2 B3 )     ( 0  x  )
where

U = (   CSU    SNU ), V = (  CSV    SNV ),
( -SNU**H  CSU )      ( -SNV**H CSV )

Q = (   CSQ    SNQ )
( -SNQ**H  CSQ )

The rows of the transformed A and B are parallel. Moreover, if the
input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
of A is not zero. If the input matrices A and B are both not zero,
then the transformed (2,2) element of B is not zero, except when the
first rows of input A and B are parallel and the second rows are
zero.```
Parameters

UPPER

```          UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.```

A1

`          A1 is DOUBLE PRECISION`

A2

`          A2 is COMPLEX*16`

A3

```          A3 is DOUBLE PRECISION
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.```

B1

`          B1 is DOUBLE PRECISION`

B2

`          B2 is COMPLEX*16`

B3

```          B3 is DOUBLE PRECISION
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.```

CSU

`          CSU is DOUBLE PRECISION`

SNU

```          SNU is COMPLEX*16
The desired unitary matrix U.```

CSV

`          CSV is DOUBLE PRECISION`

SNV

```          SNV is COMPLEX*16
The desired unitary matrix V.```

CSQ

`          CSQ is DOUBLE PRECISION`

SNQ

```          SNQ is COMPLEX*16
The desired unitary matrix Q.```
Author

Univ. of Tennessee

Univ. of California Berkeley