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cgcommon.f90
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!----------- cgcommon package ------------------------------------------
! these routines are required for use by the conjugate gradient machiner
! history
! 03.01.28 (BTD) moved routines CAXPY and CSWAP to blas.f package of
! basic linear algebra subroutines
! end history
!-----------------------------------------------------------------------
FUNCTION SCSETRHSSTOP(B,WRK,EPSILON,IPAR,PRECONL,PSCNRM)
USE DDPRECISION,ONLY : WP
IMPLICIT NONE
REAL (WP) :: SCSETRHSSTOP
! .. Scalar Arguments ..
REAL (WP) :: EPSILON
! ..
! .. Array Arguments ..
COMPLEX (WP) :: B(*), WRK(*)
INTEGER :: IPAR(*)
! ..
! .. Function Arguments ..
REAL (WP) :: PSCNRM
EXTERNAL PSCNRM
! ..
! .. Subroutine Arguments ..
EXTERNAL PRECONL
! ..
! .. Local Scalars ..
INTEGER :: LOCLEN, STOPTYPE
! ..
LOCLEN = IPAR(4)
STOPTYPE = IPAR(9)
IF ((STOPTYPE==1) .OR. (STOPTYPE==4) .OR. (STOPTYPE==7)) THEN
! ||r||<epsilon or ||Q1r||<epsilon ||x(k)-x(k-1)||<epsilon
SCSETRHSSTOP = EPSILON
ELSE IF ((STOPTYPE==2) .OR. (STOPTYPE==3) .OR. (STOPTYPE==5)) THEN
! ||r||<epsilon||b|| or sqrt(r(Q1r))<epsilon||b|| or
! ||Q1r||<epsilon||b||
SCSETRHSSTOP = EPSILON*PSCNRM(LOCLEN,B)
ELSE IF (STOPTYPE==6) THEN
! ||Q1r||<epsilon||Q1b||
CALL PRECONL(B,WRK,IPAR)
SCSETRHSSTOP = EPSILON*PSCNRM(LOCLEN,WRK)
END IF
RETURN
END FUNCTION SCSETRHSSTOP
SUBROUTINE STOPCRIT(B,R,RTRUE,X,XOLD,WRK,RHSSTOP,CNVRTX,EXITNORM,STATUS, &
IPAR,MATVEC,TMATVEC,PRECONR,PCSUM,PSCNRM)
USE DDPRECISION, ONLY : WP
IMPLICIT NONE
! .. Scalar Arguments ..
REAL (WP) :: EXITNORM, RHSSTOP
INTEGER :: CNVRTX, STATUS
! ..
! .. Array Arguments ..
COMPLEX (WP) :: B(*), R(*), RTRUE(*), WRK(*), X(*), XOLD(*)
INTEGER :: IPAR(*)
! ..
! .. Function Arguments ..
REAL (WP) :: PSCNRM
EXTERNAL PSCNRM
! ..
! .. Subroutine Arguments ..
EXTERNAL MATVEC, PCSUM, PRECONR, TMATVEC
! ..
! .. Local Scalars ..
INTEGER :: LOCLEN, PRECONTYPE, STOPTYPE
! ..
! .. Local Arrays ..
COMPLEX (WP) :: DOTS(1)
! ..
! .. External Functions ..
! 98.04.27 BTD: CDOTC is defined as a complex function!
! 98.12.03 (BTD) this error also pointed out by Rodolphe Vaillon
! REAL CDOTC
COMPLEX (WP) :: CDOTC
!------------------------------------------------
EXTERNAL CDOTC
! ..
! .. External Subroutines ..
EXTERNAL CAXPY, CCOPY
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
! ..
! .. Parameters ..
COMPLEX (WP) :: CONE
PARAMETER (CONE=(1.0E0_WP,0.0E0_WP))
! ..
