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SUBROUTINE PDSYEVD( JOBZ, UPLO, N, A, IA, JA, DESCA, W, Z, IZ, JZ,
$ DESCZ, WORK, LWORK, IWORK, LIWORK, INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* March 14, 2000
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER IA, INFO, IZ, JA, JZ, LIWORK, LWORK, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCZ( * ), IWORK( * )
DOUBLE PRECISION A( * ), W( * ), WORK( * ), Z( * )
* ..
*
* Purpose
* =======
*
* PDSYEVD computes all the eigenvalues and eigenvectors
* of a real symmetric matrix A by calling the recommended sequence
* of ScaLAPACK routines.
*
* In its present form, PDSYEVD assumes a homogeneous system and makes
* no checks for consistency of the eigenvalues or eigenvectors across
* the different processes. Because of this, it is possible that a
* heterogeneous system may return incorrect results without any error
* messages.
*
* Arguments
* =========
*
* NP = the number of rows local to a given process.
* NQ = the number of columns local to a given process.
*
* JOBZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only; (NOT IMPLEMENTED YET)
* = 'V': Compute eigenvalues and eigenvectors.
*
* UPLO (global input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (global input) INTEGER
* The number of rows and columns to be operated on, i.e. the
* order of the distributed submatrix sub( A ). N >= 0.
*
* A (local input/workspace) block cyclic DOUBLE PRECISION array,
* global dimension (N, N), local dimension ( LLD_A,
* LOCc(JA+N-1) )
* On entry, the symmetric matrix A. If UPLO = 'U', only the
* upper triangular part of A is used to define the elements of
* the symmetric matrix. If UPLO = 'L', only the lower
* triangular part of A is used to define the elements of the
* symmetric matrix.
* On exit, the lower triangle (if UPLO='L') or the upper
* triangle (if UPLO='U') of A, including the diagonal, is
* destroyed.
*
* IA (global input) INTEGER
* A's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JA (global input) INTEGER
* A's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* W (global output) DOUBLE PRECISION array, dimension (N)
* If INFO=0, the eigenvalues in ascending order.
*
* Z (local output) DOUBLE PRECISION array,
* global dimension (N, N),
* local dimension ( LLD_Z, LOCc(JZ+N-1) )
* Z contains the orthonormal eigenvectors
* of the symmetric matrix A.
*
* IZ (global input) INTEGER
* Z's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JZ (global input) INTEGER
* Z's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCZ (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix Z.
* DESCZ( CTXT_ ) must equal DESCA( CTXT_ )
*
* WORK (local workspace/output) DOUBLE PRECISION array,
* dimension (LWORK)
* On output, WORK(1) returns the workspace required.
*
* LWORK (local input) INTEGER
* LWORK >= MAX( 1+6*N+2*NP*NQ, TRILWMIN ) + 2*N
* TRILWMIN = 3*N + MAX( NB*( NP+1 ), 3*NB )
* NP = NUMROC( N, NB, MYROW, IAROW, NPROW )
* NQ = NUMROC( N, NB, MYCOL, IACOL, NPCOL )
*
* If LWORK = -1, the LWORK is global input and a workspace
* query is assumed; the routine only calculates the minimum
* size for the WORK array. The required workspace is returned
* as the first element of WORK and no error message is issued
* by PXERBLA.
*
* IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
* On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK.
* LIWORK = 7*N + 8*NPCOL + 2
*
* INFO (global output) INTEGER
* = 0: successful exit
* < 0: If the i-th argument is an array and the j-entry had
* an illegal value, then INFO = -(i*100+j), if the i-th
* argument is a scalar and had an illegal value, then
* INFO = -i.
* > 0: The algorithm failed to compute the INFO/(N+1) th
* eigenvalue while working on the submatrix lying in
* global rows and columns mod(INFO,N+1).
*
* Alignment requirements
* ======================
*
* The distributed submatrices sub( A ), sub( Z ) must verify
* some alignment properties, namely the following expression
* should be true:
* ( MB_A.EQ.NB_A.EQ.MB_Z.EQ.NB_Z .AND. IROFFA.EQ.ICOFFA .AND.
