SUBROUTINE PDSYNGST( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, $ DESCB, SCALE, WORK, LWORK, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * October 15, 1999 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER IA, IB, IBTYPE, INFO, JA, JB, LWORK, N DOUBLE PRECISION SCALE * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ) DOUBLE PRECISION A( * ), B( * ), WORK( * ) * .. * * Purpose * * ======= * * PDSYNGST reduces a complex Hermitian-definite generalized * eigenproblem to standard form. * * PDSYNGST performs the same function as PDHEGST, but is based on * rank 2K updates, which are faster and more scalable than * triangular solves (the basis of PDSYNGST). * * PDSYNGST calls PDHEGST when UPLO='U', hence PDHENGST provides * improved performance only when UPLO='L', IBTYPE=1. * * PDSYNGST also calls PDHEGST when insufficient workspace is * provided, hence PDSYNGST provides improved * performance only when LWORK >= 2 * NP0 * NB + NQ0 * NB + NB * NB * * In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and * sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). * * If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, * and sub( A ) is overwritten by inv(U**H)*sub( A )*inv(U) or * inv(L)*sub( A )*inv(L**H) * * If IBTYPE = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or * sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by * U*sub( A )*U**H or L**H*sub( A )*L. * * sub( B ) must have been previously factorized as U**H*U or L*L**H by * PDPOTRF. * * Notes * ===== * * Each global data object is described by an associated description * vector. This vector stores the information required to establish * the mapping between an object element and its corresponding process * and memory location. * * Let A be a generic term for any 2D block cyclicly distributed array. * Such a global array has an associated description vector DESCA. * In the following comments, the character _ should be read as * "of the global array". * * NOTATION STORED IN EXPLANATION * --------------- -------------- -------------------------------------- * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, * DTYPE_A = 1. * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating * the BLACS process grid A is distribu- * ted over. The context itself is glo- * bal, but the handle (the integer * value) may vary. * M_A (global) DESCA( M_ ) The number of rows in the global * array A. * N_A (global) DESCA( N_ ) The number of columns in the global * array A. * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute * the rows of the array. * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute * the columns of the array. * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first * row of the array A is distributed. * CSRC_A (global) DESCA( CSRC_ ) The process column over which the * first column of the array A is * distributed. * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local * array. LLD_A >= MAX(1,LOCr(M_A)). * * Let K be the number of rows or columns of a distributed matrix, * and assume that its process grid has dimension p x q. * LOCr( K ) denotes the number of elements of K that a process * would receive if K were distributed over the p processes of its * process column. * Similarly, LOCc( K ) denotes the number of elements of K that a * process would receive if K were distributed over the q processes of * its process row. * The values of LOCr() and LOCc() may be determined via a call to the * ScaLAPACK tool function, NUMROC: * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). * An upper bound for these quantities may be computed by: * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A * * Arguments * ========= * * IBTYPE (global input) INTEGER * = 1: compute inv(U**H)*sub( A )*inv(U) or * inv(L)*sub( A )*inv(L**H); * = 2 or 3: compute U*sub( A )*U**H or L**H*sub( A )*L. * * UPLO (global input) CHARACTER * = 'U': Upper triangle of sub( A ) is stored and sub( B ) is * factored as U**H*U; * = 'L': Lower triangle of sub( A ) is stored and sub( B ) is * factored as L*L**H. * * N (global input) INTEGER * The order of the