LOCLEN = IPAR(4)
PRECONTYPE = IPAR(8)
STOPTYPE = IPAR(9)
IF ((STOPTYPE==1) .OR. (STOPTYPE==2) .OR. (STOPTYPE==3)) THEN
! Compute true residual if needed
CALL CCOPY(LOCLEN,B,1,RTRUE,1)
IF ((PRECONTYPE==2) .OR. (PRECONTYPE==3)) THEN
CALL PRECONR(X,WRK,IPAR)
IF (CNVRTX==1) THEN
CALL TMATVEC(WRK,XOLD,IPAR)
CALL MATVEC(XOLD,WRK,IPAR)
CALL CAXPY(LOCLEN,-CONE,WRK,1,RTRUE,1)
ELSE
CALL MATVEC(WRK,XOLD,IPAR)
CALL CAXPY(LOCLEN,-CONE,XOLD,1,RTRUE,1)
END IF
ELSE IF (CNVRTX==1) THEN
CALL TMATVEC(X,XOLD,IPAR)
CALL MATVEC(XOLD,WRK,IPAR)
CALL CAXPY(LOCLEN,-CONE,WRK,1,RTRUE,1)
ELSE
CALL MATVEC(X,WRK,IPAR)
CALL CAXPY(LOCLEN,-CONE,WRK,1,RTRUE,1)
END IF
END IF
IF ((STOPTYPE==1) .OR. (STOPTYPE==2)) THEN
! ||r|| < epsilon or ||r|| < epsilon ||b||
EXITNORM = PSCNRM(LOCLEN,RTRUE)
IF (EXITNORM<RHSSTOP) THEN
STATUS = 0
ELSE
STATUS = -99
END IF
ELSE IF (STOPTYPE==3) THEN
! sqrt(r(Q1r))<epsilon||b||
! BTD 98.04.27 CDOTC is defined as a complex function!
! DOTS(1) = CDOTC(LOCLEN,RTRUE,1,R,1)
DOTS(1) = REAL(CDOTC(LOCLEN,RTRUE,1,R,1))
CALL PCSUM(1,DOTS(1))
EXITNORM = ABS(SQRT(DOTS(1)))
IF (EXITNORM<RHSSTOP) THEN
STATUS = 0
ELSE
STATUS = -99
END IF
ELSE IF ((STOPTYPE==4) .OR. (STOPTYPE==5) .OR. (STOPTYPE==6)) THEN
! ||Q1r|| < epsilon or ||Q1r|| < epsilon||b|| or ||Q1r|| < epsilon||Q1b
EXITNORM = PSCNRM(LOCLEN,R)
IF (EXITNORM<RHSSTOP) THEN
STATUS = 0
ELSE
STATUS = -99
END IF
ELSE IF (STOPTYPE==7) THEN
! ||x-x0||<epsilon
CALL CCOPY(LOCLEN,X,1,WRK,1)
CALL CAXPY(LOCLEN,-CONE,XOLD,1,WRK,1)
EXITNORM = PSCNRM(LOCLEN,WRK)
IF (EXITNORM<RHSSTOP) THEN
STATUS = 0
ELSE
STATUS = -99
END IF
END IF
RETURN
END SUBROUTINE STOPCRIT
SUBROUTINE PROGRESS(LOCLEN,ITNO,NORMRES,X,RES,TRUERES)
USE DDPRECISION,ONLY : WP
USE DDCOMMON_9,ONLY : ERRSCAL,IDVOUT2,ITERMX,ITERN
IMPLICIT NONE
! Arguments:
REAL (WP) :: NORMRES
INTEGER :: ITNO, LOCLEN
COMPLEX (WP) :: RES(*), TRUERES(*), X(*)
! Common:
! INTEGER :: IDVOUT2, ITERMX, ITERN
! REAL (WP) :: ERRSCAL
!-----------------------------------------------------------------------
! COMMON /NORMERR/ERRSCAL, IDVOUT2, ITERMX, ITERN
!-----------------------------------------------------------------------
! Local:
INTEGER :: ITNOL
REAL (WP) :: ERRMIN, NORMERR, RATE
SAVE ERRMIN, ITNOL
! part of PIM
! history
! 95.08.14 (BTD): modified to include COMMON/NORMERR/ERRSCAL to allow
! desired normalization of error.
! 96.11.21 (BTD): added IDVOUT2 to COMMON/NORMERR/ to allow passing
! of device number for standard output (so that it
! doesn't need to be hardwired here).
! 98.10.08 (BTD): modified to keep track of minimum error, and to
! note when new error minimum is attained. This is
! to observe convergence behavior of PBCGST.
