GCC Code Coverage Report


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File: misc/pchfe.f
Date: 2022-01-11 19:19:34
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1 *DECK PCHFE
2 SUBROUTINE PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR)
3 C***BEGIN PROLOGUE PCHFE
4 C***PURPOSE Evaluate a piecewise cubic Hermite function at an array of
5 C points. May be used by itself for Hermite interpolation,
6 C or as an evaluator for PCHIM or PCHIC.
7 C***LIBRARY SLATEC (PCHIP)
8 C***CATEGORY E3
9 C***TYPE SINGLE PRECISION (PCHFE-S, DPCHFE-D)
10 C***KEYWORDS CUBIC HERMITE EVALUATION, HERMITE INTERPOLATION, PCHIP,
11 C PIECEWISE CUBIC EVALUATION
12 C***AUTHOR Fritsch, F. N., (LLNL)
13 C Lawrence Livermore National Laboratory
14 C P.O. Box 808 (L-316)
15 C Livermore, CA 94550
16 C FTS 532-4275, (510) 422-4275
17 C***DESCRIPTION
18 C
19 C PCHFE: Piecewise Cubic Hermite Function Evaluator
20 C
21 C Evaluates the cubic Hermite function defined by N, X, F, D at
22 C the points XE(J), J=1(1)NE.
23 C
24 C To provide compatibility with PCHIM and PCHIC, includes an
25 C increment between successive values of the F- and D-arrays.
26 C
27 C ----------------------------------------------------------------------
28 C
29 C Calling sequence:
30 C
31 C PARAMETER (INCFD = ...)
32 C INTEGER N, NE, IERR
33 C REAL X(N), F(INCFD,N), D(INCFD,N), XE(NE), FE(NE)
34 C LOGICAL SKIP
35 C
36 C CALL PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR)
37 C
38 C Parameters:
39 C
40 C N -- (input) number of data points. (Error return if N.LT.2 .)
41 C
42 C X -- (input) real array of independent variable values. The
43 C elements of X must be strictly increasing:
44 C X(I-1) .LT. X(I), I = 2(1)N.
45 C (Error return if not.)
46 C
47 C F -- (input) real array of function values. F(1+(I-1)*INCFD) is
48 C the value corresponding to X(I).
49 C
50 C D -- (input) real array of derivative values. D(1+(I-1)*INCFD) is
51 C the value corresponding to X(I).
52 C
53 C INCFD -- (input) increment between successive values in F and D.
54 C (Error return if INCFD.LT.1 .)
55 C
56 C SKIP -- (input/output) logical variable which should be set to
57 C .TRUE. if the user wishes to skip checks for validity of
58 C preceding parameters, or to .FALSE. otherwise.
59 C This will save time in case these checks have already
60 C been performed (say, in PCHIM or PCHIC).
61 C SKIP will be set to .TRUE. on normal return.
62 C
63 C NE -- (input) number of evaluation points. (Error return if
64 C NE.LT.1 .)
65 C
66 C XE -- (input) real array of points at which the function is to be
67 C evaluated.
68 C
69 C NOTES:
70 C 1. The evaluation will be most efficient if the elements
71 C of XE are increasing relative to X;
72 C that is, XE(J) .GE. X(I)
73 C implies XE(K) .GE. X(I), all K.GE.J .
74 C 2. If any of the XE are outside the interval [X(1),X(N)],
75 C values are extrapolated from the nearest extreme cubic,
76 C and a warning error is returned.
77 C
78 C FE -- (output) real array of values of the cubic Hermite function
79 C defined by N, X, F, D at the points XE.
80 C
81 C IERR -- (output) error flag.
82 C Normal return:
83 C IERR = 0 (no errors).
84 C Warning error:
85 C IERR.GT.0 means that extrapolation was performed at
86 C IERR points.
87 C "Recoverable" errors:
88 C IERR = -1 if N.LT.2 .
89 C IERR = -2 if INCFD.LT.1 .