matrices sub( A ) and sub( B ). N >= 0. * * A (local input/local output) DOUBLE PRECISION pointer into the * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). * On entry, this array contains the local pieces of the * N-by-N Hermitian distributed matrix sub( A ). If UPLO = 'U', * the leading N-by-N upper triangular part of sub( A ) contains * the upper triangular part of the matrix, and its strictly * lower triangular part is not referenced. If UPLO = 'L', the * leading N-by-N lower triangular part of sub( A ) contains * the lower triangular part of the matrix, and its strictly * upper triangular part is not referenced. * * On exit, if INFO = 0, the transformed matrix, stored in the * same format as sub( A ). * * 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. * * B (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry, * this array contains the local pieces of the triangular factor * from the Cholesky factorization of sub( B ), as returned by * PDPOTRF. * * IB (global input) INTEGER * B's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JB (global input) INTEGER * B's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCB (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix B. * * SCALE (global output) DOUBLE PRECISION * Amount by which the eigenvalues should be scaled to * compensate for the scaling performed in this routine. * At present, SCALE is always returned as 1.0, it is * returned here to allow for future enhancement. * * WORK (local workspace/local output) DOUBLE PRECISION array, * dimension (LWORK) * On exit, WORK( 1 ) returns the minimal and optimal LWORK. * * LWORK (local or global input) INTEGER * The dimension of the array WORK. * LWORK is local input and must be at least * LWORK >= MAX( NB * ( NP0 +1 ), 3 * NB ) * * When IBTYPE = 1 and UPLO = 'L', PDSYNGST provides improved * performance when LWORK >= 2 * NP0 * NB + NQ0 * NB + NB * NB * * where NB = MB_A = NB_A, * NP0 = NUMROC( N, NB, 0, 0, NPROW ), * NQ0 = NUMROC( N, NB, 0, 0, NPROW ), * * NUMROC ia a ScaLAPACK tool functions * MYROW, MYCOL, NPROW and NPCOL can be determined by calling * the subroutine BLACS_GRIDINFO. * * If LWORK = -1, then LWORK is global input and a workspace * query is assumed; the routine only calculates the * optimal size for all work arrays. Each of these * values is returned in the first entry of the corresponding * work array, and no error message is issued by PXERBLA. * * 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. * * ===================================================================== * * * * .. Parameters .. DOUBLE PRECISION ONEHALF, ONE, MONE PARAMETER ( ONEHALF = 0.5D0, ONE = 1.0D0, MONE = -1.0D0 ) INTEGER DLEN_, CTXT_, MB_, NB_, RSRC_, CSRC_, LLD_ PARAMETER ( DLEN_ = 9, CTXT_ = 2, MB_ = 5, NB_ = 6, $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER INTEGER I, IACOL, IAROW, IBCOL, IBROW, ICOFFA, ICOFFB, $ ICTXT, INDAA, INDG, INDR, INDRT, IROFFA, $ IROFFB, J, K, KB, LWMIN, LWOPT, MYCOL, MYROW, $ NB, NP0, NPCOL, NPK, NPROW, NQ0, POSTK * .. * .. Local Arrays .. INTEGER DESCAA( DLEN_ ), DESCG( DLEN_ ), $ DESCR( DLEN_ ), DESCRT( DLEN_ ), IDUM1( 2 ), $ IDUM2( 2 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER INDXG2P, NUMROC EXTERNAL LSAME, INDXG2P, NUMROC * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, DESCSET, PCHK2MAT, $ PDGEMM, PDLACPY, PDSYGST, PDSYMM, PDSYR2K, $ PDTRSM, PXERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, ICHAR, MAX, MIN, MOD * .. * .. Executable Statements .. ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) SCALE = 1.0D0 * NB = DESCA( MB_ ) * * * Test the input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -( 700+CTXT_ ) ELSE UPPER = LSAME( UPLO, 'U' ) CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO ) CALL CHK1MAT( N, 3, N, 3, IB, JB, DESCB, 11, INFO ) IF( INFO.EQ.0 ) THEN IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ), $ NPROW ) IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), $ NPCOL ) IBCOL = INDXG2P( JB, DESCB( NB_ ), MYCOL, DESCB( CSRC_ ), $ NPCOL ) IROFFA = MOD( IA-1, DESCA( MB_ ) ) ICOFFA = MOD( JA-1, DESCA( NB_ ) ) IROFFB = MOD( IB-1, DESCB( MB_ ) ) ICOFFB = MOD( JB-1, DESCB( NB_ ) ) NP0 = NUMROC( N, NB, 0, 0, NPROW ) NQ0 = NUMROC( N, NB, 0, 0, NPCOL ) LWMIN = MAX( NB*( NP0+1 ), 3*NB ) IF( IBTYPE.EQ.1 .AND. .NOT.UPPER ) THEN LWOPT = 2*NP0*NB + NQ0*NB + NB*NB ELSE LWOPT = LWMIN END IF WORK( 1 ) = DBLE( LWOPT ) LQUERY = ( LWORK.EQ.