*
*
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