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SUBROUTINE DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
$ LDA, AF, LDAF, IPIV, COLEQU, C, B,
$ LDB, Y, LDY, BERR_OUT, N_NORMS,
$ ERRS_N, ERRS_C, RES, AYB, DY,
$ Y_TAIL, RCOND, ITHRESH, RTHRESH,
$ DZ_UB, IGNORE_CWISE, INFO )
*
* -- LAPACK routine (version 3.2) --
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
* -- Jason Riedy of Univ. of California Berkeley. --
* -- November 2008 --
*
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley and NAG Ltd. --
*
IMPLICIT NONE
* ..
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
$ TRANS_TYPE, N_NORMS, ITHRESH
LOGICAL COLEQU, IGNORE_CWISE
DOUBLE PRECISION RTHRESH, DZ_UB
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
$ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
$ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
CHARACTER TRANS
INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE
DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
$ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
$ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
$ EPS, HUGEVAL, INCR_THRESH
LOGICAL INCR_PREC
* ..
* .. Parameters ..
INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
$ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
$ EXTRA_Y
PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
$ CONV_STATE = 2, NOPROG_STATE = 3 )
PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
$ EXTRA_Y = 2 )
INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
INTEGER CMP_ERR_I, PIV_GROWTH_I
PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
$ BERR_I = 3 )
PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
$ PIV_GROWTH_I = 9 )
INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
$ LA_LINRX_CWISE_I
PARAMETER ( LA_LINRX_ITREF_I = 1,
$ LA_LINRX_ITHRESH_I = 2 )
PARAMETER ( LA_LINRX_CWISE_I = 3 )
INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
$ LA_LINRX_RCOND_I
PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
PARAMETER ( LA_LINRX_RCOND_I = 3 )
INTEGER LA_LINRX_MAX_N_ERRS
PARAMETER ( LA_LINRX_MAX_N_ERRS = 3 )
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, DGETRS, DGEMV, BLAS_DGEMV_X,
$ BLAS_DGEMV2_X, DLA_GEAMV, DLA_WWADDW, DLAMCH,
$ CHLA_TRANSTYPE, DLA_LIN_BERR
DOUBLE PRECISION DLAMCH
CHARACTER CHLA_TRANSTYPE
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. Executable Statements ..
*
IF ( INFO.NE.0 ) RETURN
TRANS = CHLA_TRANSTYPE(TRANS_TYPE)
EPS = DLAMCH( 'Epsilon' )
HUGEVAL = DLAMCH( 'Overflow' )
* Force HUGEVAL to Inf
HUGEVAL = HUGEVAL * HUGEVAL
* Using HUGEVAL may lead to spurious underflows.
INCR_THRESH = DBLE( N ) * EPS
*
DO J = 1, NRHS
Y_PREC_STATE = EXTRA_RESIDUAL
IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
DO I = 1, N
Y_TAIL( I ) = 0.0D+0
END DO
END IF
DXRAT = 0.0D+0
DXRATMAX = 0.0D+0
DZRAT = 0.0D+0
DZRATMAX = 0.0D+0
FINAL_DX_X = HUGEVAL
FINAL_DZ_Z = HUGEVAL
PREVNORMDX = HUGEVAL
PREV_DZ_Z = HUGEVAL
DZ_Z = HUGEVAL
DX_X = HUGEVAL
X_STATE = WORKING_STATE
Z_STATE = UNSTABLE_STATE
INCR_PREC = .FALSE.
DO CNT = 1, ITHRESH
*
* Compute residual RES = B_s - op(A_s) * Y,
* op(A) = A, A**T, or A**H depending on TRANS (and type).
*
CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
CALL DGEMV( TRANS, N, N, -1.0D+0, A, LDA, Y( 1, J ), 1,
$ 1.0D+0, RES, 1 )
ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN
CALL BLAS_DGEMV_X( TRANS_TYPE, N, N, -1.0D+0, A, LDA,
$ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
ELSE
CALL BLAS_DGEMV2_X( TRANS_TYPE, N, N, -1.0D+0, A, LDA,
$ Y( 1, J ), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE )
END IF
! XXX: RES is no longer needed.
CALL DCOPY( N, RES, 1, DY, 1 )
CALL DGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO )
*
* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
*
NORMX = 0.0D+0
NORMY = 0.0D+0
NORMDX = 0.0D+0
DZ_Z = 0.0D+0
YMIN = HUGEVAL
*
DO I = 1, N
YK = ABS( Y( I, J ) )
DYK = ABS( DY( I ) )
IF ( YK .NE. 0.0D+0 ) THEN
DZ_Z = MAX( DZ_Z, DYK / YK )
ELSE IF ( DYK .NE. 0.0D+0 ) THEN
DZ_Z = HUGEVAL
END IF
YMIN = MIN( YMIN, YK )
NORMY = MAX( NORMY, YK )
IF ( COLEQU ) THEN
NORMX = MAX( NORMX, YK * C( I ) )
NORMDX = MAX( NORMDX, DYK * C( I ) )
ELSE
NORMX = NORMY
NORMDX = MAX( NORMDX, DYK )
END IF
END DO
IF ( NORMX .NE. 0.0D+0 ) THEN
DX_X = NORMDX / NORMX
ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
DX_X = 0.0D+0
ELSE
DX_X = HUGEVAL
END IF
DXRAT = NORMDX / PREVNORMDX
DZRAT = DZ_Z / PREV_DZ_Z
*
* Check termination criteria
*
IF (.NOT.IGNORE_CWISE
$ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY
$ .AND. Y_PREC_STATE .LT. EXTRA_Y)
$ INCR_PREC = .TRUE.
IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
$ X_STATE = WORKING_STATE
IF ( X_STATE .EQ. WORKING_STATE ) THEN
IF ( DX_X .LE. EPS ) THEN
X_STATE = CONV_STATE
ELSE IF ( DXRAT .GT. RTHRESH ) THEN
IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
INCR_PREC = .TRUE.
ELSE
X_STATE = NOPROG_STATE
END IF
ELSE
IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
END IF
IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
END IF
IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
$ Z_STATE = WORKING_STATE
IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
$ Z_STATE = WORKING_STATE
IF ( Z_STATE .EQ. WORKING_STATE ) THEN
IF ( DZ_Z .LE. EPS ) THEN
Z_STATE = CONV_STATE
ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
Z_STATE = UNSTABLE_STATE
DZRATMAX = 0.0D+0
FINAL_DZ_Z = HUGEVAL
ELSE IF ( DZRAT .GT. RTHRESH ) THEN
IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
INCR_PREC = .TRUE.
ELSE
Z_STATE = NOPROG_STATE
END IF
ELSE
IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
END IF
IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
END IF
*
* Exit if both normwise and componentwise stopped working,
* but if componentwise is unstable, let it go at least two
* iterations.
*
IF ( X_STATE.NE.WORKING_STATE ) THEN
IF ( IGNORE_CWISE) GOTO 666
IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE )
$ GOTO 666
IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666
END IF
IF ( INCR_PREC ) THEN
INCR_PREC = .FALSE.
Y_PREC_STATE = Y_PREC_STATE + 1
DO I = 1, N
Y_TAIL( I ) = 0.0D+0
END DO
END IF
PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z
*
* Update soluton.
*
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL DAXPY( N, 1.0D+0, DY, 1, Y( 1, J ), 1 )
ELSE
CALL DLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
END IF
END DO
* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
666 CONTINUE
*
* Set final_* when cnt hits ithresh.
*
IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
*
* Compute error bounds
*
IF (N_NORMS .GE. 1) THEN
ERRS_N( J, LA_LINRX_ERR_I ) = FINAL_DX_X / (1 - DXRATMAX)
END IF
IF ( N_NORMS .GE. 2 ) THEN
ERRS_C( J, LA_LINRX_ERR_I ) = FINAL_DZ_Z / (1 - DZRATMAX)
END IF
*
* Compute componentwise relative backward error from formula
* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
* where abs(Z) is the componentwise absolute value of the matrix
* or vector Z.
*
* Compute residual RES = B_s - op(A_s) * Y,
* op(A) = A, A**T, or A**H depending on TRANS (and type).
*
CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
CALL DGEMV( TRANS, N, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0,
$ RES, 1 )
DO I = 1, N
AYB( I ) = ABS( B( I, J ) )
END DO
*
* Compute abs(op(A_s))*abs(Y) + abs(B_s).
*
CALL DLA_GEAMV ( TRANS_TYPE, N, N, 1.0D+0,
$ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
CALL DLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) )
*
* End of loop for each RHS.
*
END DO
*
RETURN
END
|
