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ft_pdpotrf.f90
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SUBROUTINE FT_PDPOTRF( UPLO, N, A, IA, JA, DESCA, INFO )
USE FTCHOL
IMPLICIT NONE
!
! -- ScaLAPACK routine (version 1.7) --
! University of Tennessee, Knoxville, Oak Ridge National Laboratory,
! and University of California, Berkeley.
! May 25, 2001
!
! .. Scalar Arguments ..
CHARACTER UPLO
INTEGER IA, INFO, JA, N
! ..
! .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION A( * )
! ..
!
! Purpose
! =======
!
! PDPOTRF computes the Cholesky factorization of an N-by-N real
! symmetric positive definite distributed matrix sub( A ) denoting
! A(IA:IA+N-1, JA:JA+N-1).
!
! The factorization has the form
!
! sub( A ) = U' * U , if UPLO = 'U', or
!
! sub( A ) = L * L', if UPLO = 'L',
!
! where U is an upper triangular matrix and L is lower triangular.
!
! 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
!
! This routine requires square block decomposition ( MB_A = NB_A ).
!
! Arguments
! =========
!
! UPLO (global input) CHARACTER
! = 'U': Upper triangle of sub( A ) is stored;
! = 'L': Lower triangle of sub( A ) is stored.
!
! 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/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 symmetric distributed matrix sub( A ) to be factored.
! 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 distribu-
! ted matrix, and its strictly upper triangular part is not
! referenced. On exit, if UPLO = 'U', the upper triangular
! part of the distributed matrix contains the Cholesky factor
! U, if UPLO = 'L', the lower triangular part of the distribu-
! ted matrix contains the Cholesky factor L.
!
! IA (global input) INTEGER
! The row index in the global array A indicating the first
! row of sub( A ).
!
! JA (global input) INTEGER
! The column index in the global array A indicating the
! first column of sub( A ).
!
! DESCA (global and local input) INTEGER array of dimension DLEN_.
! The array descriptor for the distributed matrix A.
!
! 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: If INFO = K, the leading minor of order K,
! A(IA:IA+K-1,JA:JA+K-1) is not positive definite, and
! the factorization could not be completed.
!
! =====================================================================
!
! .. Parameters ..
!INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, &
!& LLD_, MB_, M_, NB_, N_, RSRC_
!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 ONE
!PARAMETER ( ONE = 1.0D+0 )
! ..
! .. Local Scalars ..
LOGICAL UPPER
CHARACTER COLBTOP, ROWBTOP
INTEGER I, ICOFF, ICTXT, IROFF, J, JB, JN, MYCOL, &
& MYROW, NPCOL, NPROW
! ..
! .. Local Arrays ..
INTEGER IDUM1( 1 ), IDUM2( 1 )
! ..
! .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PB_TOPGET, &
& PB_TOPSET, PDPOTF2, PDSYRK, PDTRSM, &
& PXERBLA
! ..
! .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL
EXTERNAL ICEIL, LSAME
! ..
! .. Intrinsic Functions ..
INTRINSIC ICHAR, MIN, MOD
! ..
! .. FT variables ..
!
! ..
! .. Executable Statements ..
!
! 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 = -(600+CTXT_)
ELSE
CALL CHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, INFO )
UPPER = LSAME( UPLO, 'U' )
IF( INFO.EQ.0 ) THEN
IROFF = MOD( IA-1, DESCA( MB_ ) )
ICOFF = MOD( JA-1, DESCA( NB_ ) )
IF ( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( IROFF.NE.0 ) THEN
INFO = -4
ELSE IF( ICOFF.NE.0 ) THEN
INFO = -5
ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(600+NB_)
END IF
END IF
IF( UPPER ) THEN
IDUM1( 1 ) = ICHAR( 'U' )
ELSE
IDUM1( 1 ) = ICHAR( 'L' )
END IF
IDUM2( 1 ) = 1
CALL PCHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, 1, IDUM1, IDUM2, &
& INFO )
END IF
!
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PDPOTRF', -INFO )
RETURN
END IF
!
! Quick return if possible
!
IF( N.EQ.0 ) &
& RETURN
!
! Build the checksum matrices for A into AC and AR
!
!CALL RANDOM_NUMBER( CHKVEC )
!CHKVEC = CHKVEC / SUM( CHKVEC )
!SUBROUTINE DSYBC2(UPLO, A, DESCA, NB, INFO)
CALL DSYBC2(UPLO, A, DESCA, DESCA( MB_ ), INFO)
!CALL DSYBC2(UPLO, A, DESCA, AR, DESCAR, AC, DESCAC, CHKVEC, DESCA( MB_ ), INFO )
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
!
IF( UPPER ) THEN
!
! Split-ring topology for the communication along process
! columns, 1-tree topology along process rows.
!
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' )
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'S-ring' )
!
! A is upper triangular, compute Cholesky factorization A = U'*U.
