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SUBROUTINE <a name="CLAED8.1"></a><a href="claed8.f.html#CLAED8.1">CLAED8</a>( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
$ Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
$ GIVCOL, GIVNUM, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK 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 CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ
REAL RHO
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ),
$ INDXQ( * ), PERM( * )
REAL D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ),
$ Z( * )
COMPLEX Q( LDQ, * ), Q2( LDQ2, * )
<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="CLAED8.24"></a><a href="claed8.f.html#CLAED8.1">CLAED8</a> merges the two sets of eigenvalues together into a single
</span><span class="comment">*</span><span class="comment"> sorted set. Then it tries to deflate the size of the problem.
</span><span class="comment">*</span><span class="comment"> There are two ways in which deflation can occur: when two or more
</span><span class="comment">*</span><span class="comment"> eigenvalues are close together or if there is a tiny element in the
</span><span class="comment">*</span><span class="comment"> Z vector. For each such occurrence the order of the related secular
</span><span class="comment">*</span><span class="comment"> equation problem is reduced by one.
</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"> K (output) INTEGER
</span><span class="comment">*</span><span class="comment"> Contains the number of non-deflated eigenvalues.
</span><span class="comment">*</span><span class="comment"> This is the order of the related secular equation.
</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 dimension of the symmetric tridiagonal matrix. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> QSIZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the unitary matrix used to reduce
</span><span class="comment">*</span><span class="comment"> the dense or band matrix to tridiagonal form.
</span><span class="comment">*</span><span class="comment"> QSIZ >= N if ICOMPQ = 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (input/output) COMPLEX array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment"> On entry, Q contains the eigenvectors of the partially solved
</span><span class="comment">*</span><span class="comment"> system which has been previously updated in matrix
</span><span class="comment">*</span><span class="comment"> multiplies with other partially solved eigensystems.
</span><span class="comment">*</span><span class="comment"> On exit, Q contains the trailing (N-K) updated eigenvectors
</span><span class="comment">*</span><span class="comment"> (those which were deflated) in its last N-K columns.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q. LDQ >= max( 1, N ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On entry, D contains the eigenvalues of the two submatrices to
</span><span class="comment">*</span><span class="comment"> be combined. On exit, D contains the trailing (N-K) updated
</span><span class="comment">*</span><span class="comment"> eigenvalues (those which were deflated) sorted into increasing
</span><span class="comment">*</span><span class="comment"> order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RHO (input/output) REAL
</span><span class="comment">*</span><span class="comment"> Contains the off diagonal element associated with the rank-1
</span><span class="comment">*</span><span class="comment"> cut which originally split the two submatrices which are now
</span><span class="comment">*</span><span class="comment"> being recombined. RHO is modified during the computation to
</span><span class="comment">*</span><span class="comment"> the value required by <a name="SLAED3.66"></a><a href="slaed3.f.html#SLAED3.1">SLAED3</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CUTPNT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Contains the location of the last eigenvalue in the leading
</span><span class="comment">*</span><span class="comment"> sub-matrix. MIN(1,N) <= CUTPNT <= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On input this vector contains the updating vector (the last
</span><span class="comment">*</span><span class="comment"> row of the first sub-eigenvector matrix and the first row of
</span><span class="comment">*</span><span class="comment"> the second sub-eigenvector matrix). The contents of Z are
</span><span class="comment">*</span><span class="comment"> destroyed during the updating process.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DLAMDA (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Contains a copy of the first K eigenvalues which will be used
</span><span class="comment">*</span><span class="comment"> by <a name="SLAED3.80"></a><a href="slaed3.f.html#SLAED3.1">SLAED3</a> to form the secular equation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q2 (output) COMPLEX array, dimension (LDQ2,N)
</span><span class="comment">*</span><span class="comment"> If ICOMPQ = 0, Q2 is not referenced. Otherwise,
</span><span class="comment">*</span><span class="comment"> Contains a copy of the first K eigenvectors which will be used
</span><span class="comment">*</span><span class="comment"> by <a name="SLAED7.85"></a><a href="slaed7.f.html#SLAED7.1">SLAED7</a> in a matrix multiply (SGEMM) to update the new
</span><span class="comment">*</span><span class="comment"> eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ2 (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q2. LDQ2 >= max( 1, N ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> This will hold the first k values of the final
</span><span class="comment">*</span><span class="comment"> deflation-altered z-vector and will be passed to <a name="SLAED3.93"></a><a href="slaed3.f.html#SLAED3.1">SLAED3</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INDXP (workspace) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> This will contain the permutation used to place deflated
</span><span class="comment">*</span><span class="comment"> values of D at the end of the array. On output INDXP(1:K)
</span><span class="comment">*</span><span class="comment"> points to the nondeflated D-values and INDXP(K+1:N)
</span><span class="comment">*</span><span class="comment"> points to the deflated eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INDX (workspace) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> This will contain the permutation used to sort the contents of
</span><span class="comment">*</span><span class="comment"> D into ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INDXQ (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> This contains the permutation which separately sorts the two
</span><span class="comment">*</span><span class="comment"> sub-problems in D into ascending order. Note that elements in
</span><span class="comment">*</span><span class="comment"> the second half of this permutation must first have CUTPNT
</span><span class="comment">*</span><span class="comment"> added to their values in order to be accurate.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> PERM (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Contains the permutations (from deflation and sorting) to be
</span><span class="comment">*</span><span class="comment"> applied to each eigenblock.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVPTR (output) INTEGER
</span><span class="comment">*</span><span class="comment"> Contains the number of Givens rotations which took place in
</span><span class="comment">*</span><span class="comment"> this subproblem.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVCOL (output) INTEGER array, dimension (2, N)
</span><span class="comment">*</span><span class="comment"> Each pair of numbers indicates a pair of columns to take place
</span><span class="comment">*</span><span class="comment"> in a Givens rotation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVNUM (output) REAL array, dimension (2, N)
</span><span class="comment">*</span><span class="comment"> Each number indicates the S value to be used in the
</span><span class="comment">*</span><span class="comment"> corresponding Givens rotation.
</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"> < 0: if INFO = -i, the i-th argument had an illegal value.
</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> REAL MONE, ZERO, ONE, TWO, EIGHT
PARAMETER ( MONE = -1.0E0, ZERO = 0.0E0, ONE = 1.0E0,
$ TWO = 2.0E0, EIGHT = 8.0E0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, IMAX, J, JLAM, JMAX, JP, K2, N1, N1P1, N2
REAL C, EPS, S, T, TAU, TOL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> INTEGER ISAMAX
REAL <a name="SLAMCH.144"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLAPY2.144"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
EXTERNAL ISAMAX, <a name="SLAMCH.145"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLAPY2.145"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL CCOPY, <a name="CLACPY.148"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>, CSROT, SCOPY, <a name="SLAMRG.148"></a><a href="slamrg.f.html#SLAMRG.1">SLAMRG</a>, SSCAL,
$ <a name="XERBLA.149"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, MAX, MIN, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
<span class="comment">*</span><span class="comment">
</span> IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( QSIZ.LT.N ) THEN
INFO = -3
ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( CUTPNT.LT.MIN( 1, N ) .OR. CUTPNT.GT.N ) THEN
INFO = -8
ELSE IF( LDQ2.LT.MAX( 1, N ) ) THEN
INFO = -12
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.172"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CLAED8.172"></a><a href="claed8.f.html#CLAED8.1">CLAED8</a>'</span>, -INFO )
RETURN
END IF
<span class="comment">*</span><span class="comment">
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