1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
|
SUBROUTINE DSORT (DX, IX, N, KFLAG, IERR)
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 real (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 IX. 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 IX - 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 IX along.
C = 1 means sort DX in increasing order (ignoring IX)
C = -1 means sort DX in decreasing order (ignoring IX)
C = -2 means sort DX in decreasing order and carry IX along.
C
C IERR - the error's indicator
C = 0 - Okay
C != 0 - errors
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,IX; 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 ..
real DX(*)
INTEGER IX(*)
C .. Local Scalars ..
real R, T, TT
INTEGER I, IJ, J, K, KK, L, M, NN
C .. Local Arrays ..
INTEGER IL(21), IU(21)
C .. Intrinsic Functions ..
INTRINSIC ABS, INT
C***FIRST EXECUTABLE STATEMENT DSORT
IERR = 0
NN = N
IF (NN .LT. 1) THEN
IERR = 1201
RETURN
ENDIF
C
KK = ABS(KFLAG)
IF (KK.NE.1 .AND. KK.NE.2) THEN
IERR = 1202
RETURN
ENDIF
C
C Initializing IX
C
C DO 5 I=1,NN
C IX(I)=I
C 5 CONTINUE
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 IX 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)
ITX = IX(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)
IX(IJ) = IX(I)
IX(I) = ITX
ITX = IX(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)
IX(IJ) = IX(J)
IX(J) = ITX
ITX = IX(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)
IX(IJ) = IX(I)
IX(I) = ITX
ITX = IX(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
ITTX = IX(L)
IX(L) = IX(K)
IX(K) = ITTX
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)
ITX = IX(I+1)
IF (DX(I) .LE. T) GO TO 170
K = I
C
180 DX(K+1) = DX(K)
IX(K+1) = IX(K)
K = K-1
IF (T .LT. DX(K)) GO TO 180
DX(K+1) = T
IX(K+1) = ITX
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
|