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*DASUM
FUNCTION DASUM(N,DX,INCX) RESULT(DASUMR)
C***Begin Prologue DASUM
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A3A
C***Keywords Add,BLAS,REAL(wp),Linear Algebra,Magnitude,Sum,
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 Sum of Magnitudes of D.P. Vector Components
C***Description
C B L A S Subprogram
C Description of parameters
C --Input--
C N Number of elements in input vector(s)
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C --Output--
C DASUM REAL(wp) result (Zero IF N .LE. 0)
C Returns sum of magnitudes of REAL(wp) 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...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
INTEGER
& INCX,N
C...Array arguments
REAL(wp)
& DX(*)
C...Result
REAL(wp)
& DASUMR
C...Local scalars
INTEGER
& I,M,MP1,NS
C...Intrinsic functions
INTRINSIC
& DABS,MOD
C***First executable statement DASUM
DASUMR = 0.E0_wp
IF(N.LE.0)RETURN
IF(INCX.EQ.1)GOTO 20
C Code for increments not equal to 1.
NS = N*INCX
DO 10 I=1,NS,INCX
DASUMR = DASUMR + DABS(DX(I))
10 CONTINUE
RETURN
C Code for increments equal to 1.
C Clean-up loop so remaining vector length is a multiple of 6.
20 M = MOD(N,6)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DASUMR = DASUMR + DABS(DX(I))
30 CONTINUE
IF( N .LT. 6 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,6
DASUMR = DASUMR + 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
*DAXPY
SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
C***Begin Prologue DAXPY
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A7
C***Keywords BLAS,REAL(wp),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 B L A S Subprogram
C Description of parameters
C --Input--
C N Number of elements in input vector(s)
C DA REAL(wp) scalar multiplier
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C DY REAL(wp) vector with N elements
C INCY Storage spacing between elements of DY
C --Output--
C DY REAL(wp) result (unchanged IF N .LE. 0)
C Overwrite REAL(wp) DY with REAL(wp) 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...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
REAL(wp)
& DA
INTEGER
& INCX,INCY,N
C...Array arguments
REAL(wp)
& DX(*),DY(*)
C...Local scalars
INTEGER
& I,IX,IY,M,MP1,NS
C...Intrinsic functions
INTRINSIC
& MOD
C***First executable statement DAXPY
IF(N.LE.0.OR.DA.EQ.0.E0_wp) RETURN
IF(INCX.EQ.INCY) THEN
IF(INCX-1.LT.0) THEN
GOTO 5
ELSE IF (INCX-1.EQ.0) THEN
GOTO 20
ELSE IF (INCX-1.GT.0) THEN
GOTO 60
END IF
END IF
5 CONTINUE
C Code for nonequal or nonpositive increments.
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 Code for both increments equal to 1
C Clean-up loop so remaining vector length is a multiple of 4.
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 Code for equal, positive, nonunit increments.
60 CONTINUE
NS = N*INCX
DO 70 I=1,NS,INCX
DY(I) = DA*DX(I) + DY(I)
70 CONTINUE
RETURN
END
*DCOPY
SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
C***Begin Prologue DCOPY
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A5
C***Keywords BLAS,Copy,REAL(wp),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 B L A S Subprogram
C Description of parameters
C --Input--
C N Number of elements in input vector(s)
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C DY REAL(wp) vector with N elements
C INCY Storage spacing between elements of DY
C --Output--
C DY Copy of vector DX (unchanged if N .LE. 0)
C Copy REAL(wp) DX to REAL(wp) 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...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
INTEGER
& INCX,INCY,N
C...Array arguments
REAL(wp)
& DX(*),DY(*)
C...Local scalars
INTEGER
& I,IX,IY,M,MP1,NS
C...Intrinsic functions
INTRINSIC
& MOD
C***First executable statement DCOPY
IF(N.LE.0)RETURN
IF(INCX.EQ.INCY) THEN
IF(INCX-1.LT.0) THEN
GOTO 5
ELSE IF(INCX-1.EQ.0) THEN
GOTO 20
ELSE IF(INCX-1.GT.0) THEN
GOTO 60
END IF
END IF
5 CONTINUE
C Code for unequal or nonpositive increments.
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 Code for both increments equal to 1
C Clean-up loop so remaining vector length is a multiple of 7.
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 Code for equal, positive, nonunit increments.
