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SUBROUTINE <a name="CLAHQR.1"></a><a href="clahqr.f.html#CLAHQR.1">CLAHQR</a>( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
LOGICAL WANTT, WANTZ
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX H( LDH, * ), W( * ), Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLAHQR.19"></a><a href="clahqr.f.html#CLAHQR.1">CLAHQR</a> is an auxiliary routine called by <a name="CHSEQR.19"></a><a href="chseqr.f.html#CHSEQR.1">CHSEQR</a> to update the
</span><span class="comment">*</span><span class="comment"> eigenvalues and Schur decomposition already computed by <a name="CHSEQR.20"></a><a href="chseqr.f.html#CHSEQR.1">CHSEQR</a>, by
</span><span class="comment">*</span><span class="comment"> dealing with the Hessenberg submatrix in rows and columns ILO to
</span><span class="comment">*</span><span class="comment"> IHI.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTT (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> = .TRUE. : the full Schur form T is required;
</span><span class="comment">*</span><span class="comment"> = .FALSE.: only eigenvalues are required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTZ (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> = .TRUE. : the matrix of Schur vectors Z is required;
</span><span class="comment">*</span><span class="comment"> = .FALSE.: Schur vectors are not required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix H. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ILO (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IHI (input) INTEGER
</span><span class="comment">*</span><span class="comment"> It is assumed that H is already upper triangular in rows and
</span><span class="comment">*</span><span class="comment"> columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
</span><span class="comment">*</span><span class="comment"> <a name="CLAHQR.42"></a><a href="clahqr.f.html#CLAHQR.1">CLAHQR</a> works primarily with the Hessenberg submatrix in rows
</span><span class="comment">*</span><span class="comment"> and columns ILO to IHI, but applies transformations to all of
</span><span class="comment">*</span><span class="comment"> H if WANTT is .TRUE..
</span><span class="comment">*</span><span class="comment"> 1 <= ILO <= max(1,IHI); IHI <= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> H (input/output) COMPLEX array, dimension (LDH,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper Hessenberg matrix H.
</span><span class="comment">*</span><span class="comment"> On exit, if INFO is zero and if WANTT is .TRUE., then H
</span><span class="comment">*</span><span class="comment"> is upper triangular in rows and columns ILO:IHI. If INFO
</span><span class="comment">*</span><span class="comment"> is zero and if WANTT is .FALSE., then the contents of H
</span><span class="comment">*</span><span class="comment"> are unspecified on exit. The output state of H in case
</span><span class="comment">*</span><span class="comment"> INF is positive is below under the description of INFO.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDH (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array H. LDH >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The computed eigenvalues ILO to IHI are stored in the
</span><span class="comment">*</span><span class="comment"> corresponding elements of W. If WANTT is .TRUE., the
</span><span class="comment">*</span><span class="comment"> eigenvalues are stored in the same order as on the diagonal
</span><span class="comment">*</span><span class="comment"> of the Schur form returned in H, with W(i) = H(i,i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ILOZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IHIZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specify the rows of Z to which transformations must be
</span><span class="comment">*</span><span class="comment"> applied if WANTZ is .TRUE..
</span><span class="comment">*</span><span class="comment"> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (input/output) COMPLEX array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment"> If WANTZ is .TRUE., on entry Z must contain the current
</span><span class="comment">*</span><span class="comment"> matrix Z of transformations accumulated by <a name="CHSEQR.72"></a><a href="chseqr.f.html#CHSEQR.1">CHSEQR</a>, and on
</span><span class="comment">*</span><span class="comment"> exit Z has been updated; transformations are applied only to
</span><span class="comment">*</span><span class="comment"> the submatrix Z(ILOZ:IHIZ,ILO:IHI).
</span><span class="comment">*</span><span class="comment"> If WANTZ is .FALSE., Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Z. LDZ >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> .GT. 0: if INFO = i, <a name="CLAHQR.82"></a><a href="clahqr.f.html#CLAHQR.1">CLAHQR</a> failed to compute all the
</span><span class="comment">*</span><span class="comment"> eigenvalues ILO to IHI in a total of 30 iterations
</span><span class="comment">*</span><span class="comment"> per eigenvalue; elements i+1:ihi of W contain
</span><span class="comment">*</span><span class="comment"> those eigenvalues which have been successfully
</span><span class="comment">*</span><span class="comment"> computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If INFO .GT. 0 and WANTT is .FALSE., then on exit,
</span><span class="comment">*</span><span class="comment"> the remaining unconverged eigenvalues are the
</span><span class="comment">*</span><span class="comment"> eigenvalues of the upper Hessenberg matrix
</span><span class="comment">*</span><span class="comment"> rows and columns ILO thorugh INFO of the final,
</span><span class="comment">*</span><span class="comment"> output value of H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If INFO .GT. 0 and WANTT is .TRUE., then on exit
</span><span class="comment">*</span><span class="comment"> (*) (initial value of H)*U = U*(final value of H)
</span><span class="comment">*</span><span class="comment"> where U is an orthognal matrix. The final
</span><span class="comment">*</span><span class="comment"> value of H is upper Hessenberg and triangular in
</span><span class="comment">*</span><span class="comment"> rows and columns INFO+1 through IHI.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If INFO .GT. 0 and WANTZ is .TRUE., then on exit
</span><span class="comment">*</span><span class="comment"> (final value of Z) = (initial value of Z)*U
</span><span class="comment">*</span><span class="comment"> where U is the orthogonal matrix in (*)
</span><span class="comment">*</span><span class="comment"> (regardless of the value of WANTT.)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 02-96 Based on modifications by
</span><span class="comment">*</span><span class="comment"> David Day, Sandia National Laboratory, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 12-04 Further modifications by
</span><span class="comment">*</span><span class="comment"> Ralph Byers, University of Kansas, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This is a modified version of <a name="CLAHQR.114"></a><a href="clahqr.f.html#CLAHQR.1">CLAHQR</a> from LAPACK version 3.0.
</span><span class="comment">*</span><span class="comment"> It is (1) more robust against overflow and underflow and
</span><span class="comment">*</span><span class="comment"> (2) adopts the more conservative Ahues & Tisseur stopping
</span><span class="comment">*</span><span class="comment"> criterion (LAWN 122, 1997).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =========================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> INTEGER ITMAX
PARAMETER ( ITMAX = 30 )
COMPLEX ZERO, ONE
PARAMETER ( ZERO = ( 0.0e0, 0.0e0 ),
$ ONE = ( 1.0e0, 0.0e0 ) )
REAL RZERO, RONE, HALF
PARAMETER ( RZERO = 0.0e0, RONE = 1.0e0, HALF = 0.5e0 )
REAL DAT1
PARAMETER ( DAT1 = 3.0e0 / 4.0e0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> COMPLEX CDUM, H11, H11S, H22, SC, SUM, T, T1, TEMP, U,
$ V2, X, Y
REAL AA, AB, BA, BB, H10, H21, RTEMP, S, SAFMAX,
$ SAFMIN, SMLNUM, SX, T2, TST, ULP
INTEGER I, I1, I2, ITS, J, JHI, JLO, K, L, M, NH, NZ
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> COMPLEX V( 2 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> COMPLEX <a name="CLADIV.143"></a><a href="cladiv.f.html#CLADIV.1">CLADIV</a>
REAL <a name="SLAMCH.144"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="CLADIV.145"></a><a href="cladiv.f.html#CLADIV.1">CLADIV</a>, <a name="SLAMCH.145"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
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