! 98.10.26 (BTD): modified to PROGRESS to also print information on
! rate of convergence (variable RATE).
! 03.04.13 (BTD): added ITERMX and ITERN to COMMON/NORMERR/
! to communicate number of iterations and max number
! of iterations allowed.
! 07.08.04 (BTD): DDSCAT Version 7.0.3
! Replaced COMMON/NORMERR/ with USE MODULE DDCOMMON_9
! end history
! Note: when used with STOPTYPE=5, NORMRES=|Ax-b|.
! If quantity ERRSCAL is set to |b| elsewhere, then NORMRES/ERRSCAL
! is a measure of the fractional error in the solution vector x.
ITERN=ITERN+1
NORMERR=NORMRES/ERRSCAL
IF(ITERN<=2)THEN
ERRMIN=NORMERR
ITNOL=ITERN
WRITE (IDVOUT2,FMT=9000) ITERN, NORMERR
ELSE
IF(NORMERR<ERRMIN)THEN
RATE=LOG(ERRMIN/NORMERR)/(ITERN-ITNOL)
ERRMIN=NORMERR
ITNOL=ITERN
WRITE(IDVOUT2,FMT=9001)ITERN,NORMERR,ERRMIN,RATE
ELSE
WRITE(IDVOUT2,FMT=9000)ITERN,NORMERR
ENDIF
ENDIF
RETURN
9000 FORMAT(1X,'iter= ',I4,' frac.err= ',0P,F11.7)
9001 FORMAT(1X,'iter= ',I4,' frac.err= ',0P,F11.7,' min.err=',0P,F11.7, &
' rate=',0P,F8.6)
END SUBROUTINE PROGRESS
SUBROUTINE CVPROD(N,CX,INCX,CY,INCY)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
! Modified from saxpy level 1 BLAS
! element-wise vector multiplication, y<-x*y
! Rudnei Dias da Cunha, 16/6/93
! constant times a vector plus a vector.
! uses unrolled loops for increments equal to one.
! jack dongarra, linpack, 3/11/78.
! .. Scalar Arguments ..
INTEGER :: INCX, INCY, N
! ..
! .. Array Arguments ..
COMPLEX (WP) :: CX(*), CY(*)
! ..
! .. Local Scalars ..
INTEGER :: I, IX, IY, M, MP1
! ..
! .. Intrinsic Functions ..
INTRINSIC MOD
! ..
IF (N<=0) RETURN
IF (INCX==1 .AND. INCY==1) GO TO 20
! code for unequal increments or equal increments
! not equal to 1
IX = 1
IY = 1
IF (INCX<0) IX = (-N+1)*INCX + 1
IF (INCY<0) IY = (-N+1)*INCY + 1
DO I = 1, N
CY(IY) = CY(IY)*CX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
RETURN
! code for both increments equal to 1
! clean-up loop
20 M = MOD(N,4)
IF (M==0) GO TO 40
DO I = 1, M
CY(I) = CY(I)*CX(I)
END DO
IF (N<4) RETURN
40 MP1 = M + 1
DO I = MP1, N, 4
CY(I) = CY(I)*CX(I)
CY(I+1) = CY(I+1)*CX(I+1)
CY(I+2) = CY(I+2)*CX(I+2)
CY(I+3) = CY(I+3)*CX(I+3)
END DO
RETURN
END SUBROUTINE CVPROD
SUBROUTINE PRINTV(N,U)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
! .. Scalar Arguments ..
INTEGER :: N
! ..
! .. Array Arguments ..
COMPLEX (WP) :: U(*)
! ..
! .. Local Scalars ..
INTEGER :: I
! ..
WRITE (6,FMT=9000) (U(I),I=1,N)
RETURN
9000 FORMAT (8(E14.8,1X))
END SUBROUTINE PRINTV
SUBROUTINE CINIT(N,ALPHA,CX,INCX)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
! Initialises a vector x with a scalar alpha.
! Modified from scopy, BLAS Level 1.
! Rudnei Dias da Cunha, 14/6/93.
! copies a vector, x, to a vector, y.
! uses unrolled loops for increments equal to one.
! jack dongarra, linpack, 3/11/78.
