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OpenBLAS/lapack-netlib/SRC/claed0.f

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*> \brief \b CLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLAED0 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claed0.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claed0.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claed0.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
* IWORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDQ, LDQS, N, QSIZ
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* REAL D( * ), E( * ), RWORK( * )
* COMPLEX Q( LDQ, * ), QSTORE( LDQS, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Using the divide and conquer method, CLAED0 computes all eigenvalues
*> of a symmetric tridiagonal matrix which is one diagonal block of
*> those from reducing a dense or band Hermitian matrix and
*> corresponding eigenvectors of the dense or band matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] QSIZ
*> \verbatim
*> QSIZ is INTEGER
*> The dimension of the unitary matrix used to reduce
*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The dimension of the symmetric tridiagonal matrix. N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is REAL array, dimension (N)
*> On entry, the diagonal elements of the tridiagonal matrix.
*> On exit, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is REAL array, dimension (N-1)
*> On entry, the off-diagonal elements of the tridiagonal matrix.
*> On exit, E has been destroyed.
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> Q is COMPLEX array, dimension (LDQ,N)
*> On entry, Q must contain an QSIZ x N matrix whose columns
*> unitarily orthonormal. It is a part of the unitary matrix
*> that reduces the full dense Hermitian matrix to a
*> (reducible) symmetric tridiagonal matrix.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array,
*> the dimension of IWORK must be at least
*> 6 + 6*N + 5*N*lg N
*> ( lg( N ) = smallest integer k
*> such that 2^k >= N )
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array,
*> dimension (1 + 3*N + 2*N*lg N + 3*N**2)
*> ( lg( N ) = smallest integer k
*> such that 2^k >= N )
*> \endverbatim
*>
*> \param[out] QSTORE
*> \verbatim
*> QSTORE is COMPLEX array, dimension (LDQS, N)
*> Used to store parts of
*> the eigenvector matrix when the updating matrix multiplies
*> take place.
*> \endverbatim
*>
*> \param[in] LDQS
*> \verbatim
*> LDQS is INTEGER
*> The leading dimension of the array QSTORE.
*> LDQS >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: The algorithm failed to compute an eigenvalue while
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
$ IWORK, INFO )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER INFO, LDQ, LDQS, N, QSIZ
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
REAL D( * ), E( * ), RWORK( * )
COMPLEX Q( LDQ, * ), QSTORE( LDQS, * )
* ..
*
* =====================================================================
*
* Warning: N could be as big as QSIZ!
*
* .. Parameters ..
REAL TWO
PARAMETER ( TWO = 2.E+0 )
* ..
* .. Local Scalars ..
INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
$ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
$ J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1,
$ SPM1, SPM2, SUBMAT, SUBPBS, TLVLS
REAL TEMP
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CLACRM, CLAED7, SCOPY, SSTEQR, XERBLA
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, INT, LOG, MAX, REAL
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
*
* IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN
* INFO = -1
* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) )
* $ THEN
IF( QSIZ.LT.MAX( 0, N ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLAED0', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
SMLSIZ = ILAENV( 9, 'CLAED0', ' ', 0, 0, 0, 0 )
*
* Determine the size and placement of the submatrices, and save in
* the leading elements of IWORK.
*
IWORK( 1 ) = N
SUBPBS = 1
TLVLS = 0
10 CONTINUE
IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN
DO 20 J = SUBPBS, 1, -1
IWORK( 2*J ) = ( IWORK( J )+1 ) / 2
IWORK( 2*J-1 ) = IWORK( J ) / 2
20 CONTINUE
TLVLS = TLVLS + 1
SUBPBS = 2*SUBPBS
GO TO 10
END IF
DO 30 J = 2, SUBPBS
IWORK( J ) = IWORK( J ) + IWORK( J-1 )
30 CONTINUE
*
* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
* using rank-1 modifications (cuts).
