table of contents
| laev2(3) | LAPACK | 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 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 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.
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 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 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.
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 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 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.
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 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 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.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |