      SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DCOPY
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A5
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SCOPY-S DCOPY-D CCOPY-C),COPY,
C             LINEAR ALGEBRA,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P. vector copy y = x
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C       DY  copy of vector DX (unchanged if N .LE. 0)
C
C     Copy double precision DX to double precision DY.
C     For I = 0 to N-1, copy DX(LX+I*INCX) to DY(LY+I*INCY),
C     where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is
C     defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DCOPY
C
      DOUBLE PRECISION DX(1),DY(1)
C***FIRST EXECUTABLE STATEMENT  DCOPY
      IF(N.LE.0)RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C        CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DY(IY) = DX(IX)
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C        CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 7.
C
   20 M = MOD(N,7)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DY(I) = DX(I)
   30 CONTINUE
      IF( N .LT. 7 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,7
        DY(I) = DX(I)
        DY(I + 1) = DX(I + 1)
        DY(I + 2) = DX(I + 2)
        DY(I + 3) = DX(I + 3)
        DY(I + 4) = DX(I + 4)
        DY(I + 5) = DX(I + 5)
        DY(I + 6) = DX(I + 6)
   50 CONTINUE
      RETURN
C
C        CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
C
   60 CONTINUE
      NS=N*INCX
          DO 70 I=1,NS,INCX
          DY(I) = DX(I)
   70     CONTINUE
      RETURN
      END

      SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DAXPY
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A7
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SAXPY-S DAXPY-D CAXPY-C),
C             LINEAR ALGEBRA,TRIAD,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P computation y = a*x + y
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DA  double precision scalar multiplier
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C       DY  double precision result (unchanged if N .LE. 0)
C
C     Overwrite double precision DY with double precision DA*DX + DY.
C     For I = 0 to N-1, replace  DY(LY+I*INCY) with DA*DX(LX+I*INCX) +
C       DY(LY+I*INCY), where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N
C       and LY is defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DAXPY
C
      DOUBLE PRECISION DX(1),DY(1),DA
C***FIRST EXECUTABLE STATEMENT  DAXPY
      IF(N.LE.0.OR.DA.EQ.0.D0) RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C        CODE FOR NONEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DY(IY) = DY(IY) + DA*DX(IX)
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C        CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 4.
C
   20 M = MOD(N,4)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DY(I) = DY(I) + DA*DX(I)
   30 CONTINUE
      IF( N .LT. 4 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,4
        DY(I) = DY(I) + DA*DX(I)
        DY(I + 1) = DY(I + 1) + DA*DX(I + 1)
        DY(I + 2) = DY(I + 2) + DA*DX(I + 2)
        DY(I + 3) = DY(I + 3) + DA*DX(I + 3)
   50 CONTINUE
      RETURN
C
C        CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
C
   60 CONTINUE
      NS = N*INCX
          DO 70 I=1,NS,INCX
          DY(I) = DA*DX(I) + DY(I)
   70     CONTINUE
      RETURN
      END

      DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DDOT
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A4
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SDOT-S DDOT-D CDOTU-C),
C             INNER PRODUCT,LINEAR ALGEBRA,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P. inner product of d.p. vectors
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C     DDOT  double precision dot product (zero if N .LE. 0)
C
C     Returns the dot product of double precision DX and DY.
C     DDOT = sum for I = 0 to N-1 of  DX(LX+I*INCX) * DY(LY+I*INCY)
C     where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is
C     defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DDOT
C
      DOUBLE PRECISION DX(1),DY(1)
C***FIRST EXECUTABLE STATEMENT  DDOT
      DDOT = 0.D0
      IF(N.LE.0)RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C         CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
         DDOT = DDOT + DX(IX)*DY(IY)
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C        CODE FOR BOTH INCREMENTS EQUAL TO 1.
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 5.
C
   20 M = MOD(N,5)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
         DDOT = DDOT + DX(I)*DY(I)
   30 CONTINUE
      IF( N .LT. 5 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,5
         DDOT = DDOT + DX(I)*DY(I) + DX(I+1)*DY(I+1) +
     1   DX(I + 2)*DY(I + 2) + DX(I + 3)*DY(I + 3) + DX(I + 4)*DY(I + 4)
   50 CONTINUE
      RETURN
C
C         CODE FOR POSITIVE EQUAL INCREMENTS .NE.1.
