SUBROUTINE DSORT (DX, DY, N, KFLAG)
C***BEGIN PROLOGUE DSORT
C***PURPOSE Sort an array and optionally make the same interchanges in
C an auxiliary array. The array may be sorted in increasing
C or decreasing order. A slightly modified QUICKSORT
C algorithm is used.
C***LIBRARY SLATEC
C***CATEGORY N6A2B
C***TYPE DOUBLE PRECISION (SSORT-S, DSORT-D, ISORT-I)
C***KEYWORDS SINGLETON QUICKSORT, SORT, SORTING
C***AUTHOR Jones, R. E., (SNLA)
C Wisniewski, J. A., (SNLA)
C***DESCRIPTION
C
C DSORT sorts array DX and optionally makes the same interchanges in
C array DY. The array DX may be sorted in increasing order or
C decreasing order. A slightly modified quicksort algorithm is used.
C
C Description of Parameters
C DX - array of values to be sorted (usually abscissas)
C DY - array to be (optionally) carried along
C N - number of values in array DX to be sorted
C KFLAG - control parameter
C = 2 means sort DX in increasing order and carry DY along.
C = 1 means sort DX in increasing order (ignoring DY)
C = -1 means sort DX in decreasing order (ignoring DY)
C = -2 means sort DX in decreasing order and carry DY along.
C
C***REFERENCES R. C. Singleton, Algorithm 347, An efficient algorithm
C for sorting with minimal storage, Communications of
C the ACM, 12, 3 (1969), pp. 185-187.
C***ROUTINES CALLED XERMSG
C***REVISION HISTORY (YYMMDD)
C 761101 DATE WRITTEN
C 761118 Modified to use the Singleton quicksort algorithm. (JAW)
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 891009 Removed unreferenced statement labels. (WRB)
C 891024 Changed category. (WRB)
C 891024 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 901012 Declared all variables; changed X,Y to DX,DY; changed
C code to parallel SSORT. (M. McClain)
C 920501 Reformatted the REFERENCES section. (DWL, WRB)
C 920519 Clarified error messages. (DWL)
C 920801 Declarations section rebuilt and code restructured to use
C IF-THEN-ELSE-ENDIF. (RWC, WRB)
C***END PROLOGUE DSORT
C .. Scalar Arguments ..
INTEGER KFLAG, N
C .. Array Arguments ..
DOUBLE PRECISION DX(*), DY(*)
C .. Local Scalars ..
DOUBLE PRECISION R, T, TT, TTY, TY
INTEGER I, IJ, J, K, KK, L, M, NN
C .. Local Arrays ..
INTEGER IL(21), IU(21)
C .. External Subroutines ..
C EXTERNAL XERMSG
C .. Intrinsic Functions ..
INTRINSIC ABS, INT
C***FIRST EXECUTABLE STATEMENT DSORT
NN = N
C IF (NN .LT. 1) THEN
C CALL XERMSG ('SLATEC', 'DSORT',
C + 'The number of values to be sorted is not positive.', 1, 1)
C RETURN
C ENDIF
C
KK = ABS(KFLAG)
C IF (KK.NE.1 .AND. KK.NE.2) THEN
C CALL XERMSG ('SLATEC', 'DSORT',
C + 'The sort control parameter, K, is not 2, 1, -1, or -2.', 2,
C + 1)
C RETURN
C ENDIF
C
C Alter array DX to get decreasing order if needed
C
IF (KFLAG .LE. -1) THEN
DO 10 I=1,NN
DX(I) = -DX(I)
10 CONTINUE
ENDIF
C
IF (KK .EQ. 2) GO TO 100
C
C Sort DX only
C
M = 1
I = 1
J = NN
R = 0.375D0
C
20 IF (I .EQ. J) GO TO 60
IF (R .LE. 0.5898437D0) THEN
R = R+3.90625D-2
ELSE
R = R-0.21875D0
ENDIF
C
30 K = I
C
C Select a central element of the array and save it in location T
C
IJ = I + INT((J-I)*R)
T = DX(IJ)
C
C If first element of array is greater than T, interchange with T
