lags2(3)

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, 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

    Univ. of Colorado Denver

    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

    Univ. of Colorado Denver

    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

    Univ. of Colorado Denver

    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

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 156 of file zlags2.f.

Author

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