* IROFFA.EQ.0 .AND.IROFFA.EQ.IROFFZ. AND. IAROW.EQ.IZROW)
* with IROFFA = MOD( IA-1, MB_A )
* and ICOFFA = MOD( JA-1, NB_A ).
*
* Further Details
* ======= =======
*
* Contributed by Francoise Tisseur, University of Manchester.
*
* Reference: F. Tisseur and J. Dongarra, "A Parallel Divide and
* Conquer Algorithm for the Symmetric Eigenvalue Problem
* on Distributed Memory Architectures",
* SIAM J. Sci. Comput., 6:20 (1999), pp. 2223--2236.
* (see also LAPACK Working Note 132)
* http://www.netlib.org/lapack/lawns/lawn132.ps
*
* =====================================================================
*
* .. Parameters ..
*
INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY, UPPER
INTEGER IACOL, IAROW, ICOFFA, ICOFFZ, ICTXT, IINFO,
$ INDD, INDE, INDE2, INDTAU, INDWORK, INDWORK2,
$ IROFFA, IROFFZ, ISCALE, LIWMIN, LLWORK,
$ LLWORK2, LWMIN, MYCOL, MYROW, NB, NP, NPCOL,
$ NPROW, NQ, OFFSET, TRILWMIN
DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. Local Arrays ..
* ..
INTEGER IDUM1( 2 ), IDUM2( 2 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER INDXG2P, NUMROC
DOUBLE PRECISION PDLAMCH, PDLANSY
EXTERNAL LSAME, INDXG2P, NUMROC, PDLAMCH, PDLANSY
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, DSCAL, PCHK1MAT,
$ PDLARED1D, PDLASCL, PDLASET, PDORMTR, PDSTEDC,
$ PDSYTRD, PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, ICHAR, MAX, MIN, MOD, SQRT
* ..
* .. Executable Statements ..
* This is just to keep ftnchek and toolpack/1 happy
IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
$ RSRC_.LT.0 )RETURN
*
* Quick return
*
IF( N.EQ.0 )
$ RETURN
*
* Test the input arguments.
*
ICTXT = DESCZ( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -( 600+CTXT_ )
ELSE
CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO )
CALL CHK1MAT( N, 3, N, 3, IZ, JZ, DESCZ, 12, INFO )
IF( INFO.EQ.0 ) THEN
UPPER = LSAME( UPLO, 'U' )
NB = DESCA( NB_ )
IROFFA = MOD( IA-1, DESCA( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
IROFFZ = MOD( IZ-1, DESCZ( MB_ ) )
ICOFFZ = MOD( JZ-1, DESCZ( NB_ ) )
IAROW = INDXG2P( IA, NB, MYROW, DESCA( RSRC_ ), NPROW )
IACOL = INDXG2P( JA, NB, MYCOL, DESCA( CSRC_ ), NPCOL )
NP = NUMROC( N, NB, MYROW, IAROW, NPROW )
NQ = NUMROC( N, NB, MYCOL, IACOL, NPCOL )
*
LQUERY = ( LWORK.EQ.-1 )
TRILWMIN = 3*N + MAX( NB*( NP+1 ), 3*NB )
LWMIN = MAX( 1+6*N+2*NP*NQ, TRILWMIN ) + 2*N
LIWMIN = 7*N + 8*NPCOL + 2
WORK( 1 ) = DBLE( LWMIN )
IWORK( 1 ) = LIWMIN
IF( .NOT.LSAME( JOBZ, 'V' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( IROFFA.NE.ICOFFA .OR. ICOFFA.NE.0 ) THEN
INFO = -6
ELSE IF( IROFFA.NE.IROFFZ .OR. ICOFFA.NE.ICOFFZ ) THEN
INFO = -10
ELSE IF( DESCA( M_ ).NE.DESCZ( M_ ) ) THEN