60 CONTINUE
NS=N*INCX
DO 70 I=1,NS,INCX
DY(I) = DX(I)
70 CONTINUE
RETURN
END
*DDOT
FUNCTION DDOT(N,DX,INCX,DY,INCY) RESULT(DDOTR)
C***Begin Prologue DDOT
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A4
C***Keywords BLAS,REAL(wp),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 B L A S Subprogram
C Description of parameters
C --Input--
C N Number of elements in input vector(s)
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C DY REAL(wp) vector with N elements
C INCY Storage spacing between elements of DY
C --Output--
C DDOT REAL(wp) dot product (zero if N .LE. 0)
C returns the dot product of REAL(wp) 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...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
INTEGER
& INCX,INCY,N
C...Array arguments
REAL(wp)
& DX(*),DY(*)
C...Result
REAL(wp)
& DDOTR
C...Local scalars
INTEGER
& I,IX,IY,M,MP1,NS
C...Intrinsic functions
INTRINSIC
& MOD
C***First executable statement DDOT
DDOTR = 0.E0_wp
IF(N.LE.0)RETURN
IF(INCX.EQ.INCY) THEN
IF(INCX-1.LT.0) THEN
GOTO 5
ELSE IF(INCX-1.EQ.0) THEN
GOTO 20
ELSE IF(INCX-1.GT.0) THEN
GOTO 60
END IF
END IF
5 CONTINUE
C Code for unequal or nonpositive increments.
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
DDOTR = DDOTR + DX(IX)*DY(IY)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C Code for both increments equal to 1.
C Clean-up loop so remaining vector length is a multiple of 5.
20 M = MOD(N,5)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DDOTR = DDOTR + DX(I)*DY(I)
30 CONTINUE
IF( N .LT. 5 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,5
DDOTR = DDOTR + 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 Code for positive equal increments .NE.1.
60 CONTINUE
NS = N*INCX
DO 70 I=1,NS,INCX
DDOTR = DDOTR + DX(I)*DY(I)
70 CONTINUE
RETURN
END
*DNRM2
FUNCTION DNRM2(N,DX,INCX) RESULT(DNRM2R)
C***Begin Prologue DNRM2
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A3B
C***Keywords BLAS,REAL(wp),Euclidean,L2,Length,Linear Algebra,
C Norm,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 B L A S Subprogram
C Description of parameters
C --Input--
C N Number of elements in input vector(s)
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C --Output--
C DNRM2 REAL(wp) result (zero if N .LE. 0)
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.L. Lawson, 1978 Jan 08
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 Brief outline of algorithm..
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 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_wp
C CUTHI, S.P. V = 2**127 for UNIVAC, Honeywell, and DEC.
C thus CUTHI = 2**(63.5) = 1.30438E19_wp
C CUTLO, D.P. U/EPS = 2**(-67) for Honeywell and DEC.
C thus CUTLO = 2**(-33.5) = 8.23181E-11_wp
C CUTHI, D.P. Same as S.P. CUTHI = 1.30438E19_wp
C DATA CUTLO, CUTHI / 8.232E-11_wp, 1.304E19_wp /
C DATA CUTLO, CUTHI / 4.441E-16_wp, 1.304E19_wp /
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
C...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
INTEGER
& INCX,N
C...Array arguments
REAL(wp)
& DX(*)
C...Result
REAL(wp)
& DNRM2R
C...Local scalars
REAL(wp)
& CUTHI,CUTLO,HITEST,ONE,SUM,XMAX,ZERO
INTEGER
& I,J,NEXT,NN
C...Intrinsic functions
INTRINSIC
& DABS,DSQRT,FLOAT
C...Data statements
DATA
& ZERO,ONE/0.0E0_wp,1.0E0_wp/
DATA
& CUTLO,CUTHI/8.232E-11_wp,1.304E19_wp/
C***First executable statement DNRM2
XMAX = ZERO
IF(N .GT. 0) GO TO 10
DNRM2R = ZERO
GO TO 300
10 NEXT=30
SUM = ZERO
NN = N * INCX
C Begin main loop
I = 1
20 IF (NEXT.EQ.30) THEN; GOTO 30; END IF
IF (NEXT.EQ.50) THEN; GOTO 50; END IF
IF (NEXT.EQ.70) THEN; GOTO 70; END IF
IF (NEXT.EQ.110) THEN; GOTO 110; END IF
30 IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
NEXT=50
XMAX = ZERO
C Phase 1. Sum is zero
50 IF( DX(I) .EQ. ZERO) GO TO 200
IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
C Prepare for Phase 2.
NEXT=70
GO TO 105
C Prepare for Phase 4.
100 I = J
NEXT=110
SUM = (SUM / DX(I)) / DX(I)
105 XMAX = DABS(DX(I))
GO TO 115
C Phase 2. Sum is small.
C Scale to avoid destructive underflow.