! .. Scalar Arguments ..
COMPLEX (WP) :: ALPHA
INTEGER :: INCX, N
! ..
! .. Array Arguments ..
COMPLEX (WP) :: CX(*)
! ..
! .. Local Scalars ..
INTEGER :: I, IX, M, MP1
! ..
! .. Intrinsic Functions ..
INTRINSIC MOD
! ..
IF (N<=0) RETURN
IF (INCX==1) GO TO 20
! code for unequal increments or equal increments
! not equal to 1
IX = 1
IF (INCX<0) IX = (-N+1)*INCX + 1
DO I = 1, N
CX(IX) = ALPHA
IX = IX + INCX
END DO
RETURN
! code for both increments equal to 1
! clean-up loop
20 M = MOD(N,7)
IF (M==0) GO TO 40
DO I = 1, M
CX(I) = ALPHA
END DO
IF (N<7) RETURN
40 MP1 = M + 1
DO I = MP1, N, 7
CX(I) = ALPHA
CX(I+1) = ALPHA
CX(I+2) = ALPHA
CX(I+3) = ALPHA
CX(I+4) = ALPHA
CX(I+5) = ALPHA
CX(I+6) = ALPHA
END DO
RETURN
END SUBROUTINE CINIT
FUNCTION CSIGN(X)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
COMPLEX (WP) :: CSIGN
! .. Scalar Arguments ..
COMPLEX (WP) :: X
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS
! ..
CSIGN = X/ABS(X)
RETURN
END FUNCTION CSIGN
SUBROUTINE DECODE(RHO,C,S)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
! .. Scalar Arguments ..
COMPLEX (WP) :: C, RHO, S
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
! ..
! .. Parameters ..
REAL (WP) :: ONE
PARAMETER (ONE=1.0_WP)
COMPLEX (WP) :: CZERO
PARAMETER (CZERO=(0.0_WP,0.0_WP))
COMPLEX (WP) :: CONE
PARAMETER (CONE=(1.0_WP,0.0_WP))
! ..
IF (RHO==CONE) THEN
C = CZERO
S = CONE
ELSE IF (ABS(RHO)<ONE) THEN
S = 2.0_WP*RHO
C = SQRT(CONE-S**2)
ELSE
C = 2.0_WP/RHO
S = SQRT(CONE-C**2)
END IF
RETURN
END SUBROUTINE DECODE
SUBROUTINE ENCODE(RHO,C,S)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
! .. Scalar Arguments ..
COMPLEX (WP) :: C, RHO, S
! ..
! .. External Functions ..
COMPLEX (WP) :: CSIGN
EXTERNAL CSIGN
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS
! ..
! .. Parameters ..
COMPLEX (WP) :: CZERO
PARAMETER (CZERO=(0.0_WP,0.0_WP))
COMPLEX (WP) :: CONE
PARAMETER (CONE=(1.0_WP,0.0_WP))
! ..
IF (C==CZERO) THEN
RHO = CONE
ELSE IF (ABS(S)<ABS(C)) THEN
RHO = CSIGN(C)*S/2.0_WP
ELSE
RHO = 2.0_WP*CSIGN(S)/C
END IF
RETURN
END SUBROUTINE ENCODE
SUBROUTINE GIVENS(A,B,C,S)
USE DDPRECISION, ONLY : WP
! part of PIM
IMPLICIT NONE
! .. Scalar Arguments ..
COMPLEX (WP) :: A, B, C, S
! ..
! .. Local Scalars ..
COMPLEX (WP) :: TAU
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
! ..
! .. Parameters ..
COMPLEX (WP) :: CZERO
PARAMETER (CZERO=(0.0_WP,0.0_WP))
COMPLEX (WP) :: CONE
PARAMETER (CONE=(1.0_WP,0.0_WP))
! ..
IF (B==CZERO) THEN
C = CONE
S = CZERO
ELSE IF (ABS(B)>ABS(A)) THEN
TAU = -A/B
S = CONE/SQRT(CONE+TAU**2)
C = S*TAU
ELSE
TAU = -B/A
C = CONE/SQRT(CONE+TAU**2)
S = C*TAU
END IF
RETURN
END SUBROUTINE GIVENS
FUNCTION PSCNRM2(LOCLEN,U)
USE DDPRECISION, ONLY : WP
REAL (WP) :: PSCNRM2
! part of PIM package
! .. Scalar Arguments ..