C
   60 CONTINUE
      NS = N*INCX
          DO 70 I=1,NS,INCX
          DDOT = DDOT + DX(I)*DY(I)
   70     CONTINUE
      RETURN
      END

      DOUBLE PRECISION FUNCTION DNRM2(N,DX,INCX)
C***BEGIN PROLOGUE  DNRM2
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A3B
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SNRM2-S DNRM2-D SCNRM2-C),
C             EUCLIDEAN LENGTH,EUCLIDEAN NORM,L2,LINEAR ALGEBRA,UNITARY,
C             VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Euclidean length (L2 norm) of d.p. vector
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C    DNRM2  double precision result (zero if N .LE. 0)
C
C     Euclidean norm of the N-vector stored in DX() 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
C     Four phase method     using two built-in constants that are
C     hopefully applicable to all machines.
C         CUTLO = maximum of  DSQRT(U/EPS)  over all known machines.
C         CUTHI = minimum of  DSQRT(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 are
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
      SAVE CUTLO, CUTHI, ZERO, ONE
C     DATA CUTLO, CUTHI / 8.232D-11,  1.304D19 /
C     DATA CUTLO, CUTHI / 4.441E-16,  1.304E19 /
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DNRM2
      INTEGER          NEXT
      DOUBLE PRECISION   DX(1), CUTLO, CUTHI, HITEST, SUM, XMAX,ZERO,ONE
      DATA   ZERO, ONE /0.0D0, 1.0D0/
C
      DATA CUTLO, CUTHI / 8.232D-11,  1.304D19 /
C***FIRST EXECUTABLE STATEMENT  DNRM2
      IF(N .GT. 0) GO TO 10
         DNRM2  = ZERO
         GO TO 300
C
   10 ASSIGN 30 TO NEXT
      SUM = ZERO
      NN = N * INCX
C                                                 BEGIN MAIN LOOP
      I = 1
   20    GO TO NEXT,(30, 50, 70, 110)
   30 IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
      ASSIGN 50 TO NEXT
      XMAX = ZERO
C
C                        PHASE 1.  SUM IS ZERO
C
   50 IF( DX(I) .EQ. ZERO) GO TO 200
      IF( DABS(DX(I)) .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 I = J
      ASSIGN 110 TO NEXT
      SUM = (SUM / DX(I)) / DX(I)
  105 XMAX = DABS(DX(I))
      GO TO 115
C
C                   PHASE 2.  SUM IS SMALL.
C                             SCALE TO AVOID DESTRUCTIVE UNDERFLOW.
C
   70 IF( DABS(DX(I)) .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( DABS(DX(I)) .LE. XMAX ) GO TO 115
         SUM = ONE + SUM * (XMAX / DX(I))**2
         XMAX = DABS(DX(I))
         GO TO 200
C
  115 SUM = SUM + (DX(I)/XMAX)**2
      GO TO 200
C
C
C                  PREPARE FOR PHASE 3.
C
   75 SUM = (SUM * XMAX) * XMAX
C
C
C     FOR REAL OR D.P. SET HITEST = CUTHI/N
C     FOR COMPLEX      SET HITEST = CUTHI/(2*N)
C
   85 HITEST = CUTHI/FLOAT( N )
C
C                   PHASE 3.  SUM IS MID-RANGE.  NO SCALING.
C
      DO 95 J =I,NN,INCX
      IF(DABS(DX(J)) .GE. HITEST) GO TO 100
   95    SUM = SUM + DX(J)**2
      DNRM2 = DSQRT( SUM )
      GO TO 300
C
  200 CONTINUE
      I = I + INCX
      IF ( I .LE. NN ) GO TO 20
C
C              END OF MAIN LOOP.
C
C              COMPUTE SQUARE ROOT AND ADJUST FOR SCALING.
