SUBROUTINE PSSYEVD( 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( * ) REAL A( * ), W( * ), WORK( * ), Z( * ) * .. * * Purpose * ======= * * PSSYEVD computes all the eigenvalues and eigenvectors * of a real symmetric matrix A by calling the recommended sequence * of ScaLAPACK routines. * * In its present form, PSSYEVD 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 REAL 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) REAL array, dimension (N) * If INFO=0, the eigenvalues in ascending order. * * Z (local output) REAL 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) REAL 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 ) REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+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 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. Local Arrays .. INTEGER IDUM1( 2 ), IDUM2( 2 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER INDXG2P, NUMROC REAL PSLAMCH, PSLANSY EXTERNAL LSAME, INDXG2P, NUMROC, PSLAMCH, PSLANSY * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PSLARED1D, \$ PSLASCL, PSLASET, PSORMTR, PSSTEDC, PSSYTRD, \$ PXERBLA, SSCAL * .. * .. Intrinsic Functions .. INTRINSIC ICHAR, MAX, MIN, MOD, REAL, 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. * CALL BLACS_GRIDINFO( DESCZ( CTXT_ ), 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 .OR. LIWORK.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 ) = REAL( 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, 'PSSYEVD', -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 = PSLAMCH( DESCA( CTXT_ ), 'Safe minimum' ) EPS = PSLAMCH( DESCA( CTXT_ ), 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) ANRM = PSLANSY( '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 PSLASCL( UPLO, ONE, SIGMA, N, N, A, IA, JA, DESCA, IINFO ) END IF * * Reduce symmetric matrix to tridiagonal form. * * CALL PSSYTRD( 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 PSLARED1D( N, IA, JA, DESCA, WORK( INDD ), W, \$ WORK( INDWORK ), LLWORK ) * CALL PSLARED1D( N, IA, JA, DESCA, WORK( INDE2 ), WORK( INDE ), \$ WORK( INDWORK ), LLWORK ) * CALL PSLASET( 'Full', N, N, ZERO, ONE, Z, 1, 1, DESCZ ) * IF( UPPER ) THEN OFFSET = 1 ELSE OFFSET = 0 END IF CALL PSSTEDC( 'I', N, W, WORK( INDE+OFFSET ), Z, IZ, JZ, DESCZ, \$ WORK( INDWORK2 ), LLWORK2, IWORK, LIWORK, INFO ) * CALL PSORMTR( '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 SSCAL( N, ONE / SIGMA, W, 1 ) END IF * RETURN * * End of PSSYEVD * END