INTEGER :: LOCLEN
! ..
! .. Array Arguments ..
COMPLEX (WP) :: U(*)
! ..
! .. External Functions ..
REAL (WP) :: SCNRM2
EXTERNAL SCNRM2
! ..
PSCNRM2 = SCNRM2(LOCLEN,U,1)
RETURN
END FUNCTION PSCNRM2
SUBROUTINE PCSUM(ISIZE,X)
USE DDPRECISION, ONLY : WP
! .. Scalar Arguments ..
INTEGER :: ISIZE
! ..
! .. Array Arguments ..
COMPLEX (WP) :: X(*)
! ..
RETURN
END SUBROUTINE PCSUM
SUBROUTINE CCOPY(N,CX,INCX,CY,INCY)
USE DDPRECISION, ONLY : WP
! copies a vector, x, to a vector, y.
! jack dongarra, linpack, 4/11/78.
COMPLEX (WP) :: CX(1), CY(1)
INTEGER :: I, INCX, INCY, IX, IY, N
IF (N<=0) RETURN
IF (INCX==1 .AND. INCY==1) GO TO 20
! code for unequal increments or equal increments
! not equal to 1
IX = 1
IY = 1
IF (INCX<0) IX = (-N+1)*INCX + 1
IF (INCY<0) IY = (-N+1)*INCY + 1
DO I = 1, N
CY(IY) = CX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
RETURN
! code for both increments equal to 1
20 DO I = 1, N
CY(I) = CX(I)
END DO
RETURN
END SUBROUTINE CCOPY
FUNCTION CDOTC(N,CX,INCX,CY,INCY)
USE DDPRECISION, ONLY : WP
COMPLEX (WP) :: CDOTC
! forms the dot product of a vector.
! jack dongarra, 3/11/78.
COMPLEX (WP) :: CX(1), CY(1), CTEMP
INTEGER :: I, IX, IY, N, INCX, INCY
CTEMP = (0.0E0_WP,0.0E0_WP)
CDOTC = (0.0E0_WP,0.0E0_WP)
IF (N<=0) RETURN
IF (INCX==1 .AND. INCY==1) GO TO 20
! code for unequal increments or equal increments
! not equal to 1
IX = 1
IY = 1
IF (INCX<0) IX = (-N+1)*INCX + 1
IF (INCY<0) IY = (-N+1)*INCY + 1
DO I = 1, N
CTEMP = CTEMP + CONJG(CX(IX))*CY(IY)
IX = IX + INCX
IY = IY + INCY
END DO
CDOTC = CTEMP
RETURN
! code for both increments equal to 1
20 DO I = 1, N
CTEMP = CTEMP + CONJG(CX(I))*CY(I)
END DO
CDOTC = CTEMP
RETURN
END FUNCTION CDOTC
FUNCTION CDOTU(N,CX,INCX,CY,INCY)
USE DDPRECISION, ONLY : WP
COMPLEX (WP) :: CDOTU
! forms the dot product of a vector.
! jack dongarra, 3/11/78.