-1 ) IF( IBTYPE.LT.1 .OR. IBTYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( IROFFA.NE.0 ) THEN INFO = -5 ELSE IF( ICOFFA.NE.0 ) THEN INFO = -6 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -( 700+NB_ ) ELSE IF( IROFFB.NE.0 .OR. IBROW.NE.IAROW ) THEN INFO = -9 ELSE IF( ICOFFB.NE.0 .OR. IBCOL.NE.IACOL ) THEN INFO = -10 ELSE IF( DESCB( MB_ ).NE.DESCA( MB_ ) ) THEN INFO = -( 1100+MB_ ) ELSE IF( DESCB( NB_ ).NE.DESCA( NB_ ) ) THEN INFO = -( 1100+NB_ ) ELSE IF( ICTXT.NE.DESCB( CTXT_ ) ) THEN INFO = -( 1100+CTXT_ ) ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -13 END IF END IF IDUM1( 1 ) = IBTYPE IDUM2( 1 ) = 1 IF( UPPER ) THEN IDUM1( 2 ) = ICHAR( 'U' ) ELSE IDUM1( 2 ) = ICHAR( 'L' ) END IF IDUM2( 2 ) = 2 CALL PCHK2MAT( N, 3, N, 3, IA, JA, DESCA, 7, N, 3, N, 3, IB, $ JB, DESCB, 11, 2, IDUM1, IDUM2, INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PDSYNGST', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * IF( IBTYPE.NE.1 .OR. UPPER .OR. LWORK.LT.LWOPT ) THEN CALL PDSYGST( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, $ DESCB, SCALE, INFO ) RETURN END IF * CALL DESCSET( DESCG, N, NB, NB, NB, IAROW, IACOL, ICTXT, NP0 ) CALL DESCSET( DESCR, N, NB, NB, NB, IAROW, IACOL, ICTXT, NP0 ) CALL DESCSET( DESCRT, NB, N, NB, NB, IAROW, IACOL, ICTXT, NB ) CALL DESCSET( DESCAA, NB, NB, NB, NB, IAROW, IACOL, ICTXT, NB ) * INDG = 1 INDR = INDG + DESCG( LLD_ )*NB INDAA = INDR + DESCR( LLD_ )*NB INDRT = INDAA + DESCAA( LLD_ )*NB * DO 30 K = 1, N, NB * KB = MIN( N-K+1, NB ) POSTK = K + KB NPK = N - POSTK + 1 * * CALL PDLACPY( 'A', N-POSTK+1, KB, B, POSTK+IB-1, K+JB-1, DESCB, $ WORK( INDG ), POSTK, 1, DESCG ) CALL PDLACPY( 'A', N-POSTK+1, KB, A, POSTK+IA-1, K+JA-1, DESCA, $ WORK( INDR ), POSTK, 1, DESCR ) CALL PDLACPY( 'A', KB, K-1, A, K+IA-1, JA, DESCA, $ WORK( INDRT ), 1, 1, DESCRT ) * CALL PDLACPY( 'L', KB, KB, A, K+IA-1, K+JA-1, DESCA, $ WORK( INDR ), K, 1, DESCR ) CALL PDTRSM( 'Right', 'L', 'N', 'N', NPK, KB, MONE, B, K+IB-1, $ K+JB-1, DESCB, WORK( INDG ), POSTK, 1, DESCG ) * CALL PDSYMM( 'Right', 'L', NPK, KB, ONEHALF, A, K+IA-1, K+JA-1, $ DESCA, WORK( INDG ), POSTK, 1, DESCG, ONE, $ WORK( INDR ), POSTK, 1, DESCR ) * CALL PDSYR2K( 'Lower', 'No T', NPK, KB, ONE, WORK( INDG ), $ POSTK, 1, DESCG, WORK( INDR ), POSTK, 1, DESCR, $ ONE, A, POSTK+IA-1, POSTK+JA-1, DESCA ) * CALL PDGEMM( 'No T', 'No Conj', NPK, K-1, KB, ONE, $ WORK( INDG ), POSTK, 1, DESCG, WORK( INDRT ), 1, $ 1, DESCRT, ONE, A, POSTK+IA-1, JA, DESCA ) * CALL PDSYMM( 'Right', 'L', NPK, KB, ONE, WORK( INDR ), K, 1, $ DESCR, WORK( INDG ), POSTK, 1, DESCG, ONE, A, $ POSTK+IA-1, K+JA-1, DESCA ) * CALL PDTRSM( 'Left', 'Lower', 'No Conj', 'Non-unit', KB, K-1, $ ONE, B, K+IB-1, K+JB-1, DESCB, A, K+IA-1, JA, $ DESCA ) * CALL PDLACPY( 'L', KB, KB, A, K+IA-1, K+JA-1, DESCA, $ WORK( INDAA ), 1, 1, DESCAA ) * IF( MYROW.EQ.DESCAA( RSRC_ ) .AND. MYCOL.EQ.DESCAA( CSRC_ ) ) $ THEN DO 20 I = 1, KB DO 10 J = 1, I WORK( INDAA+J-1+( I-1 )*DESCAA( LLD_ ) ) $ = WORK( INDAA+I-1+( J-1 )*DESCAA( LLD_ ) ) 10 CONTINUE 20 CONTINUE END IF * CALL PDTRSM( 'Left', 'Lower', 'No Conj', 'Non-unit', KB, KB, $ ONE, B, K+IB-1, K+JB-1, DESCB, WORK( INDAA ), 1, $ 1, DESCAA ) * CALL PDTRSM( 'Right', 'Lower', 'Conj', 'Non-unit', KB, KB, ONE, $ B, K+IB-1, K+JB-1, DESCB, WORK( INDAA ), 1, 1, $ DESCAA ) * CALL PDLACPY( 'L', KB, KB, WORK( INDAA ), 1, 1, DESCAA, A, $ K+IA-1, K+JA-1, DESCA ) * CALL PDTRSM( 'Right', 'Lower', 'Conj', 'Non-unit', NPK, KB, $ ONE, B, K+IB-1, K+JB-1, DESCB, A, POSTK+IA-1, $ K+JA-1, DESCA ) * DESCR( CSRC_ ) = MOD( DESCR( CSRC_ )+1, NPCOL ) DESCG( CSRC_ ) = MOD( DESCG( CSRC_ )+1, NPCOL ) DESCRT( RSRC_ ) = MOD( DESCRT( RSRC_ )+1, NPROW ) DESCAA( RSRC_ ) = MOD( DESCAA( RSRC_ )+1, NPROW ) DESCAA( CSRC_ ) = MOD( DESCAA( CSRC_ )+1, NPCOL ) 30 CONTINUE * WORK( 1 ) = DBLE( LWOPT ) * RETURN END