C
      DNRM2 = XMAX * DSQRT(SUM)
  300 CONTINUE
      RETURN
      END

      SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DSWAP
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A5
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SSWAP-S DSWAP-D CSWAP-C ISWAP-I),
C             INTERCHANGE,LINEAR ALGEBRA,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Interchange d.p. vectors
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C       DX  input vector DY (unchanged if N .LE. 0)
C       DY  input vector DX (unchanged if N .LE. 0)
C
C     Interchange double precision DX and double precision DY.
C     For I = 0 to N-1, interchange  DX(LX+I*INCX) and DY(LY+I*INCY),
C     where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is
C     defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DSWAP
C
      DOUBLE PRECISION DX(1),DY(1),DTEMP1,DTEMP2,DTEMP3
C***FIRST EXECUTABLE STATEMENT  DSWAP
      IF(N.LE.0)RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C       CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DTEMP1 = DX(IX)
        DX(IX) = DY(IY)
        DY(IY) = DTEMP1
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C       CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C       CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 3.
C
   20 M = MOD(N,3)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DTEMP1 = DX(I)
        DX(I) = DY(I)
        DY(I) = DTEMP1
   30 CONTINUE
      IF( N .LT. 3 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,3
        DTEMP1 = DX(I)
        DTEMP2 = DX(I+1)
        DTEMP3 = DX(I+2)
        DX(I) = DY(I)
        DX(I+1) = DY(I+1)
        DX(I+2) = DY(I+2)
        DY(I) = DTEMP1
        DY(I+1) = DTEMP2
        DY(I+2) = DTEMP3
   50 CONTINUE
      RETURN
   60 CONTINUE
C
C     CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
C
      NS = N*INCX
        DO 70 I=1,NS,INCX
        DTEMP1 = DX(I)
        DX(I) = DY(I)
        DY(I) = DTEMP1
   70   CONTINUE
      RETURN
      END

      SUBROUTINE DSCAL(N,DA,DX,INCX)
C***BEGIN PROLOGUE  DSCAL
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A6
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SSCAL-S DSCAL-D CSCAL-C),
C             LINEAR ALGEBRA,SCALE,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P. vector scale x = a*x
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DA  double precision scale factor
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C       DX  double precision result (unchanged if N.LE.0)
C
C     Replace double precision DX by double precision DA*DX.
C     For I = 0 to N-1, replace DX(1+I*INCX) with  DA * DX(1+I*INCX)
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DSCAL
C
      DOUBLE PRECISION DA,DX(1)
C***FIRST EXECUTABLE STATEMENT  DSCAL
      IF(N.LE.0)RETURN
      IF(INCX.EQ.1)GOTO 20
C
C        CODE FOR INCREMENTS NOT EQUAL TO 1.
C
      NS = N*INCX
          DO 10 I = 1,NS,INCX
          DX(I) = DA*DX(I)
   10     CONTINUE
      RETURN
C
C        CODE FOR INCREMENTS EQUAL TO 1.
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 5.
C
   20 M = MOD(N,5)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DX(I) = DA*DX(I)
   30 CONTINUE
      IF( N .LT. 5 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,5
        DX(I) = DA*DX(I)
        DX(I + 1) = DA*DX(I + 1)
        DX(I + 2) = DA*DX(I + 2)
        DX(I + 3) = DA*DX(I + 3)
        DX(I + 4) = DA*DX(I + 4)
   50 CONTINUE
      RETURN
      END
      DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX)
C***BEGIN PROLOGUE  DASUM
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A3A
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SASUM-S DASUM-D SCASUM-C),ADD,
C             LINEAR ALGEBRA,MAGNITUDE,SUM,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Sum of magnitudes of d.p. vector components
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C    DASUM  double precision result (zero if N .LE. 0)
C
C     Returns sum of magnitudes of double precision DX.
C     DASUM = sum from 0 to N-1 of DABS(DX(1+I*INCX))
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DASUM
C
      DOUBLE PRECISION DX(1)
C***FIRST EXECUTABLE STATEMENT  DASUM
      DASUM = 0.D0
      IF(N.LE.0)RETURN
      IF(INCX.EQ.1)GOTO 20
C
C        CODE FOR INCREMENTS NOT EQUAL TO 1.
C
      NS = N*INCX
          DO 10 I=1,NS,INCX
          DASUM = DASUM + DABS(DX(I))
   10     CONTINUE
      RETURN
C
C        CODE FOR INCREMENTS EQUAL TO 1.