COMPLEX (WP) :: CX(1), CY(1), CTEMP
INTEGER :: I, IX, IY, N, INCX, INCY
CTEMP = (0.0E0_WP,0.0E0_WP)
CDOTU = (0.0E0_WP,0.0E0_WP)
IF (N<=0) RETURN
IF (INCX==1 .AND. INCY==1) GO TO 20
! code for unequal increments or equal increments
! not equal to 1
IX = 1
IY = 1
IF (INCX<0) IX = (-N+1)*INCX + 1
IF (INCY<0) IY = (-N+1)*INCY + 1
DO I = 1, N
CTEMP = CTEMP + CX(IX)*CY(IY)
IX = IX + INCX
IY = IY + INCY
END DO
CDOTU = CTEMP
RETURN
! code for both increments equal to 1
20 DO I = 1, N
CTEMP = CTEMP + CX(I)*CY(I)
END DO
CDOTU = CTEMP
RETURN
END FUNCTION CDOTU
SUBROUTINE CROTG(CA,CB,C,S)
USE DDPRECISION, ONLY : WP
COMPLEX (WP) :: CA, CB, S
REAL (WP) :: C
REAL (WP) :: NORM, SCALE
COMPLEX (WP) :: ALPHA
IF (ABS(CA)/=0.0E0_WP) GO TO 10
C = 0.0E0_WP
S = (1.0E0_WP,0.0E0_WP)
CA = CB
GO TO 20
10 CONTINUE
SCALE = ABS(CA) + ABS(CB)
NORM = SCALE*SQRT((ABS(CA/CMPLX(SCALE,0.0E0_WP,KIND=WP)))**2+(ABS(CB/ &
CMPLX(SCALE,0.0E0_WP,KIND=WP)))**2)
ALPHA = CA/ABS(CA)
C = ABS(CA)/NORM
S = ALPHA*CONJG(CB)/NORM
CA = ALPHA*NORM
20 CONTINUE
RETURN
END SUBROUTINE CROTG
SUBROUTINE CSROT(N,CX,INCX,CY,INCY,C,S)
USE DDPRECISION, ONLY : WP
! applies a plane rotation, where the cos and sin (c and s) are
! real and the vectors cx and cy are complex.
! jack dongarra, linpack, 3/11/78.
COMPLEX (WP) :: CX(1), CY(1), CTEMP
REAL (WP) :: C, S
INTEGER :: I, INCX, INCY, IX, IY, N
IF (N<=0) RETURN
IF (INCX==1 .AND. INCY==1) GO TO 20
! code for unequal increments or equal increments not equal
! to 1
IX = 1
IY = 1
IF (INCX<0) IX = (-N+1)*INCX + 1
IF (INCY<0) IY = (-N+1)*INCY + 1
DO I = 1, N
CTEMP = C*CX(IX) + S*CY(IY)
CY(IY) = C*CY(IY) - S*CX(IX)
CX(IX) = CTEMP
IX = IX + INCX
IY = IY + INCY
END DO
RETURN
! code for both increments equal to 1
20 DO I = 1, N
CTEMP = C*CX(I) + S*CY(I)
CY(I) = C*CY(I) - S*CX(I)
CX(I) = CTEMP
END DO
RETURN
END SUBROUTINE CSROT
FUNCTION SCNRM2(N,CX,INCX)
USE DDPRECISION, ONLY : WP
REAL (WP) :: SCNRM2
! Arguments:
INTEGER :: INCX, N
COMPLEX (WP) :: CX(1)
! Local variables:
INTEGER :: I, J
REAL (WP) :: SUM
!***********************************************************************
! Returns SCNRM2=unitary norm of complex n-vector stored in CX with
! storage increment INCX.
! Written to replace SCNRM2 written by C.L.Lawson, as g77 compiler
! produces bad code when optimizing Lawson's routine.
! In any event, Lawson's routine appears to be unnecessarily complicated
! for needs of DDSCAT.
! History:
! 98.10.07 (BTD) Created by B.T. Draine, Princeton Univ. Observatory,
! for use by DDSCAT
! 00.06.13 (BTD) Make data conversion explicit.
! end history
!***********************************************************************
SUM = 0._WP
DO I = 1, N
J = 1 + (I-1)*INCX
SUM = SUM + REAL(CX(J)*CONJG(CX(J)))
END DO
SCNRM2 = REAL(SQRT(SUM),KIND=WP)
RETURN
END FUNCTION SCNRM2
!-----------------------------------------------------------------------
! Following code due to C.L. Lawson has been replaced by above module
! because it generated bad code when compiled with g77.
! For use by DDSCAT the overflow/underflow avoidance strategies
! used by this routine do not appear to be necessary, so they can
! be omitted in interests of speed and clean code.
! 98.10.07 BTD
! real function scnrm2( n, cx, incx)
! logical imag, scale
! integer i, incx, ix, n, next
! real cutlo, cuthi, hitest, sum, xmax, absx, zero, one
! complex cx(1)
! real real,aimag
! complex zdumr,zdumi
! real(zdumr) = zdumr
! aimag(zdumi) = (0.0e0,-1.0e0)*zdumi
! data zero, one /0.0e0, 1.0e0/
!c
!c unitary norm of the complex n-vector stored in cx() with storage
!c increment incx .