INFO = -( 1200+M_ )
ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -( 700+NB_ )
ELSE IF( DESCZ( MB_ ).NE.DESCZ( NB_ ) ) THEN
INFO = -( 1200+NB_ )
ELSE IF( DESCA( MB_ ).NE.DESCZ( MB_ ) ) THEN
INFO = -( 1200+MB_ )
ELSE IF( DESCA( CTXT_ ).NE.DESCZ( CTXT_ ) ) THEN
INFO = -( 1200+CTXT_ )
ELSE IF( DESCA( RSRC_ ).NE.DESCZ( RSRC_ ) ) THEN
INFO = -( 1200+RSRC_ )
ELSE IF( DESCA( CSRC_ ).NE.DESCZ( CSRC_ ) ) THEN
INFO = -( 1200+CSRC_ )
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -14
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -16
END IF
END IF
IF( UPPER ) THEN
IDUM1( 1 ) = ICHAR( 'U' )
ELSE
IDUM1( 1 ) = ICHAR( 'L' )
END IF
IDUM2( 1 ) = 2
IF( LWORK.EQ.-1 ) THEN
IDUM1( 2 ) = -1
ELSE
IDUM1( 2 ) = 1
END IF
IDUM2( 2 ) = 14
CALL PCHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, 2, IDUM1, IDUM2,
$ INFO )
END IF
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PDSYEVD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Set up pointers into the WORK array
*
INDTAU = 1
INDE = INDTAU + N
INDD = INDE + N
INDE2 = INDD + N
INDWORK = INDE2 + N
LLWORK = LWORK - INDWORK + 1
INDWORK2 = INDD
LLWORK2 = LWORK - INDWORK2 + 1
*
* Scale matrix to allowable range, if necessary.
*
ISCALE = 0
SAFMIN = PDLAMCH( DESCA( CTXT_ ), 'Safe minimum' )
EPS = PDLAMCH( DESCA( CTXT_ ), 'Precision' )
SMLNUM = SAFMIN / EPS
BIGNUM = ONE / SMLNUM
RMIN = SQRT( SMLNUM )
RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
ANRM = PDLANSY( 'M', UPLO, N, A, IA, JA, DESCA, WORK( INDWORK ) )
*
IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / ANRM
ELSE IF( ANRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / ANRM
END IF
*
IF( ISCALE.EQ.1 ) THEN
CALL PDLASCL( UPLO, ONE, SIGMA, N, N, A, IA, JA, DESCA, IINFO )
END IF
*
* Reduce symmetric matrix to tridiagonal form.
*
*
CALL PDSYTRD( UPLO, N, A, IA, JA, DESCA, WORK( INDD ),
$ WORK( INDE2 ), WORK( INDTAU ), WORK( INDWORK ),
$ LLWORK, IINFO )
*
* Copy the values of D, E to all processes.
*
CALL PDLARED1D( N, IA, JA, DESCA, WORK( INDD ), W,
$ WORK( INDWORK ), LLWORK )
*
CALL PDLARED1D( N, IA, JA, DESCA, WORK( INDE2 ), WORK( INDE ),
$ WORK( INDWORK ), LLWORK )
*
CALL PDLASET( 'Full', N, N, ZERO, ONE, Z, 1, 1, DESCZ )
*
IF( UPPER ) THEN
OFFSET = 1
ELSE
OFFSET = 0
END IF
CALL PDSTEDC( 'I', N, W, WORK( INDE+OFFSET ), Z, IZ, JZ, DESCZ,
$ WORK( INDWORK2 ), LLWORK2, IWORK, LIWORK, INFO )
*
CALL PDORMTR( 'L', UPLO, 'N', N, N, A, IA, JA, DESCA,
$ WORK( INDTAU ), Z, IZ, JZ, DESCZ, WORK( INDWORK2 ),
$ LLWORK2, IINFO )
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 ) THEN
CALL DSCAL( N, ONE / SIGMA, W, 1 )
END IF
*
RETURN
*
* End of PDSYEVD
*
END
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