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| zlaev2.f(3) | LAPACK | zlaev2.f(3) |
NAME¶
zlaev2.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
Function/Subroutine Documentation¶
subroutine zlaev2 (complex*16A, complex*16B, complex*16C, double precisionRT1, double precisionRT2, double precisionCS1, complex*16SN1)¶
ZLAEV2 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 ].
A
B
C
RT1
RT2
CS1
SN1
Author:
A is COMPLEX*16
The (1,1) element of the 2-by-2 matrix.
B is COMPLEX*16
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.
C is COMPLEX*16
The (2,2) element of the 2-by-2 matrix.
RT1 is DOUBLE PRECISION
The eigenvalue of larger absolute value.
RT2 is DOUBLE PRECISION
The eigenvalue of smaller absolute value.
CS1 is DOUBLE PRECISION
SN1 is COMPLEX*16
The vector (CS1, SN1) is a unit right eigenvector for RT1.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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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