.TH "laein" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laein \- laein: eigvec by Hessenberg inverse iteration
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclaein\fP (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)"
.br
.RI "\fBCLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&. "
.ti -1c
.RI "subroutine \fBdlaein\fP (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info)"
.br
.RI "\fBDLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&. "
.ti -1c
.RI "subroutine \fBslaein\fP (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info)"
.br
.RI "\fBSLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&. "
.ti -1c
.RI "subroutine \fBzlaein\fP (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)"
.br
.RI "\fBZLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine claein (logical rightv, logical noinit, integer n, complex, dimension( ldh, * ) h, integer ldh, complex w, complex, dimension( * ) v, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real eps3, real smlnum, integer info)"

.PP
\fBCLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAEIN uses inverse iteration to find a right or left eigenvector
 corresponding to the eigenvalue W of a complex upper Hessenberg
 matrix H\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIRIGHTV\fP 
.PP
.nf
          RIGHTV is LOGICAL
          = \&.TRUE\&. : compute right eigenvector;
          = \&.FALSE\&.: compute left eigenvector\&.
.fi
.PP
.br
\fINOINIT\fP 
.PP
.nf
          NOINIT is LOGICAL
          = \&.TRUE\&. : no initial vector supplied in V
          = \&.FALSE\&.: initial vector supplied in V\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix H\&.  N >= 0\&.
.fi
.PP
.br
\fIH\fP 
.PP
.nf
          H is COMPLEX array, dimension (LDH,N)
          The upper Hessenberg matrix H\&.
.fi
.PP
.br
\fILDH\fP 
.PP
.nf
          LDH is INTEGER
          The leading dimension of the array H\&.  LDH >= max(1,N)\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is COMPLEX
          The eigenvalue of H whose corresponding right or left
          eigenvector is to be computed\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX array, dimension (N)
          On entry, if NOINIT = \&.FALSE\&., V must contain a starting
          vector for inverse iteration; otherwise V need not be set\&.
          On exit, V contains the computed eigenvector, 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|\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB,N)
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (N)
.fi
.PP
.br
\fIEPS3\fP 
.PP
.nf
          EPS3 is REAL
          A small machine-dependent value which is used to perturb
          close eigenvalues, and to replace zero pivots\&.
.fi
.PP
.br
\fISMLNUM\fP 
.PP
.nf
          SMLNUM is REAL
          A machine-dependent value close to the underflow threshold\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          = 1:  inverse iteration did not converge; V is set to the
                last iterate\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine dlaein (logical rightv, logical noinit, integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision wr, double precision wi, double precision, dimension( * ) vr, double precision, dimension( * ) vi, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, double precision eps3, double precision smlnum, double precision bignum, integer info)"

.PP
\fBDLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAEIN uses inverse iteration to find a right or left eigenvector
 corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
 matrix H\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIRIGHTV\fP 
.PP
.nf
          RIGHTV is LOGICAL
          = \&.TRUE\&. : compute right eigenvector;
          = \&.FALSE\&.: compute left eigenvector\&.
.fi
.PP
.br
\fINOINIT\fP 
.PP
.nf
          NOINIT is LOGICAL
          = \&.TRUE\&. : no initial vector supplied in (VR,VI)\&.
          = \&.FALSE\&.: initial vector supplied in (VR,VI)\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix H\&.  N >= 0\&.
.fi
.PP
.br
\fIH\fP 
.PP
.nf
          H is DOUBLE PRECISION array, dimension (LDH,N)
          The upper Hessenberg matrix H\&.
.fi
.PP
.br
\fILDH\fP 
.PP
.nf
          LDH is INTEGER
          The leading dimension of the array H\&.  LDH >= max(1,N)\&.
.fi
.PP
.br
\fIWR\fP 
.PP
.nf
          WR is DOUBLE PRECISION
.fi
.PP
.br
\fIWI\fP 
.PP
.nf
          WI is DOUBLE PRECISION
          The real and imaginary parts of the eigenvalue of H whose
          corresponding right or left eigenvector is to be computed\&.
.fi
.PP
.br
\fIVR\fP 
.PP
.nf
          VR is DOUBLE PRECISION array, dimension (N)
.fi
.PP
.br
\fIVI\fP 
.PP
.nf
          VI is DOUBLE PRECISION 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\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,N)
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= N+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (N)
.fi
.PP
.br
\fIEPS3\fP 
.PP
.nf
          EPS3 is DOUBLE PRECISION
          A small machine-dependent value which is used to perturb
          close eigenvalues, and to replace zero pivots\&.
.fi
.PP
.br
\fISMLNUM\fP 
.PP
.nf
          SMLNUM is DOUBLE PRECISION
          A machine-dependent value close to the underflow threshold\&.
.fi
.PP
.br
\fIBIGNUM\fP 
.PP
.nf
          BIGNUM is DOUBLE PRECISION
          A machine-dependent value close to the overflow threshold\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine slaein (logical rightv, logical noinit, integer n, real, dimension( ldh, * ) h, integer ldh, real wr, real wi, real, dimension( * ) vr, real, dimension( * ) vi, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real eps3, real smlnum, real bignum, integer info)"