70 IF( DABS(DX(I)) .GT. CUTLO ) GO TO 75
C Common code for Phases 2 and 4.
C In Phase 4 sum is large. Scale to avoid overflow.
110 IF( DABS(DX(I)) .LE. XMAX ) GO TO 115
SUM = ONE + SUM * (XMAX / DX(I))**2
XMAX = DABS(DX(I))
GO TO 200
115 SUM = SUM + (DX(I)/XMAX)**2
GO TO 200
C Prepare for Phase 3.
75 SUM = (SUM * XMAX) * XMAX
C For REAL OR D.P. set HITEST = CUTHI/N
C For COMPLEX set HITEST = CUTHI/(2*N)
85 HITEST = CUTHI/FLOAT( N )
C Phase 3. Sum is mid-range. No scaling.
DO 95 J =I,NN,INCX
IF(DABS(DX(J)) .GE. HITEST) GO TO 100
SUM = SUM + DX(J)**2
95 CONTINUE
DNRM2R = DSQRT( SUM )
GO TO 300
200 CONTINUE
I = I + INCX
IF ( I .LE. NN ) GO TO 20
C End of main loop.
C Compute square root and adjust for scaling.
DNRM2R = XMAX * DSQRT(SUM)
300 CONTINUE
RETURN
END
*DROT
SUBROUTINE DROT(N,DX,INCX,DY,INCY,DC,DS)
C***Begin Prologue DROT
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A8
C***Keywords BLAS,Givens Rotation,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 Apply D.P. Givens Rotation
C***Description
C B L A S Subprogram
C Description of Parameters
C --Input--
C N Number of elements in input vector(s)
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C DY REAL(wp) vector with N elements
C INCY Storage spacing between elements of DY
C DC D.P. element of rotation matrix
C DS D.P. element of rotation matrix
C --Output--
C DX Rotated vector (unchanged if N .LE. 0)
C DY Rotated vector (unchanged if N .LE. 0)
C Multiply the 2 x 2 matrix ( DC DS) times the 2 x N matrix (DX**T)
C (-DS DC) (DY**T)
C where **T indicates transpose. The elements of DX are in
C DX(LX+I*INCX), I = 0 to N-1, where LX = 1 if INCX .GE. 0, else
C LX = (-INCX)*N, and similarly for DY using LY and 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 DROT
C...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
REAL(wp)
& DC,DS
INTEGER
& INCX,INCY,N
C...Array arguments
REAL(wp)
& DX(*),DY(*)
C...Local scalars
REAL(wp)
& ONE,W,Z,ZERO
INTEGER
& I,KX,KY,NSTEPS
C...Data statements
DATA
& ZERO,ONE/0.E0_wp,1.E0_wp/
C***First executable statement DROT
IF(N .LE. 0 .OR. (DS .EQ. ZERO .AND. DC .EQ. ONE)) GO TO 40
IF(.NOT. (INCX .EQ. INCY .AND. INCX .GT. 0)) GO TO 20
NSTEPS=INCX*N
DO 10 I=1,NSTEPS,INCX
W=DX(I)
Z=DY(I)
DX(I)=DC*W+DS*Z
DY(I)=-DS*W+DC*Z
10 CONTINUE
GO TO 40
20 CONTINUE
KX=1
KY=1
IF(INCX .LT. 0) KX=1-(N-1)*INCX
IF(INCY .LT. 0) KY=1-(N-1)*INCY
DO 30 I=1,N
W=DX(KX)
Z=DY(KY)
DX(KX)=DC*W+DS*Z
DY(KY)=-DS*W+DC*Z
KX=KX+INCX
KY=KY+INCY
30 CONTINUE
40 CONTINUE
RETURN
END
*DROTG
SUBROUTINE DROTG(DA,DB,DC,DS)
C***Begin Prologue DROTG
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1B10
C***Keywords BLAS,Givens Rotation,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 Construct D.P. Plane Givens Rotation
C***Description
C B L A S Subprogram
C Description of Parameters
C --Input--
C DA REAL(wp) scalar
C DB REAL(wp) scalar
C --Output--
C DA REAL(wp) result R
C DB REAL(wp) result Z
C DC REAL(wp) result
C DS REAL(wp) result
C Designed By C. L. Lawson, JPL, 1977 Sept 08
C Construct the Givens Transformation
C ( DC DS )
C G = ( ) , DC**2 + DS**2 = 1 ,
C (-DS DC )
C which zeros the second entry of the 2-vector (DA,DB)**T .
C the quantity R = (+/-)DSQRT(DA**2 + DB**2) overwrites DA in
C storage. The value of DB is overwritten by a value Z which
C allows DC and DS to be recovered by the following algorithm.