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 6.
C
   20 M = MOD(N,6)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
         DASUM = DASUM + DABS(DX(I))
   30 CONTINUE
      IF( N .LT. 6 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,6
         DASUM = DASUM + DABS(DX(I)) + DABS(DX(I+1)) + DABS(DX(I+2))
     1   + DABS(DX(I+3)) + DABS(DX(I+4)) + DABS(DX(I+5))
   50 CONTINUE
      RETURN
      END
      INTEGER FUNCTION IDAMAX(N,DX,INCX)
C***BEGIN PROLOGUE  IDAMAX
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A2
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(ISAMAX-S IDAMAX-D ICAMAX-C),
C             LINEAR ALGEBRA,MAXIMUM COMPONENT,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Find the smallest index of that component of a d.p. vector
C            having the maximum magnitude.
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C   IDAMAX  smallest index (zero if N .LE. 0)
C
C     Find smallest index of maximum magnitude of double precision DX.
C     IDAMAX =  first I, I = 1 to N, to minimize  ABS(DX(1-INCX+I*INCX)
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  IDAMAX
C
      DOUBLE PRECISION DX(*),DMAX,XMAG
C***FIRST EXECUTABLE STATEMENT  IDAMAX
      IDAMAX = 0
      IF(N.LE.0) RETURN
      IDAMAX = 1
      IF(N.LE.1)RETURN
      IF(INCX.EQ.1)GOTO 20
C
C        CODE FOR INCREMENTS NOT EQUAL TO 1.
C
      DMAX = DABS(DX(1))
      NS = N*INCX
      II = 1
          DO 10 I = 1,NS,INCX
          XMAG = DABS(DX(I))
          IF(XMAG.LE.DMAX) GO TO 5
          IDAMAX = II
          DMAX = XMAG
    5     II = II + 1
   10     CONTINUE
      RETURN
C
C        CODE FOR INCREMENTS EQUAL TO 1.
C
   20 DMAX = DABS(DX(1))
      DO 30 I = 2,N
          XMAG = DABS(DX(I))
          IF(XMAG.LE.DMAX) GO TO 30
          IDAMAX = I
          DMAX = XMAG
   30 CONTINUE
      RETURN
      END
      SUBROUTINE  DROT (N,DX,INCX,DY,INCY,C,S)
C
C     APPLIES A PLANE ROTATION.
C     JACK DONGARRA, LINPACK, 3/11/78.
C
      DOUBLE PRECISION DX(1),DY(1),DTEMP,C,S
      INTEGER I,INCX,INCY,IX,IY,N
C
      IF(N.LE.0)RETURN
      IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20
C
C       CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS NOT EQUAL
C         TO 1
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DTEMP = C*DX(IX) + S*DY(IY)
        DY(IY) = C*DY(IY) - S*DX(IX)
        DX(IX) = DTEMP
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C       CODE FOR BOTH INCREMENTS EQUAL TO 1
C
   20 DO 30 I = 1,N
        DTEMP = C*DX(I) + S*DY(I)
        DY(I) = C*DY(I) - S*DX(I)
        DX(I) = DTEMP
   30 CONTINUE
      RETURN
      END
      subroutine drotg(da,db,c,s)
c
c     construct givens plane rotation.
c     jack dongarra, linpack, 3/11/78.
c
      double precision da,db,c,s,roe,scale,r,z
c
      roe = db
      if( dabs(da) .gt. dabs(db) ) roe = da
      scale = dabs(da) + dabs(db)
      if( scale .ne. 0.0d0 ) go to 10
         c = 1.0d0
         s = 0.0d0
         r = 0.0d0
         go to 20
   10 r = scale*dsqrt((da/scale)**2 + (db/scale)**2)
      r = dsign(1.0d0,roe)*r
      c = da/r
      s = db/r
   20 z = 1.0d0
      if( dabs(da) .gt. dabs(db) ) z = s
      if( dabs(db) .ge. dabs(da) .and. c .ne. 0.0d0 ) z = 1.0d0/c
      da = r
      db = z
      return
      end
