.TH "SRC/dhsein.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dhsein.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdhsein\fP (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)"
.br
.RI "\fBDHSEIN\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dhsein (character side, character eigsrc, character initv, logical, dimension( * ) select, integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( ldvl, * ) vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, double precision, dimension( * ) work, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)"

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\fBDHSEIN\fP  
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\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DHSEIN uses inverse iteration to find specified right and/or left
!> eigenvectors of a real upper Hessenberg matrix H\&.
!>
!> The right eigenvector x and the left eigenvector y of the matrix H
!> corresponding to an eigenvalue w are defined by:
!>
!>              H * x = w * x,     y**h * H = w * y**h
!>
!> where y**h denotes the conjugate transpose of the vector y\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'R': compute right eigenvectors only;
!>          = 'L': compute left eigenvectors only;
!>          = 'B': compute both right and left eigenvectors\&.
!> 
.fi
.PP
.br
\fIEIGSRC\fP 
.PP
.nf
!>          EIGSRC is CHARACTER*1
!>          Specifies the source of eigenvalues supplied in (WR,WI):
!>          = 'Q': the eigenvalues were found using DHSEQR; thus, if
!>                 H has zero subdiagonal elements, and so is
!>                 block-triangular, then the j-th eigenvalue can be
!>                 assumed to be an eigenvalue of the block containing
!>                 the j-th row/column\&.  This property allows DHSEIN to
!>                 perform inverse iteration on just one diagonal block\&.
!>          = 'N': no assumptions are made on the correspondence
!>                 between eigenvalues and diagonal blocks\&.  In this
!>                 case, DHSEIN must always perform inverse iteration
!>                 using the whole matrix H\&.
!> 
.fi
.PP
.br
\fIINITV\fP 
.PP
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!>          INITV is CHARACTER*1
!>          = 'N': no initial vectors are supplied;
!>          = 'U': user-supplied initial vectors are stored in the arrays
!>                 VL and/or VR\&.
!> 
.fi
.PP
.br
\fISELECT\fP 
.PP
.nf
!>          SELECT is LOGICAL array, dimension (N)
!>          Specifies the eigenvectors to be computed\&. To select the
!>          real eigenvector corresponding to a real eigenvalue WR(j),
!>          SELECT(j) must be set to \&.TRUE\&.\&. To select the complex
!>          eigenvector corresponding to a complex eigenvalue
!>          (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)),
!>          either SELECT(j) or SELECT(j+1) or both must be set to
!>          \&.TRUE\&.; then on exit SELECT(j) is \&.TRUE\&. and SELECT(j+1) is
!>          \&.FALSE\&.\&.
!> 
.fi
.PP
.br
\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrix H\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIH\fP 
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.nf
!>          H is DOUBLE PRECISION array, dimension (LDH,N)
!>          The upper Hessenberg matrix H\&.
!>          If a NaN is detected in H, the routine will return with INFO=-6\&.
!> 
.fi
.PP
.br
\fILDH\fP 
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!>          LDH is INTEGER
!>          The leading dimension of the array H\&.  LDH >= max(1,N)\&.
!> 
.fi
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\fIWR\fP 
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!>          WR is DOUBLE PRECISION array, dimension (N)
!> 
.fi
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\fIWI\fP 
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!>          WI is DOUBLE PRECISION array, dimension (N)
!>
!>          On entry, the real and imaginary parts of the eigenvalues of
!>          H; a complex conjugate pair of eigenvalues must be stored in
!>          consecutive elements of WR and WI\&.
!>          On exit, WR may have been altered since close eigenvalues
!>          are perturbed slightly in searching for independent
!>          eigenvectors\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is DOUBLE PRECISION array, dimension (LDVL,MM)
!>          On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
!>          contain starting vectors for the inverse iteration for the
!>          left eigenvectors; the starting vector for each eigenvector
!>          must be in the same column(s) in which the eigenvector will
!>          be stored\&.
!>          On exit, if SIDE = 'L' or 'B', the left eigenvectors
!>          specified by SELECT will be stored consecutively in the
!>          columns of VL, in the same order as their eigenvalues\&. A
!>          complex eigenvector corresponding to a complex eigenvalue is
!>          stored in two consecutive columns, the first holding the real
!>          part and the second the imaginary part\&.
!>          If SIDE = 'R', VL is not referenced\&.
!> 
.fi
.PP
.br
\fILDVL\fP 
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!>          LDVL is INTEGER
!>          The leading dimension of the array VL\&.
!>          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise\&.
!> 
.fi
.PP
.br
\fIVR\fP 
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!>          VR is DOUBLE PRECISION array, dimension (LDVR,MM)
!>          On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
!>          contain starting vectors for the inverse iteration for the
!>          right eigenvectors; the starting vector for each eigenvector
!>          must be in the same column(s) in which the eigenvector will
!>          be stored\&.
!>          On exit, if SIDE = 'R' or 'B', the right eigenvectors
!>          specified by SELECT will be stored consecutively in the
!>          columns of VR, in the same order as their eigenvalues\&. A
!>          complex eigenvector corresponding to a complex eigenvalue is
!>          stored in two consecutive columns, the first holding the real
!>          part and the second the imaginary part\&.
!>          If SIDE = 'L', VR is not referenced\&.
!> 
.fi
.PP
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\fILDVR\fP 
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!>          LDVR is INTEGER
!>          The leading dimension of the array VR\&.
!>          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise\&.
!> 
.fi
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.br
\fIMM\fP 
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!>          MM is INTEGER
!>          The number of columns in the arrays VL and/or VR\&. MM >= M\&.
!> 
.fi
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.br
\fIM\fP 
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.nf
!>          M is INTEGER
!>          The number of columns in the arrays VL and/or VR required to
!>          store the eigenvectors; each selected real eigenvector
!>          occupies one column and each selected complex eigenvector
!>          occupies two columns\&.
!> 
.fi
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\fIWORK\fP 
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!>          WORK is DOUBLE PRECISION array, dimension ((N+2)*N)
!> 
.fi
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\fIIFAILL\fP 
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!>          IFAILL is INTEGER array, dimension (MM)
!>          If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left
!>          eigenvector in the i-th column of VL (corresponding to the
!>          eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
!>          eigenvector converged satisfactorily\&. If the i-th and (i+1)th
!>          columns of VL hold a complex eigenvector, then IFAILL(i) and
!>          IFAILL(i+1) are set to the same value\&.
!>          If SIDE = 'R', IFAILL is not referenced\&.
!> 
.fi
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\fIIFAILR\fP 
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!>          IFAILR is INTEGER array, dimension (MM)
!>          If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
!>          eigenvector in the i-th column of VR (corresponding to the
!>          eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
!>          eigenvector converged satisfactorily\&. If the i-th and (i+1)th
!>          columns of VR hold a complex eigenvector, then IFAILR(i) and
!>          IFAILR(i+1) are set to the same value\&.
!>          If SIDE = 'L', IFAILR is not referenced\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
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!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, i is the number of eigenvectors which
!>                failed to converge; see IFAILL and IFAILR for further
!>                details\&.
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

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!>
!>  Each eigenvector is normalized so that the element of largest
!>  magnitude has magnitude 1; here the magnitude of a complex number
!>  (x,y) is taken to be |x|+|y|\&.
!> 
.fi
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.RE
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Definition at line \fB260\fP of file \fBdhsein\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.