C If Z=1 set DC=0.E0_wp and DS=1.E0_wp
C If DABS(Z) .LT. 1 set DC=DSQRT(1-Z**2) and DS=Z
C If DABS(Z) .GT. 1 set DC=1/Z and DS=DSQRT(1-DC**2)
C Normally, the subprogram DROT(N,DX,INCX,DY,INCY,DC,DS) will
C next be called to apply the transformation to a 2 by N matrix.
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 DROTG
C...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
REAL(wp)
& DA,DB,DC,DS
C...Local scalars
REAL(wp)
& R,U,V
C...Intrinsic functions
INTRINSIC
& DABS,DSQRT
C***First executable statement DROTG
IF (DABS(DA) .LE. DABS(DB)) GO TO 10
C *** Here DABS(DA) .GT. DABS(DB) ***
U = DA + DA
V = DB / U
C Note that U and R have the sign of DA
R = DSQRT(.25E0_wp + V**2) * U
C Note that DC is positive
DC = DA / R
DS = V * (DC + DC)
DB = DS
DA = R
RETURN
C *** Here DABS(DA) .LE. DABS(DB) ***
10 IF (DB .EQ. 0.E0_wp) GO TO 20
U = DB + DB
V = DA / U
C Note that U and R have the sign of DB
C (R is immediately stored in DA)
DA = DSQRT(.25E0_wp + V**2) * U
C Note that DS is positive
DS = DB / DA
DC = V * (DS + DS)
IF (DC .EQ. 0.E0_wp) GO TO 15
DB = 1.E0_wp / DC
RETURN
15 DB = 1.E0_wp
RETURN
C *** Here DA = DB = 0.E0_wp ***
20 DC = 1.E0_wp
DS = 0.E0_wp
RETURN
END
*DSCAL
SUBROUTINE DSCAL(N,DA,DX,INCX)
C***Begin Prologue DSCAL
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A6
C***Keywords BLAS,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 B L A S Subprogram
C Description of Parameters
C --Input--
C N Number of elements in input vector(s)
C DA REAL(wp) scale factor
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C --Output--
C DX REAL(wp) result (unchanged if N.LE.0)
C Replace REAL(wp) DX by REAL(wp) 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...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
REAL(wp)
& DA
INTEGER
& INCX,N
C...Array arguments
REAL(wp)
& DX(*)
C...Local scalars
INTEGER
& I,M,MP1,NS
C...Intrinsic functions
INTRINSIC
& MOD
C***First executable statement DSCAL
IF(N.LE.0)RETURN
IF(INCX.EQ.1)GOTO 20
C Code for increments not equal to 1.
NS = N*INCX
DO 10 I = 1,NS,INCX
DX(I) = DA*DX(I)
10 CONTINUE
RETURN
C Code for increments equal to 1.
C Clean-up loop so remaining vector length is a multiple of 5.
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
*DSWAP
SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
C***Begin Prologue DSWAP
C***Date Written 791001 (YYMMDD)
C***Revision Date 820801 (YYMMDD)
C***Category No. D1A5
C***Keywords BLAS,REAL(wp),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 B L A S Subprogram
C Description of Parameters
C --Input--
C N Number of elements in input vector(s)
C DX REAL(wp) vector with N elements
C INCX Storage spacing between elements of DX
C DY REAL(wp) vector with N elements
C INCY Storage spacing between elements of DY
C --Output--
C DX Input vector DY (unchanged if N .LE. 0)
C DY Input vector DX (unchanged if N .LE. 0)
C Interchange REAL(wp) DX and REAL(wp) 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...Used modules
use odrpack_kinds, only: wp
C...Scalar arguments
INTEGER
& INCX,INCY,N
C...Array arguments
REAL(wp)
& DX(*),DY(*)
C...Local scalars
REAL(wp)
& DTEMP1,DTEMP2,DTEMP3
INTEGER
& I,IX,IY,M,MP1,NS
C...Intrinsic functions
INTRINSIC
& MOD
C***First executable statement DSWAP
IF(N.LE.0)RETURN
IF(INCX.EQ.INCY) THEN
IF(INCX-1.LT.0) THEN
GOTO 5
ELSE IF(INCX-1.EQ.0) THEN
GOTO 20
ELSE IF(INCX-1.GT.0) THEN
GOTO 60
END IF
END IF
5 CONTINUE
C Code for unequal or nonpositive increments.
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 Code for both increments equal to 1
C Clean-up loop so remaining vector length is a multiple of 3.
20 M = MOD(N,3)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DTEMP1 = DX(I)
DX(I) = DY(I)