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ftdpotrf.f90
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! Authors:
! ========
!
!> \author Univ. of Tennessee
!> \author Univ. of California Berkeley
!> \author Univ. of Colorado Denver
!> \author NAG Ltd.
!
!> \date November 2011
!
!> \ingroup doublePOcomputational
!
!
! Add Fault tolerant functionality by
! Panruo Wu([email protected])
! December 2011
! =====================================================================
SUBROUTINE FTDPOTRF( UPLO, N, A, LDA, INFO , NB)
IMPLICIT NONE
!
! -- LAPACK computational routine (version 3.4.0) --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd
! November 2011
!
! .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
! ..
! .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
! ..
!
! =====================================================================
!
! .. Parameters ..
DOUBLE PRECISION ONE, ZERO, EPS, TMPA(NB, NB)
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0, EPS = 1.0D-7 )
! ..
! .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JB, NB, II, JJ , ERR
! ..
! .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
! ..
! .. External Subroutines ..
EXTERNAL DGEMM, MYDPOTF2, DSYRK, DTRSM, XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX, MIN
DOUBLE PRECISION, ALLOCATABLE :: CHKSUM(:)
REAL :: T1, T2
! ..
! .. Executable Statements ..
!
! Test the input parameters.
!
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DPOTRF', -INFO )
RETURN
END IF
!
! Quick return if possible
!
IF( N.EQ.0 ) &
& RETURN
!
! Determine the block size for this environment.
!
!NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
!write (*,*) "bs",ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
!NB = 96
!CALL CPU_TIME(T1)
ALLOCATE(CHKSUM(NB-2))
CALL RANDOM_NUMBER(CHKSUM)
CALL BLDCHK3(NB, A, N, CHKSUM )
!CALL CPU_TIME(T2)
!PRINT *, 'BLDCHK3 takes', T2-T1
IF( NB.LE.1 .OR. NB.GE.N ) THEN
!
! Use unblocked code.
!
CALL MYDPOTF3( UPLO, N, A, LDA, INFO )
ELSE
!
! Use blocked code.
!
IF( UPPER ) THEN
!
! Compute the Cholesky factorization A = U**T*U.
!
DO 10 J = 1, N, NB
!
! Update and factorize the current diagonal block and test
! for non-positive-definiteness.
!
JB = MIN( NB, N-J+1 )
CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, &
& A( 1, J ), LDA, ONE, A( J, J ), LDA )
CALL MYDPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 ) &
& GO TO 30
IF( J+JB.LE.N ) THEN
!
! Compute the current block row.
!
CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,&
& J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), &
& LDA, ONE, A( J, J+JB ), LDA )
CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', &
& JB, N-J-JB+1, ONE, A( J, J ), LDA, &
& A( J, J+JB ), LDA )
END IF
10 CONTINUE
!
ELSE
!
! Compute the Cholesky factorization A = L*L**T.
!
DO 20 J = 1, N, NB
!
! Update and factorize the current diagonal block and test
! for non-positive-definiteness.
!
200 JB = MIN( NB, N-J+1 )
CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, &
& A( J, 1 ), LDA, ONE, A( J, J ), LDA )
TMPA = A(J:J+NB-1, J:J+NB-1)
A(J,J) = 12.24
CALL MYDPOTF3( 'Lower', JB, A( J, J ), LDA, INFO )
IF (INFO .NE. 0) THEN
A(J:J+NB-1, J:J+NB-1) = TMPA
CALL MYDPOTF3( 'Lower', JB, A( J, J ), LDA, INFO )
END IF
!CALL CHK1(NB, A, N, J, ERR)
!IF ( ERR.EQ.-1 ) THEN
!GOTO 200
!END IF
!
! if the right-bottom corner is (almost) zero,
! set it to 1. Threshold needs reviewing.
! make sure the head block factorizes correctly
!
IF ( ABS( A( J+JB-1, J+JB-1) ) .LT. 1.0D-7 ) THEN
A( J+JB-1, J+JB-1) = ONE
END IF
IF ( ABS( A( J+JB-2, J+JB-2) ) .LT. 1.0D-7 ) THEN
A( J+JB-2, J+JB-2) = ONE
END IF
IF( INFO.NE.0 ) &
& GO TO 30
IF( J+JB.LE.N ) THEN
!
! Compute the current block column.
!
! Here we should use ftdgemm instead..
!CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,&
!& J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), &
!& LDA, ONE, A( J+JB, J ), LDA )
IF (J > 1) THEN
!PRINT *,'original', 'A(',J+JB,1,')=',A(J+JB,1)
A(J+JB,1) = 12.34
!PRINT *, 'before ftdgemm','A(',J+JB,1,')=',A(J+JB,1)
END IF
!PRINT *,'Calling FTDGEMM, J=', J
CALL FTDGEMM( 'N', 'T', N-J-JB+1, JB,&
& J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), &
& LDA, ONE, A( J+JB, J ), LDA, NB, CHKSUM)
!PRINT *, 'after ftdgemm','A(',J+JB,1,')=',A(J+JB,1)
CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',&
& N-J-JB+1, JB, ONE, A( J, J ), LDA, &
& A( J+JB, J ), LDA )
!CALL CHK2(NB, A, N, J, ERR)
END IF
IF ( A(J+JB-2, J+JB-2).EQ.ONE .AND. A(J+JB-1, J+JB-1).EQ.ONE) THEN
A(J+JB-2, J+JB-2) = ZERO
A(J+JB-1, J+JB-1) = ZERO
END IF
20 CONTINUE
END IF
END IF
GO TO 40
!
30 CONTINUE
INFO = INFO + J - 1
!
40 CONTINUE
DEALLOCATE(CHKSUM)
RETURN
!
! End of DPOTRF
!
END
!
! Build local and global unit checksum matrix of A
! assuming that additional memory space are allocated
!
SUBROUTINE BLDCHK(NB, A, N)
IMPLICIT NONE
! N must be divisible by block size NB
INTEGER NB, N
DOUBLE PRECISION A(N, N)
!=====================
DOUBLE PRECISION S, ZERO, ONE
INTEGER I, J, K, L, II, JJ
PARAMETER ( ZERO = 0.0D+0, ONE = 0.0D+0 )
DO J = 1, N-NB, NB
DO I = J, N-NB, NB
! make sure the blocks on diagonal is symmetric
IF ( I.EQ.J ) THEN
DO II = I, I+NB-1
DO JJ = I+1, J+NB-1
A(II, JJ) = A(JJ, II)
END DO
END DO
DO II = I, I+NB-1
A(II, J+NB-1) = A(J+NB-1, II)
END DO
END IF
DO K = J, J+NB-2
S = ZERO
DO L = I, I+NB-2
S = S + A(L, K)
END DO
A(I+NB-1, K) = S
END DO
DO K = I, I+NB-1
S = ZERO
DO L = J, J+NB-2
S = S + A(K, L)
END DO
A(K, J+NB-1) = S
END DO
END DO
END DO
! Now build the global checksum matrix
A(N-NB+1:N, 1: N-NB) = ZERO
DO J = 1, N-NB, NB
DO I = 1, N-NB, NB
DO JJ = 0, NB-1
DO II = 0, NB-1
IF (I.GE.J) THEN
A(N-NB+1+II, J+JJ) = A(N-NB+1+II, J+JJ) + A(I+II,J+JJ)
ELSE
A(N-NB+1+II, J+JJ) = A(N-NB+1+II, J+JJ) + A(J+JJ,I+II)
END IF
END DO
END DO
END DO
END DO
END
!
! Build local and global random checksum matrix of A
! assuming that additional memory space are allocated
!