!c if n .le. 0 return with result = 0.
!c if n .ge. 1 then incx must be .ge. 1
!c
!c c.l.lawson , 1978 jan 08
!c modified to correct problem with negative increment, 8/21/90.
!c
!c four phase method using two built-in constants that are
!c hopefully applicable to all machines.
!c cutlo = maximum of sqrt(u/eps) over all known machines.
!c cuthi = minimum of sqrt(v) over all known machines.
!c where
!c eps = smallest no. such that eps + 1. .gt. 1.
!c u = smallest positive no. (underflow limit)
!c v = largest no. (overflow limit)
!c
!c brief outline of algorithm..
!c
!c phase 1 scans zero components.
!c move to phase 2 when a component is nonzero and .le. cutlo
!c move to phase 3 when a component is .gt. cutlo
!c move to phase 4 when a component is .ge. cuthi/m
!c where m = n for x() real and m = 2*n for complex.
!c
!c values for cutlo and cuthi..
!c from the environmental parameters listed in the imsl converter
!c document the limiting values are as follows..
!c cutlo, s.p. u/eps = 2**(-102) for honeywell. close seconds ar
!c univac and dec at 2**(-103)
!c thus cutlo = 2**(-51) = 4.44089e-16
!c cuthi, s.p. v = 2**127 for univac, honeywell, and dec.
!c thus cuthi = 2**(63.5) = 1.30438e19
!c cutlo, d.p. u/eps = 2**(-67) for honeywell and dec.
!c thus cutlo = 2**(-33.5) = 8.23181d-11
!c cuthi, d.p. same as s.p. cuthi = 1.30438d19
!c data cutlo, cuthi / 8.232d-11, 1.304d19 /
!c data cutlo, cuthi / 4.441e-16, 1.304e19 /
! data cutlo, cuthi / 8.232d-11, 1.304d19 /
!c
! if(n .gt. 0) go to 10
! scnrm2 = zero
! go to 300
!c
! 10 assign 30 to next
! sum = zero
! i = 1
! if( incx .lt. 0 )i = (-n+1)*incx + 1
!c begin main loop
! do 220 ix = 1,n
! absx = abs(real(cx(i)))
! imag = .false.
! go to next,(30, 50, 70, 90, 110)
! 30 if( absx .gt. cutlo) go to 85
! assign 50 to next
! scale = .false.
!c
!c phase 1. sum is zero
!c
! 50 if( absx .eq. zero) go to 200
! if( absx .gt. cutlo) go to 85
!c
!c prepare for phase 2.
! assign 70 to next
! go to 105
!c
!c prepare for phase 4.
!c
! 100 assign 110 to next
! sum = (sum / absx) / absx
! 105 scale = .true.
! xmax = absx
! go to 115
!c
!c phase 2. sum is small.
!c scale to avoid destructive underflow.
!c
! 70 if( absx .gt. cutlo ) go to 75
!c
!c common code for phases 2 and 4.
!c in phase 4 sum is large. scale to avoid overflow
!c
! 110 if( absx .le. xmax ) go to 115
! sum = one + sum * (xmax / absx)**2
! xmax = absx
! go to 200
!c
! 115 sum = sum + (absx/xmax)**2
! go to 200
!c
!c
!c prepare for phase 3.
!c
! 75 sum = (sum * xmax) * xmax
!c
! 85 assign 90 to next
! scale = .false.
!c
!c for real or d.p. set hitest = cuthi/n
!c for complex set hitest = cuthi/(2*n)
!c
! hitest = cuthi/float( 2*n )
!c
!c phase 3. sum is mid-range. no scaling.
!c
! 90 if(absx .ge. hitest) go to 100
! sum = sum + absx**2
! 200 continue
!c control selection of real and imaginary parts.
!c
! if(imag) go to 210
! absx = abs(aimag(cx(i)))
! imag = .true.
! go to next,( 50, 70, 90, 110 )
!c
! 210 continue
! i = i + incx
! 220 continue
!c
!c end of main loop.
!c compute square root and adjust for scaling.