C
IF (DX(I) .GT. T) THEN
DX(IJ) = DX(I)
DX(I) = T
T = DX(IJ)
ENDIF
L = J
C
C If last element of array is less than than T, interchange with T
C
IF (DX(J) .LT. T) THEN
DX(IJ) = DX(J)
DX(J) = T
T = DX(IJ)
C
C If first element of array is greater than T, interchange with T
C
IF (DX(I) .GT. T) THEN
DX(IJ) = DX(I)
DX(I) = T
T = DX(IJ)
ENDIF
ENDIF
C
C Find an element in the second half of the array which is smaller
C than T
C
40 L = L-1
IF (DX(L) .GT. T) GO TO 40
C
C Find an element in the first half of the array which is greater
C than T
C
50 K = K+1
IF (DX(K) .LT. T) GO TO 50
C
C Interchange these elements
C
IF (K .LE. L) THEN
TT = DX(L)
DX(L) = DX(K)
DX(K) = TT
GO TO 40
ENDIF
C
C Save upper and lower subscripts of the array yet to be sorted
C
IF (L-I .GT. J-K) THEN
IL(M) = I
IU(M) = L
I = K
M = M+1
ELSE
IL(M) = K
IU(M) = J
J = L
M = M+1
ENDIF
GO TO 70
C
C Begin again on another portion of the unsorted array
C
60 M = M-1
IF (M .EQ. 0) GO TO 190
I = IL(M)
J = IU(M)
C
70 IF (J-I .GE. 1) GO TO 30
IF (I .EQ. 1) GO TO 20
I = I-1
C
80 I = I+1
IF (I .EQ. J) GO TO 60
T = DX(I+1)
IF (DX(I) .LE. T) GO TO 80
K = I
C
90 DX(K+1) = DX(K)
K = K-1
IF (T .LT. DX(K)) GO TO 90
DX(K+1) = T
GO TO 80
C
C Sort DX and carry DY along
C
100 M = 1
I = 1
J = NN
R = 0.375D0
C
110 IF (I .EQ. J) GO TO 150
IF (R .LE. 0.5898437D0) THEN
R = R+3.90625D-2
ELSE
R = R-0.21875D0
ENDIF
C
120 K = I
C
C Select a central element of the array and save it in location T
C
IJ = I + INT((J-I)*R)
T = DX(IJ)
TY = DY(IJ)
C
C If first element of array is greater than T, interchange with T
C
IF (DX(I) .GT. T) THEN
DX(IJ) = DX(I)
DX(I) = T
T = DX(IJ)
DY(IJ) = DY(I)
DY(I) = TY
TY = DY(IJ)
ENDIF
L = J
C
C If last element of array is less than T, interchange with T
C
IF (DX(J) .LT. T) THEN
DX(IJ) = DX(J)
DX(J) = T
T = DX(IJ)
DY(IJ) = DY(J)
DY(J) = TY
TY = DY(IJ)
C
C If first element of array is greater than T, interchange with T
C
IF (DX(I) .GT. T) THEN
DX(IJ) = DX(I)
DX(I) = T
T = DX(IJ)
DY(IJ) = DY(I)
DY(I) = TY
TY = DY(IJ)
ENDIF
ENDIF
C
C Find an element in the second half of the array which is smaller
C than T
C
130 L = L-1
IF (DX(L) .GT. T) GO TO 130
C
C Find an element in the first half of the array which is greater
C than T
C
140 K = K+1
IF (DX(K) .LT. T) GO TO 140
C
C Interchange these elements
C
IF (K .LE. L) THEN
TT = DX(L)
DX(L) = DX(K)
DX(K) = TT
TTY = DY(L)
DY(L) = DY(K)
DY(K) = TTY
GO TO 130
ENDIF
C
C Save upper and lower subscripts of the array yet to be sorted
C
IF (L-I .GT. J-K) THEN
IL(M) = I
IU(M) = L
I = K
M = M+1
ELSE
IL(M) = K
IU(M) = J
J = L
M = M+1
ENDIF
GO TO 160
C
C Begin again on another portion of the unsorted array
C
150 M = M-1
IF (M .EQ. 0) GO TO 190
I = IL(M)
J = IU(M)
C
160 IF (J-I .GE. 1) GO TO 120
IF (I .EQ. 1) GO TO 110
I = I-1
C
170 I = I+1
IF (I .EQ. J) GO TO 150
T = DX(I+1)
TY = DY(I+1)
IF (DX(I) .LE. T) GO TO 170
K = I
C
180 DX(K+1) = DX(K)
DY(K+1) = DY(K)
K = K-1
IF (T .LT. DX(K)) GO TO 180
DX(K+1) = T
DY(K+1) = TY
GO TO 170
C
C Clean up
C
190 IF (KFLAG .LE. -1) THEN
DO 200 I=1,NN
DX(I) = -DX(I)
200 CONTINUE
ENDIF
RETURN
END