SUBROUTINE BLDCHK2(NB, A, N, CHKSUM)
IMPLICIT NONE
! N must be divisible by block size NB
INTEGER NB, N
DOUBLE PRECISION A(N, N), CHKSUM(NB-1)
!=====================
DOUBLE PRECISION S, ZERO, ONE
INTEGER I, J, K, L, II, JJ
PARAMETER ( ZERO = 0.0D+0, ONE = 0.0D+0 )
DO J = 1, N-NB, NB
DO I = J, N-NB, NB
! make sure the blocks on diagonal is symmetric
IF ( I.EQ.J ) THEN
DO II = I, I+NB-1
DO JJ = I+1, J+NB-1
A(II, JJ) = A(JJ, II)
END DO
END DO
DO II = I, I+NB-1
A(II, J+NB-1) = A(J+NB-1, II)
END DO
END IF
DO JJ = J, J+NB-2
A(I+NB-1, JJ) = SUM( A(I:I+NB-2, JJ) * CHKSUM )
END DO
DO II = I, I+NB-1
A(II, J+NB-1) = SUM( A(II, J:J+NB-2) * CHKSUM )
END DO
!DO K = J, J+NB-2
!S = ZERO
!DO L = I, I+NB-2
!S = S + A(L, K)
!END DO
!A(I+NB-1, K) = S
!END DO
!DO K = I, I+NB-1
!S = ZERO
!DO L = J, J+NB-2
!S = S + A(K, L)
!END DO
!A(K, J+NB-1) = S
!END DO
END DO
END DO
! Now build the global checksum matrix
A(N-NB+1:N, 1: N-NB) = ZERO
DO J = 1, N-NB, NB
DO I = 1, N-NB, NB
DO JJ = 0, NB-1
DO II = 0, NB-1
IF (I.GE.J) THEN
A(N-NB+1+II, J+JJ) = A(N-NB+1+II, J+JJ) + A(I+II,J+JJ)
ELSE
A(N-NB+1+II, J+JJ) = A(N-NB+1+II, J+JJ) + A(J+JJ,I+II)
END IF
END DO
END DO
END DO
END DO
END
! 2 local checksums no global
SUBROUTINE BLDCHK3(NB, A, N, CHKSUM)
IMPLICIT NONE
DOUBLE PRECISION A(N,N), CHKSUM(NB-2)
INTEGER NB, N
INTEGER I, J, II, JJ
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
DO J = 1, N, NB
DO I = J, N, NB
IF (I.EQ.J) THEN
DO JJ = J, J+NB-3
DO II = 1, JJ-1
A(II, JJ) = A(JJ, II)
END DO
END DO
END IF
A(I+NB-2:I+NB-1, J:J+NB-1) = ZERO
A(I:I+NB-1, J+NB-2:J+NB-1) = ZERO
DO II = I, I+NB-3
A(I+NB-2, J:J+NB-3) = A(I+NB-2, J:J+NB-3) + A(II, J:J+NB-3)
A(I+NB-1, J:J+NB-3) = A(I+NB-1, J:J+NB-3) + A(II, J:J+NB-3) * CHKSUM(II-I+1)
END DO
DO JJ = J, J+NB-3
A(I:I+NB-3, J+NB-2) = A(I:I+NB-3, J+NB-2) + A(I:I+NB-3, JJ)
A(I:I+NB-3, J+NB-1) = A(I:I+NB-3, J+NB-1) + A(I:I+NB-3, JJ) * CHKSUM(JJ-J+1)
END DO
A(I+NB-2, J+NB-2) = SUM( A(I+NB-2, J:J+NB-3) )
A(I+NB-1, J+NB-1) = SUM( A(I+NB-1, J:J+NB-3) * CHKSUM )
A(I+NB-1, J+NB-2) = SUM( A(I:I+NB-3, j+NB-2) * CHKSUM )
A(I+NB-2, J+NB-1) = SUM( A(I+NB-2, J:J+NB-3) * CHKSUM )
END DO
END DO
END SUBROUTINE BLDCHK3
SUBROUTINE CHK1(NB, A, N, I, INFO)
IMPLICIT NONE
DOUBLE PRECISION A(N, N)
INTEGER N, I, INFO, NB
!=================
INTEGER II, JJ
DOUBLE PRECISION ZERO, EPS
PARAMETER (ZERO = 0.0D+0, EPS = 1.0D-7)
! ABS(I+NB-1, I+NB-1) should be ZERO; if not then there's
! something wrong. Use global chkmat to recover it and signal
! a recomputation
INFO = 0
IF ( ABS( A(I+NB-1, I+NB-1) ) > EPS ) THEN
INFO = -1
A(I:I+NB-1, I:I+NB-1) = A(N-NB+1:N, I:I+NB-1)
DO II = I+NB,N-NB,NB
A(I:I+NB-1, I:I+NB-1) = A(I:I+NB-1, I:I+NB-1) - A(II:II+NB-1, I:I+NB-1);
END DO
! pass the check.
END IF
END SUBROUTINE CHK1
SUBROUTINE CHK2(NB, A, N, I, INFO)
IMPLICIT NONE
DOUBLE PRECISION A(N, N)
INTEGER N, I, INFO, NB
!=================
INTEGER II, JJ
DOUBLE PRECISION ZERO, EPS
PARAMETER (ZERO = 0.0D+0, EPS = 1.0D-7)
DOUBLE PRECISION WORK(N)
DO II = I+NB, N
IF ( ABS( A(II, I+NB-1) ) > EPS ) THEN
INFO = II
END IF
END DO
!DO II = I+NB, N, NB
END SUBROUTINE CHK2