!c
! scnrm2 = sqrt(sum)
! if(scale) scnrm2 = scnrm2 * xmax
! 300 continue
! return
! end
!-----------------------------------------------------------------------
SUBROUTINE SROTG(DA,DB,C,S)
USE DDPRECISION, ONLY : WP
! construct givens plane rotation.
! jack dongarra, linpack, 3/11/78.
! modified 9/27/86.
REAL (WP) :: DA, DB, C, S, ROE, SCALE, R, Z
ROE = DB
IF (ABS(DA)>ABS(DB)) ROE = DA
SCALE = ABS(DA) + ABS(DB)
IF (SCALE/=0.0E0_WP) GO TO 10
C = 1.0E0_WP
S = 0.0E0_WP
R = 0.0E0_WP
GO TO 20
10 R = SCALE*SQRT((DA/SCALE)**2+(DB/SCALE)**2)
R = SIGN(1.0E0_WP,ROE)*R
C = DA/R
S = DB/R
20 Z = S
IF (ABS(C)>0.0E0_WP .AND. ABS(C)<=S) Z = 1.0E0_WP/C
DA = R
DB = Z
RETURN
END SUBROUTINE SROTG
SUBROUTINE DMACHCONS(WHAT,RESULT)
USE DDPRECISION, ONLY : WP
! These values are for IEEE-754 arithmetic
! 07.08.05 (BTD) Modified for compatibility with both single or
! double precision -- eliminate PARAMETER statements,
! add executable statements.
! Will these slow execution??
! How often is DMACHCONS called?
! 08.08.05 (BTD) Modified to use preprocessing to modify file
! to use appropriate precision MACHEPS,OVERFlOW,
! end UNDERFLOW
! end history --------------------------------------------------------
! .. Parameters ..
REAL (WP) :: MACHEPS,OVERFLOW,UNDERFLOW
#ifdef sp
PARAMETER(MACHEPS=1.192093E-7_WP)
PARAMETER(OVERFLOW=3.402823E+38_WP)
PARAMETER(UNDERFLOW=1.17549435E-38_WP)
#endif
#ifdef dp
PARAMETER(MACHEPS=2.2204460492503E-16_WP)
PARAMETER(OVERFLOW=1.7976313E+308_WP)
PARAMETER(UNDERFLOW=2.2250739E-308_WP)
#endif
! .. Scalar Arguments ..
REAL (WP) :: RESULT
CHARACTER :: WHAT
IF((WHAT=='M').OR.(WHAT=='m'))THEN
RESULT=MACHEPS
ELSEIF((WHAT=='U').OR.(WHAT=='u'))THEN
RESULT=UNDERFLOW
ELSEIF((WHAT=='O').OR.(WHAT=='o'))THEN
RESULT=OVERFLOW
ENDIF
RETURN
END SUBROUTINE DMACHCONS
SUBROUTINE PIMDGETPAR(IPAR,DPAR,LDA,N,BLKSZ,LOCLEN,BASISDIM,NPROCS,PROCID, &
PRECONTYPE,STOPTYPE,MAXIT,ITNO,STATUS,STEPERR,EPSILON,EXITNORM)
USE DDPRECISION, ONLY : WP
! PIM -- The Parallel Iterative Methods package
! ---------------------------------------------
! Rudnei Dias da Cunha
! Centro de Processamento de Dados,
! Universidade Federal do Rio Grande do Sul, Brasil
! and
! Computing Laboratory, University of Kent at Canterbury, U.K.
! Tim Hopkins
! Computing Laboratory, University of Kent at Canterbury, U.K.
! ----------------------------------------------------------------------
! Description of parameter arrays
! IPAR (INPUT) : integer
! ipar( 1): lda (Leading dimension of a)
! 2 : n (Number of rows/columns of a)
! 3 : blksz (Size of block of data; used when data is
! partitioned using cyclic mode)
! 4 : loclen (Number of elements stored locally;
! *PARALLEL: Equal to at least m/nprocs or
! n/procs depending if row or
! column partitioning is used or,
! in the case of cyclic partitioning,
! it is a multiple of either
! m/(blksz*nprocs) or n/(blksz*nprocs).
! *SEQUENTIAL: equal to n)
! 5 : basisdim (Dimension of orthogonal basis, used in