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laev2(3) Library Functions Manual laev2(3)

NAME

laev2 - laev2: 2x2 eig

SYNOPSIS

Functions


subroutine CLAEV2 (a, b, c, rt1, rt2, cs1, sn1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. subroutine DLAEV2 (a, b, c, rt1, rt2, cs1, sn1)
DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. subroutine SLAEV2 (a, b, c, rt1, rt2, cs1, sn1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. subroutine ZLAEV2 (a, b, c, rt1, rt2, cs1, sn1)
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Detailed Description

Function Documentation

subroutine CLAEV2 (complex a, complex b, complex c, real rt1, real rt2, real cs1, complex sn1)

CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

!>
!> CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
!>    [  A         B  ]
!>    [  CONJG(B)  C  ].
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!> [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
!> [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
!>

Parameters

A 

!>          A is COMPLEX
!>         The (1,1) element of the 2-by-2 matrix.
!>

B

!>          B is COMPLEX
!>         The (1,2) element and the conjugate of the (2,1) element of
!>         the 2-by-2 matrix.
!>

C

!>          C is COMPLEX
!>         The (2,2) element of the 2-by-2 matrix.
!>

RT1

!>          RT1 is REAL
!>         The eigenvalue of larger absolute value.
!>

RT2

!>          RT2 is REAL
!>         The eigenvalue of smaller absolute value.
!>

CS1

!>          CS1 is REAL
!>

SN1

!>          SN1 is COMPLEX
!>         The vector (CS1, SN1) is a unit right eigenvector for RT1.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  RT1 is accurate to a few ulps barring over/underflow.
!>
!>  RT2 may be inaccurate if there is massive cancellation in the
!>  determinant A*C-B*B; higher precision or correctly rounded or
!>  correctly truncated arithmetic would be needed to compute RT2
!>  accurately in all cases.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
!>
!>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
!>  Underflow is harmless if the input data is 0 or exceeds
!>     underflow_threshold / macheps.
!>

Definition at line 120 of file claev2.f.

subroutine DLAEV2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2, double precision cs1, double precision sn1)

DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

!>
!> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    [  A   B  ]
!>    [  B   C  ].
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!>    [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
!>    [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
!>

Parameters

A 

!>          A is DOUBLE PRECISION
!>          The (1,1) element of the 2-by-2 matrix.
!>

B

!>          B is DOUBLE PRECISION
!>          The (1,2) element and the conjugate of the (2,1) element of
!>          the 2-by-2 matrix.
!>

C

!>          C is DOUBLE PRECISION
!>          The (2,2) element of the 2-by-2 matrix.
!>

RT1

!>          RT1 is DOUBLE PRECISION
!>          The eigenvalue of larger absolute value.
!>

RT2

!>          RT2 is DOUBLE PRECISION
!>          The eigenvalue of smaller absolute value.
!>

CS1

!>          CS1 is DOUBLE PRECISION
!>

SN1

!>          SN1 is DOUBLE PRECISION
!>          The vector (CS1, SN1) is a unit right eigenvector for RT1.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  RT1 is accurate to a few ulps barring over/underflow.
!>
!>  RT2 may be inaccurate if there is massive cancellation in the
!>  determinant A*C-B*B; higher precision or correctly rounded or
!>  correctly truncated arithmetic would be needed to compute RT2
!>  accurately in all cases.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
!>
!>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
!>  Underflow is harmless if the input data is 0 or exceeds
!>     underflow_threshold / macheps.
!>

Definition at line 119 of file dlaev2.f.

subroutine SLAEV2 (real a, real b, real c, real rt1, real rt2, real cs1, real sn1)

SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

!>
!> SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    [  A   B  ]
!>    [  B   C  ].
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!>    [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
!>    [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
!>

Parameters

A 

!>          A is REAL
!>          The (1,1) element of the 2-by-2 matrix.
!>

B

!>          B is REAL
!>          The (1,2) element and the conjugate of the (2,1) element of
!>          the 2-by-2 matrix.
!>

C

!>          C is REAL
!>          The (2,2) element of the 2-by-2 matrix.
!>

RT1

!>          RT1 is REAL
!>          The eigenvalue of larger absolute value.
!>

RT2

!>          RT2 is REAL
!>          The eigenvalue of smaller absolute value.
!>

CS1

!>          CS1 is REAL
!>

SN1

!>          SN1 is REAL
!>          The vector (CS1, SN1) is a unit right eigenvector for RT1.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  RT1 is accurate to a few ulps barring over/underflow.
!>
!>  RT2 may be inaccurate if there is massive cancellation in the
!>  determinant A*C-B*B; higher precision or correctly rounded or
!>  correctly truncated arithmetic would be needed to compute RT2
!>  accurately in all cases.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
!>
!>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
!>  Underflow is harmless if the input data is 0 or exceeds
!>     underflow_threshold / macheps.
!>

Definition at line 119 of file slaev2.f.

subroutine ZLAEV2 (complex*16 a, complex*16 b, complex*16 c, double precision rt1, double precision rt2, double precision cs1, complex*16 sn1)

ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

!>
!> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
!>    [  A         B  ]
!>    [  CONJG(B)  C  ].
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!> [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
!> [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
!>

Parameters

A 

!>          A is COMPLEX*16
!>         The (1,1) element of the 2-by-2 matrix.
!>

B

!>          B is COMPLEX*16
!>         The (1,2) element and the conjugate of the (2,1) element of
!>         the 2-by-2 matrix.
!>

C

!>          C is COMPLEX*16
!>         The (2,2) element of the 2-by-2 matrix.
!>

RT1

!>          RT1 is DOUBLE PRECISION
!>         The eigenvalue of larger absolute value.
!>

RT2

!>          RT2 is DOUBLE PRECISION
!>         The eigenvalue of smaller absolute value.
!>

CS1

!>          CS1 is DOUBLE PRECISION
!>

SN1

!>          SN1 is COMPLEX*16
!>         The vector (CS1, SN1) is a unit right eigenvector for RT1.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  RT1 is accurate to a few ulps barring over/underflow.
!>
!>  RT2 may be inaccurate if there is massive cancellation in the
!>  determinant A*C-B*B; higher precision or correctly rounded or
!>  correctly truncated arithmetic would be needed to compute RT2
!>  accurately in all cases.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
!>
!>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
!>  Underflow is harmless if the input data is 0 or exceeds
!>     underflow_threshold / macheps.
!>

Definition at line 120 of file zlaev2.f.

Author

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