* * SUBROUTINE PCHEGS2( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, $ DESCB, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER IA, IB, IBTYPE, INFO, JA, JB, N * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ) COMPLEX A( * ), B( * ) * .. * * Purpose * ======= * * PCHEGS2 reduces a complex Hermitian-definite generalized eigenproblem * to standard form. * * 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 * PCPOTRF. * * 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) COMPLEX 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) COMPLEX 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 * PCPOTRF. * * 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. * * 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 .. 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 ONE, HALF PARAMETER ( ONE = 1.0E+0, HALF = 0.5E+0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER IACOL, IAROW, IBCOL, IBROW, ICOFFA, ICOFFB, $ ICTXT, IIA, IIB, IOFFA, IOFFB, IROFFA, IROFFB, $ JJA, JJB, K, LDA, LDB, MYCOL, MYROW, NPCOL, $ NPROW REAL AKK, BKK COMPLEX CT * .. * .. External Subroutines .. EXTERNAL BLACS_EXIT, BLACS_GRIDINFO, CAXPY, CHER2, $ CHK1MAT, CLACGV, CSSCAL, CTRMV, CTRSV, INFOG2L, $ PXERBLA * .. * .. Intrinsic Functions .. INTRINSIC MOD, REAL * .. * .. External Functions .. LOGICAL LSAME INTEGER INDXG2P EXTERNAL LSAME, INDXG2P * .. * .. Executable Statements .. * This is just to keep ftnchek happy IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* $ RSRC_.LT.0 )RETURN * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * 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_ ) ) 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( N+ICOFFA.GT.DESCA( NB_ ) ) 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_ ) END IF END IF END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PCHEGS2', -INFO ) CALL BLACS_EXIT( ICTXT ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. ( MYROW.NE.IAROW .OR. MYCOL.NE.IACOL ) ) $ RETURN * * Compute local information * LDA = DESCA( LLD_ ) LDB = DESCB( LLD_ ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIB, JJB, $ IBROW, IBCOL ) * IF( IBTYPE.EQ.1 ) THEN * IF( UPPER ) THEN * IOFFA = IIA + JJA*LDA IOFFB = IIB + JJB*LDB * * Compute inv(U')*sub( A )*inv(U) * DO 10 K = 1, N * * Update the upper triangle of * A(ia+k-1:ia+n-a,ia+k-1:ia+n-1) * AKK = REAL( A( IOFFA-LDA ) ) BKK = REAL( B( IOFFB-LDB ) ) AKK = AKK / BKK**2 A( IOFFA-LDA ) = AKK IF( K.LT.N ) THEN CALL CSSCAL( N-K, ONE / BKK, A( IOFFA ), LDA ) CT = -HALF*AKK CALL CLACGV( N-K, A( IOFFA ), LDA ) CALL CLACGV( N-K, B( IOFFB ), LDB ) CALL CAXPY( N-K, CT, B( IOFFB ), LDB, A( IOFFA ), $ LDA ) CALL CHER2( UPLO, N-K, -CONE, A( IOFFA ), LDA, $ B( IOFFB ), LDB, A( IOFFA+1 ), LDA ) CALL CAXPY( N-K, CT, B( IOFFB ), LDB, A( IOFFA ), $ LDA ) CALL CLACGV( N-K, B( IOFFB ), LDB ) CALL CTRSV( UPLO, 'Conjugate transpose', 'Non-unit', $ N-K, B( IOFFB+1 ), LDB, A( IOFFA ), LDA ) CALL CLACGV( N-K, A( IOFFA ), LDA ) END IF * * A( IOFFA ) -> A( K, K+1 ) * B( IOFFB ) -> B( K, K+1 ) * IOFFA = IOFFA + LDA + 1 IOFFB = IOFFB + LDB + 1 * 10 CONTINUE * ELSE * IOFFA = IIA + 1 + ( JJA-1 )*LDA IOFFB = IIB + 1 + ( JJB-1 )*LDB * * Compute inv(L)*sub( A )*inv(L') * DO 20 K = 1, N * * Update the lower triangle of * A(ia+k-1:ia+n-a,ia+k-1:ia+n-1) * AKK = REAL( A( IOFFA-1 ) ) BKK = REAL( B( IOFFB-1 ) ) AKK = AKK / BKK**2 A( IOFFA-1 ) = AKK * IF( K.LT.N ) THEN CALL CSSCAL( N-K, ONE / BKK, A( IOFFA ), 1 ) CT = -HALF*AKK CALL CAXPY( N-K, CT, B( IOFFB ), 1, A( IOFFA ), 1 ) CALL CHER2( UPLO, N-K, -CONE, A( IOFFA ), 1, $ B( IOFFB ), 1, A( IOFFA+LDA ), LDA ) CALL CAXPY( N-K, CT, B( IOFFB ), 1, A( IOFFA ), 1 ) CALL CTRSV( UPLO, 'No transpose', 'Non-unit', N-K, $ B( IOFFB+LDB ), LDB, A( IOFFA ), 1 ) END IF * * A( IOFFA ) -> A( K+1, K ) * B( IOFFB ) -> B( K+1, K ) * IOFFA = IOFFA + LDA + 1 IOFFB = IOFFB + LDB + 1 * 20 CONTINUE * END IF * ELSE * IF( UPPER ) THEN * IOFFA = IIA + ( JJA-1 )*LDA IOFFB = IIB + ( JJB-1 )*LDB * * Compute U*sub( A )*U' * DO 30 K = 1, N * * Update the upper triangle of A(ia:ia+k-1,ja:ja+k-1) * AKK = REAL( A( IOFFA+K-1 ) ) BKK = REAL( B( IOFFB+K-1 ) ) CALL CTRMV( UPLO, 'No transpose', 'Non-unit', K-1, $ B( IIB+( JJB-1 )*LDB ), LDB, A( IOFFA ), 1 ) CT = HALF*AKK CALL CAXPY( K-1, CT, B( IOFFB ), 1, A( IOFFA ), 1 ) CALL CHER2( UPLO, K-1, CONE, A( IOFFA ), 1, B( IOFFB ), $ 1, A( IIA+( JJA-1 )*LDA ), LDA ) CALL CAXPY( K-1, CT, B( IOFFB ), 1, A( IOFFA ), 1 ) CALL CSSCAL( K-1, BKK, A( IOFFA ), 1 ) A( IOFFA+K-1 ) = AKK*BKK**2 * * A( IOFFA ) -> A( 1, K ) * B( IOFFB ) -> B( 1, K ) * IOFFA = IOFFA + LDA IOFFB = IOFFB + LDB * 30 CONTINUE * ELSE * IOFFA = IIA + ( JJA-1 )*LDA IOFFB = IIB + ( JJB-1 )*LDB * * Compute L'*sub( A )*L * DO 40 K = 1, N * * Update the lower triangle of A(ia:ia+k-1,ja:ja+k-1) * AKK = REAL( A( IOFFA+( K-1 )*LDA ) ) BKK = REAL( B( IOFFB+( K-1 )*LDB ) ) CALL CLACGV( K-1, A( IOFFA ), LDA ) CALL CTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1, $ B( IIB+( JJB-1 )*LDB ), LDB, A( IOFFA ), $ LDA ) CT = HALF*AKK CALL CLACGV( K-1, B( IOFFB ), LDB ) CALL CAXPY( K-1, CT, B( IOFFB ), LDB, A( IOFFA ), LDA ) CALL CHER2( UPLO, K-1, CONE, A( IOFFA ), LDA, B( IOFFB ), $ LDB, A( IIA+( JJA-1 )*LDA ), LDA ) CALL CAXPY( K-1, CT, B( IOFFB ), LDB, A( IOFFA ), LDA ) CALL CLACGV( K-1, B( IOFFB ), LDB ) CALL CSSCAL( K-1, BKK, A( IOFFA ), LDA ) CALL CLACGV( K-1, A( IOFFA ), LDA ) A( IOFFA+( K-1 )*LDA ) = AKK*BKK**2 * * A( IOFFA ) -> A( K, 1 ) * B( IOFFB ) -> B( K, 1 ) * IOFFA = IOFFA + 1 IOFFB = IOFFB + 1 * 40 CONTINUE * END IF * END IF * RETURN * * End of PCHEGS2 * END