Man page - lags2(3)

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Manual

lags2

NAME
SYNOPSIS
Functions
Detailed Description
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, realcsq, complex snq)
subroutine dlags2 (logical upper, double precision a1, double precision a2,double precision a3, double precision b1, double precision b2, doubleprecision b3, double precision csu, double precision snu, doubleprecision csv, double precision snv, double precision csq, doubleprecision snq)
subroutine slags2 (logical upper, real a1, real a2, real a3, real b1, realb2, real b3, real csu, real snu, real csv, real snv, real csq, realsnq)
subroutine zlags2 (logical upper, double precision a1, complex*16 a2,double precision a3, double precision b1, complex*16 b2, doubleprecision b3, double precision csu, complex*16 snu, double precisioncsv, complex*16 snv, double precision csq, complex*16 snq)
Author

NAME

lags2 - 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

Detailed Description

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, realcsq, 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

Univ. of Colorado Denver

NAG Ltd.

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

Univ. of Colorado Denver

NAG Ltd.

subroutine slags2 (logical upper, real a1, real a2, real a3, real b1, realb2, real b3, real csu, real snu, real csv, real snv, real csq, realsnq)

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

Univ. of Colorado Denver

NAG Ltd.

subroutine zlags2 (logical upper, double precision a1, complex*16 a2,double precision a3, double precision b1, complex*16 b2, doubleprecision b3, double precision csu, complex*16 snu, double precisioncsv, 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

Univ. of Colorado Denver

NAG Ltd.

Author

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