!
! Handle the first block of columns separately
!
JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA(NB_), JA+N-1 )
JB = JN - JA + 1
!
! Perform unblocked Cholesky factorization on JB block
!
CALL PDPOTF2( UPLO, JB, A, IA, JA, DESCA, INFO )
IF( INFO.NE.0 ) &
& GO TO 30
!
IF( JB+1.LE.N ) THEN
!
! Form the row panel of U using the triangular solver
!
CALL PDTRSM( 'Left', UPLO, 'Transpose', 'Non-Unit', &
& JB, N-JB, ONE, A, IA, JA, DESCA, A, IA, JA+JB, &
& DESCA )
!
! Update the trailing matrix, A = A - U'*U
!
CALL PDSYRK( UPLO, 'Transpose', N-JB, JB, -ONE, A, IA, &
& JA+JB, DESCA, ONE, A, IA+JB, JA+JB, DESCA )
END IF
!
! Loop over remaining block of columns
!
DO 10 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( N-J+JA, DESCA( NB_ ) )
I = IA + J - JA
!
! Perform unblocked Cholesky factorization on JB block
!
CALL PDPOTF2( UPLO, JB, A, I, J, DESCA, INFO )
IF( INFO.NE.0 ) THEN
INFO = INFO + J - JA
GO TO 30
END IF
!
IF( J-JA+JB+1.LE.N ) THEN
!
! Form the row panel of U using the triangular solver
!
CALL PDTRSM( 'Left', UPLO, 'Transpose', 'Non-Unit', &
& JB, N-J-JB+JA, ONE, A, I, J, DESCA, A, &
& I, J+JB, DESCA )
!
! Update the trailing matrix, A = A - U'*U
!
CALL PDSYRK( UPLO, 'Transpose', N-J-JB+JA, JB, &
& -ONE, A, I, J+JB, DESCA, ONE, A, I+JB, &
& J+JB, DESCA )
END IF
10 CONTINUE
!
ELSE
!
! 1-tree topology for the communication along process columns,
! Split-ring topology along process rows.
!
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'S-ring' )
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' )
!
! A is lower triangular, compute Cholesky factorization A = L*L'
! (right-looking)
!
! Handle the first block of columns separately
!
JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA( NB_ ), JA+N-1 )
JB = JN - JA + 1
!
! Perform unblocked Cholesky factorization on JB block
!
CALL PDPOTF2( UPLO, JB, A, IA, JA, DESCA, INFO )
IF( INFO.NE.0 ) &
& GO TO 30
!SUBROUTINE CHK1( UPLO, A, IA, JA, DA, INFO)
CALL CHK1( UPLO, A, IA, JA, DESCA, INFO )
!
IF( JB+1.LE.N ) THEN
!
! Form the column panel of L using the triangular solver
!
CALL PDTRSM( 'Right', UPLO, 'Transpose', 'Non-Unit', &
& N-JB, JB, ONE, A, IA, JA, DESCA, A, IA+JB, JA, &
& DESCA )
CALL CHK2(UPLO, N-JB, JB, A, IA, JA, DESCA, INFO)
!
! Update the trailing matrix, A = A - L*L'
!
CALL PDSYRK( UPLO, 'No Transpose', N-JB, JB, -ONE, A, IA+JB,&
& JA, DESCA, ONE, A, IA+JB, JA+JB, DESCA )
CALL CHK3(UPLO, N-JB, A, IA, JA, DESCA, INFO)
!
END IF
!
DO 20 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( N-J+JA, DESCA( NB_ ) )
I = IA + J - JA
!
! Perform unblocked Cholesky factorization on JB block
!
CALL PDPOTF2( UPLO, JB, A, I, J, DESCA, INFO )
CALL CHK1( UPLO, A, I, J, DESCA, INFO )
IF( INFO.NE.0 ) THEN
INFO = INFO + J - JA
GO TO 30
END IF
!
IF( J-JA+JB+1.LE.N ) THEN
!
! Form the column panel of L using the triangular solver
!
CALL PDTRSM( 'Right', UPLO, 'Transpose', 'Non-Unit', &
& N-J-JB+JA, JB, ONE, A, I, J, DESCA, A, I+JB,&
& J, DESCA )
CALL CHK2( UPLO, N-J-JB+JA, JB, A, I, J, DESCA, INFO)
!
! Update the trailing matrix, A = A - L*L'
!
CALL PDSYRK( UPLO, 'No Transpose', N-J-JB+JA, JB, -ONE, &
& A, I+JB, J, DESCA, ONE, A, I+JB, J+JB, &
& DESCA )
CALL CHK3( UPLO, N-J-JB+JA, A, I, J, DESCA, INFO )
!
END IF
20 CONTINUE
!
END IF
!
30 CONTINUE
!
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
!CALL DSYDC2
!
RETURN
!
! End of PDPOTRF
!
END