90 C IERR = -3 if the X-array is not strictly increasing.
91 C IERR = -4 if NE.LT.1 .
92 C (The FE-array has not been changed in any of these cases.)
93 C NOTE: The above errors are checked in the order listed,
94 C and following arguments have **NOT** been validated.
95 C
96 C***REFERENCES (NONE)
97 C***ROUTINES CALLED CHFEV, XERMSG
98 C***REVISION HISTORY (YYMMDD)
99 C 811020 DATE WRITTEN
100 C 820803 Minor cosmetic changes for release 1.
101 C 870707 Minor cosmetic changes to prologue.
102 C 890531 Changed all specific intrinsics to generic. (WRB)
103 C 890831 Modified array declarations. (WRB)
104 C 890831 REVISION DATE from Version 3.2
105 C 891214 Prologue converted to Version 4.0 format. (BAB)
106 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
107 C***END PROLOGUE PCHFE
108 C Programming notes:
109 C
110 C 1. To produce a double precision version, simply:
111 C a. Change PCHFE to DPCHFE, and CHFEV to DCHFEV, wherever they
112 C occur,
113 C b. Change the real declaration to double precision,
114 C
115 C 2. Most of the coding between the call to CHFEV and the end of
116 C the IR-loop could be eliminated if it were permissible to
117 C assume that XE is ordered relative to X.
118 C
119 C 3. CHFEV does not assume that X1 is less than X2. thus, it would
120 C be possible to write a version of PCHFE that assumes a strict-
121 C ly decreasing X-array by simply running the IR-loop backwards
122 C (and reversing the order of appropriate tests).
123 C
124 C 4. The present code has a minor bug, which I have decided is not
125 C worth the effort that would be required to fix it.
126 C If XE contains points in [X(N-1),X(N)], followed by points .LT.
127 C X(N-1), followed by points .GT.X(N), the extrapolation points
128 C will be counted (at least) twice in the total returned in IERR.
129 C
130 C DECLARE ARGUMENTS.
131 C
132 INTEGER N, INCFD, NE, IERR
133 REAL X(*), F(INCFD,*), D(INCFD,*), XE(*), FE(*)
134 LOGICAL SKIP
135 C
136 C DECLARE LOCAL VARIABLES.
137 C
138 INTEGER I, IERC, IR, J, JFIRST, NEXT(2), NJ
139 C
140 C VALIDITY-CHECK ARGUMENTS.
141 C
142 C***FIRST EXECUTABLE STATEMENT PCHFE
143 IF (SKIP) GO TO 5
144 C
145 IF ( N.LT.2 ) GO TO 5001
146 IF ( INCFD.LT.1 ) GO TO 5002
147 DO 1 I = 2, N
148 IF ( X(I).LE.X(I-1) ) GO TO 5003
149 1 CONTINUE
150 C
151 C FUNCTION DEFINITION IS OK, GO ON.
152 C
153 5 CONTINUE
154 IF ( NE.LT.1 ) GO TO 5004
155 IERR = 0
156 SKIP = .TRUE.
157 C
158 C LOOP OVER INTERVALS. ( INTERVAL INDEX IS IL = IR-1 . )
159 C ( INTERVAL IS X(IL).LE.X.LT.X(IR) . )
160 JFIRST = 1
161 IR = 2
162 10 CONTINUE
163 C
164 C SKIP OUT OF LOOP IF HAVE PROCESSED ALL EVALUATION POINTS.
165 C
166 IF (JFIRST .GT. NE) GO TO 5000
167 C
168 C LOCATE ALL POINTS IN INTERVAL.
169 C
170 DO 20 J = JFIRST, NE
171 IF (XE(J) .GE. X(IR)) GO TO 30
172 20 CONTINUE
173 J = NE + 1
174 GO TO 40
175 C
176 C HAVE LOCATED FIRST POINT BEYOND INTERVAL.
177 C
178 30 CONTINUE
179 IF (IR .EQ. N) J = NE + 1
180 C
181 40 CONTINUE
182 NJ = J - JFIRST
183 C
184 C SKIP EVALUATION IF NO POINTS IN INTERVAL.
185 C
186 IF (NJ .EQ. 0) GO TO 50
187 C
188 C EVALUATE CUBIC AT XE(I), I = JFIRST (1) J-1 .
189 C
190 C ----------------------------------------------------------------
191 CALL CHFEV (X(IR-1),X(IR), F(1,IR-1),F(1,IR), D(1,IR-1),D(1,IR),
192 * NJ, XE(JFIRST), FE(JFIRST), NEXT, IERC)
