*DECK DNRM2
DOUBLE PRECISION FUNCTION DNRM2 (N, DX, INCX)
C***BEGIN PROLOGUE DNRM2
C***PURPOSE Compute the Euclidean length (L2 norm) of a vector.
C***CATEGORY D1A3B
C***TYPE DOUBLE PRECISION (SNRM2-S, DNRM2-D, SCNRM2-C)
C***KEYWORDS BLAS, EUCLIDEAN LENGTH, EUCLIDEAN NORM, L2,
C LINEAR ALGEBRA, UNITARY, 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***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 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 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
C DATA CUTLO, CUTHI /8.232D-11, 1.304D19/
C DATA CUTLO, CUTHI /4.441E-16, 1.304E19/
C
C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
C Krogh, Basic linear algebra subprograms for Fortran
C usage, Algorithm No. 539, Transactions on Mathematical
C Software 5, 3 (September 1979), pp. 308-323.
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 791001 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DNRM2
INTEGER NEXT
DOUBLE PRECISION DX(*), CUTLO, CUTHI, HITEST, SUM, XMAX, ZERO,
+ ONE
SAVE CUTLO, CUTHI, 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
C BEGIN MAIN LOOP
C
I = 1
20 GO TO NEXT,(30, 50, 70, 110)
30 IF (ABS(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 (ABS(DX(I)) .GT. CUTLO) GO TO 85
C
C PREPARE FOR PHASE 2.
C
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 = ABS(DX(I))
GO TO 115
C
C PHASE 2. SUM IS SMALL.
C SCALE TO AVOID DESTRUCTIVE UNDERFLOW.
C
70 IF (ABS(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 (ABS(DX(I)) .LE. XMAX) GO TO 115
SUM = ONE + SUM * (XMAX / DX(I))**2
XMAX = ABS(DX(I))
GO TO 200
C
115 SUM = SUM + (DX(I)/XMAX)**2
GO TO 200
C
C PREPARE FOR PHASE 3.
C
75 SUM = (SUM * XMAX) * XMAX
C
C FOR REAL OR D.P. SET HITEST = CUTHI/N
C FOR COMPLEX SET HITEST = CUTHI/(2*N)
C
85 HITEST = CUTHI / N
C
C PHASE 3. SUM IS MID-RANGE. NO SCALING.
C
DO 95 J = I,NN,INCX
IF (ABS(DX(J)) .GE. HITEST) GO TO 100
95 SUM = SUM + DX(J)**2
DNRM2 = SQRT(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 * SQRT(SUM)
300 CONTINUE
RETURN
END