.PP
\fBSLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAEIN uses inverse iteration to find a right or left eigenvector
 corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
 matrix H\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIRIGHTV\fP 
.PP
.nf
          RIGHTV is LOGICAL
          = \&.TRUE\&. : compute right eigenvector;
          = \&.FALSE\&.: compute left eigenvector\&.
.fi
.PP
.br
\fINOINIT\fP 
.PP
.nf
          NOINIT is LOGICAL
          = \&.TRUE\&. : no initial vector supplied in (VR,VI)\&.
          = \&.FALSE\&.: initial vector supplied in (VR,VI)\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix H\&.  N >= 0\&.
.fi
.PP
.br
\fIH\fP 
.PP
.nf
          H is REAL array, dimension (LDH,N)
          The upper Hessenberg matrix H\&.
.fi
.PP
.br
\fILDH\fP 
.PP
.nf
          LDH is INTEGER
          The leading dimension of the array H\&.  LDH >= max(1,N)\&.
.fi
.PP
.br
\fIWR\fP 
.PP
.nf
          WR is REAL
.fi
.PP
.br
\fIWI\fP 
.PP
.nf
          WI is REAL
          The real and imaginary parts of the eigenvalue of H whose
          corresponding right or left eigenvector is to be computed\&.
.fi
.PP
.br
\fIVR\fP 
.PP
.nf
          VR is REAL array, dimension (N)
.fi
.PP
.br
\fIVI\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,N)
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= N+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N)
.fi
.PP
.br
\fIEPS3\fP 
.PP
.nf
          EPS3 is REAL
          A small machine-dependent value which is used to perturb
          close eigenvalues, and to replace zero pivots\&.
.fi
.PP
.br
\fISMLNUM\fP 
.PP
.nf
          SMLNUM is REAL
          A machine-dependent value close to the underflow threshold\&.
.fi
.PP
.br
\fIBIGNUM\fP 
.PP
.nf
          BIGNUM is REAL
          A machine-dependent value close to the overflow threshold\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine zlaein (logical rightv, logical noinit, integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 w, complex*16, dimension( * ) v, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) rwork, double precision eps3, double precision smlnum, integer info)"

.PP
\fBZLAEIN\fP computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLAEIN uses inverse iteration to find a right or left eigenvector
 corresponding to the eigenvalue W of a complex upper Hessenberg
 matrix H\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIRIGHTV\fP 
.PP
.nf
          RIGHTV is LOGICAL
          = \&.TRUE\&. : compute right eigenvector;
          = \&.FALSE\&.: compute left eigenvector\&.
.fi
.PP
.br
\fINOINIT\fP 
.PP
.nf
          NOINIT is LOGICAL
          = \&.TRUE\&. : no initial vector supplied in V
          = \&.FALSE\&.: initial vector supplied in V\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix H\&.  N >= 0\&.
.fi
.PP
.br
\fIH\fP 
.PP
.nf
          H is COMPLEX*16 array, dimension (LDH,N)
          The upper Hessenberg matrix H\&.
.fi
.PP
.br
\fILDH\fP 
.PP
.nf
          LDH is INTEGER
          The leading dimension of the array H\&.  LDH >= max(1,N)\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is COMPLEX*16
          The eigenvalue of H whose corresponding right or left
          eigenvector is to be computed\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX*16 array, dimension (N)
          On entry, if NOINIT = \&.FALSE\&., V must contain a starting
          vector for inverse iteration; otherwise V need not be set\&.
          On exit, V contains the computed eigenvector, 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|\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 array, dimension (LDB,N)
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (N)
.fi
.PP
.br
\fIEPS3\fP 
.PP
.nf
          EPS3 is DOUBLE PRECISION
          A small machine-dependent value which is used to perturb
          close eigenvalues, and to replace zero pivots\&.
.fi
.PP
.br
\fISMLNUM\fP 
.PP
.nf
          SMLNUM is DOUBLE PRECISION
          A machine-dependent value close to the underflow threshold\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          = 1:  inverse iteration did not converge; V is set to the
                last iterate\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.