*
SPM1 = SUBPBS - 1
DO 40 I = 1, SPM1
SUBMAT = IWORK( I ) + 1
SMM1 = SUBMAT - 1
D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) )
D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) )
40 CONTINUE
*
INDXQ = 4*N + 3
*
* Set up workspaces for eigenvalues only/accumulate new vectors
* routine
*
TEMP = LOG( REAL( N ) ) / LOG( TWO )
LGN = INT( TEMP )
IF( 2**LGN.LT.N )
$ LGN = LGN + 1
IF( 2**LGN.LT.N )
$ LGN = LGN + 1
IPRMPT = INDXQ + N + 1
IPERM = IPRMPT + N*LGN
IQPTR = IPERM + N*LGN
IGIVPT = IQPTR + N + 2
IGIVCL = IGIVPT + N*LGN
*
IGIVNM = 1
IQ = IGIVNM + 2*N*LGN
IWREM = IQ + N**2 + 1
* Initialize pointers
DO 50 I = 0, SUBPBS
IWORK( IPRMPT+I ) = 1
IWORK( IGIVPT+I ) = 1
50 CONTINUE
IWORK( IQPTR ) = 1
*
* Solve each submatrix eigenproblem at the bottom of the divide and
* conquer tree.
*
CURR = 0
DO 70 I = 0, SPM1
IF( I.EQ.0 ) THEN
SUBMAT = 1
MATSIZ = IWORK( 1 )
ELSE
SUBMAT = IWORK( I ) + 1
MATSIZ = IWORK( I+1 ) - IWORK( I )
END IF
LL = IQ - 1 + IWORK( IQPTR+CURR )
CALL SSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
$ RWORK( LL ), MATSIZ, RWORK, INFO )
CALL CLACRM( QSIZ, MATSIZ, Q( 1, SUBMAT ), LDQ, RWORK( LL ),
$ MATSIZ, QSTORE( 1, SUBMAT ), LDQS,
$ RWORK( IWREM ) )
IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2
CURR = CURR + 1
IF( INFO.GT.0 ) THEN
INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
RETURN
END IF
K = 1
DO 60 J = SUBMAT, IWORK( I+1 )
IWORK( INDXQ+J ) = K
K = K + 1
60 CONTINUE
70 CONTINUE
*
* Successively merge eigensystems of adjacent submatrices
* into eigensystem for the corresponding larger matrix.
*
* while ( SUBPBS > 1 )
*
CURLVL = 1
80 CONTINUE
IF( SUBPBS.GT.1 ) THEN
SPM2 = SUBPBS - 2
DO 90 I = 0, SPM2, 2
IF( I.EQ.0 ) THEN
SUBMAT = 1
MATSIZ = IWORK( 2 )
MSD2 = IWORK( 1 )
CURPRB = 0
ELSE
SUBMAT = IWORK( I ) + 1
MATSIZ = IWORK( I+2 ) - IWORK( I )
MSD2 = MATSIZ / 2
CURPRB = CURPRB + 1
END IF
*
* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
* into an eigensystem of size MATSIZ. CLAED7 handles the case
* when the eigenvectors of a full or band Hermitian matrix (which
* was reduced to tridiagonal form) are desired.
*
* I am free to use Q as a valuable working space until Loop 150.
*
CALL CLAED7( MATSIZ, MSD2, QSIZ, TLVLS, CURLVL, CURPRB,
$ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS,
$ E( SUBMAT+MSD2-1 ), IWORK( INDXQ+SUBMAT ),
$ RWORK( IQ ), IWORK( IQPTR ), IWORK( IPRMPT ),
$ IWORK( IPERM ), IWORK( IGIVPT ),
$ IWORK( IGIVCL ), RWORK( IGIVNM ),
$ Q( 1, SUBMAT ), RWORK( IWREM ),
$ IWORK( SUBPBS+1 ), INFO )
IF( INFO.GT.0 ) THEN
INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
RETURN
END IF
IWORK( I / 2+1 ) = IWORK( I+2 )
90 CONTINUE
SUBPBS = SUBPBS / 2
CURLVL = CURLVL + 1
GO TO 80
END IF
*
* end while
*
* Re-merge the eigenvalues/vectors which were deflated at the final
* merge step.
*
DO 100 I = 1, N
J = IWORK( INDXQ+I )
RWORK( I ) = D( J )
CALL CCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
100 CONTINUE
CALL SCOPY( N, RWORK, 1, D, 1 )
*
RETURN
*
* End of CLAED0
*
END
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