193 C ----------------------------------------------------------------
194 IF (IERC .LT. 0) GO TO 5005
195 C
196 IF (NEXT(2) .EQ. 0) GO TO 42
197 C IF (NEXT(2) .GT. 0) THEN
198 C IN THE CURRENT SET OF XE-POINTS, THERE ARE NEXT(2) TO THE
199 C RIGHT OF X(IR).
200 C
201 IF (IR .LT. N) GO TO 41
202 C IF (IR .EQ. N) THEN
203 C THESE ARE ACTUALLY EXTRAPOLATION POINTS.
204 IERR = IERR + NEXT(2)
205 GO TO 42
206 41 CONTINUE
207 C ELSE
208 C WE SHOULD NEVER HAVE GOTTEN HERE.
209 GO TO 5005
210 C ENDIF
211 C ENDIF
212 42 CONTINUE
213 C
214 IF (NEXT(1) .EQ. 0) GO TO 49
215 C IF (NEXT(1) .GT. 0) THEN
216 C IN THE CURRENT SET OF XE-POINTS, THERE ARE NEXT(1) TO THE
217 C LEFT OF X(IR-1).
218 C
219 IF (IR .GT. 2) GO TO 43
220 C IF (IR .EQ. 2) THEN
221 C THESE ARE ACTUALLY EXTRAPOLATION POINTS.
222 IERR = IERR + NEXT(1)
223 GO TO 49
224 43 CONTINUE
225 C ELSE
226 C XE IS NOT ORDERED RELATIVE TO X, SO MUST ADJUST
227 C EVALUATION INTERVAL.
228 C
229 C FIRST, LOCATE FIRST POINT TO LEFT OF X(IR-1).
230 DO 44 I = JFIRST, J-1
231 IF (XE(I) .LT. X(IR-1)) GO TO 45
232 44 CONTINUE
233 C NOTE-- CANNOT DROP THROUGH HERE UNLESS THERE IS AN ERROR
234 C IN CHFEV.
235 GO TO 5005
236 C
237 45 CONTINUE
238 C RESET J. (THIS WILL BE THE NEW JFIRST.)
239 J = I
240 C
241 C NOW FIND OUT HOW FAR TO BACK UP IN THE X-ARRAY.
242 DO 46 I = 1, IR-1
243 IF (XE(J) .LT. X(I)) GO TO 47
244 46 CONTINUE
245 C NB-- CAN NEVER DROP THROUGH HERE, SINCE XE(J).LT.X(IR-1).
246 C
247 47 CONTINUE
248 C AT THIS POINT, EITHER XE(J) .LT. X(1)
249 C OR X(I-1) .LE. XE(J) .LT. X(I) .
250 C RESET IR, RECOGNIZING THAT IT WILL BE INCREMENTED BEFORE
251 C CYCLING.
252 IR = MAX(1, I-1)
253 C ENDIF
254 C ENDIF
255 49 CONTINUE
256 C
257 JFIRST = J
258 C
259 C END OF IR-LOOP.
260 C
261 50 CONTINUE
262 IR = IR + 1
263 IF (IR .LE. N) GO TO 10
264 C
265 C NORMAL RETURN.
266 C
267 5000 CONTINUE
268 RETURN
269 C
270 C ERROR RETURNS.
271 C
272 5001 CONTINUE
273 C N.LT.2 RETURN.
274 IERR = -1
275 CALL XERMSG ('SLATEC', 'PCHFE',
276 + 'NUMBER OF DATA POINTS LESS THAN TWO', IERR, 1)
277 RETURN
278 C
279 5002 CONTINUE
280 C INCFD.LT.1 RETURN.
281 IERR = -2
282 CALL XERMSG ('SLATEC', 'PCHFE', 'INCREMENT LESS THAN ONE', IERR,
283 + 1)
284 RETURN
285 C
286 5003 CONTINUE
287 C X-ARRAY NOT STRICTLY INCREASING.
288 IERR = -3
289 CALL XERMSG ('SLATEC', 'PCHFE', 'X-ARRAY NOT STRICTLY INCREASING'
290 + , IERR, 1)
291 RETURN
292 C
293 5004 CONTINUE
294 C NE.LT.1 RETURN.
295 IERR = -4
296 CALL XERMSG ('SLATEC', 'PCHFE',
297 + 'NUMBER OF EVALUATION POINTS LESS THAN ONE', IERR, 1)
298 RETURN
299 C
300 5005 CONTINUE
301 C ERROR RETURN FROM CHFEV.
302 C *** THIS CASE SHOULD NEVER OCCUR ***
303 IERR = -5
304 CALL XERMSG ('SLATEC', 'PCHFE',
305 + 'ERROR RETURN FROM CHFEV -- FATAL', IERR, 2)
306 RETURN
307 C------------- LAST LINE OF PCHFE FOLLOWS ------------------------------
308 END
309