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template<typename T>
void laein(logical *rightv, logical *noinit, integer *n, T *h, integer *ldh, T *wr, T *wi, T *vr, T *vi, T *b, integer *ldb, T *work, T *eps3, T *smlnum, T *bignum, integer *info)# LAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.
Purpose:
LAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H.
- Parameters:
RIGHTV – [in]
RIGHTV is LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.NOINIT – [in]
NOINIT is LOGICAL
= .TRUE. : no initial vector supplied in (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).N – [in]
N is INTEGER
The order of the matrix H. N >= 0.
H – [in]
H is REAL array, dimension (LDH,N)
The upper Hessenberg matrix H.
LDH – [in]
LDH is INTEGER
The leading dimension of the array H. LDH >= fla_max(1,N).
WR – [in] WR is REAL
WI – [in]
WI is REAL
The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed.
VR – [inout] VR is REAL array, dimension (N)
VI – [inout]
VI is REAL array, dimension (N)
On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain a real starting vector for inverse iteration using the real eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain the real and imaginary parts of a complex starting vector for inverse iteration using the complex eigenvalue (WR,WI); otherwise VR and VI need not be set. On exit, if WI = 0.0 (real eigenvalue), VR contains the computed real eigenvector; if WI.ne.0.0 (complex eigenvalue), VR and VI contain the real and imaginary parts of the computed complex eigenvector. The eigenvector is normalized so that the component of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|. VI is not referenced if WI = 0.0.
B – [out] B is REAL array, dimension (LDB,N)
LDB – [in]
LDB is INTEGER
The leading dimension of the array B. LDB >= N+1.
WORK – [out] WORK is REAL array, dimension (N)
EPS3 – [in]
EPS3 is REAL
A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.
SMLNUM – [in]
SMLNUM is REAL
A machine-dependent value close to the underflow threshold.
BIGNUM – [in]
BIGNUM is REAL
A machine-dependent value close to the overflow threshold.
INFO – [out]
INFO is INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; VR is set to the last iterate, and so is VI if WI.ne.0.0.