107
108
109
110
111
112
113 CHARACTER UPLO
114 INTEGER INFO, N
115
116
117 INTEGER IPIV( * )
118 COMPLEX*16 AP( * ), WORK( * )
119
120
121
122
123
124 DOUBLE PRECISION ONE
125 COMPLEX*16 CONE, ZERO
126 parameter( one = 1.0d+0, cone = ( 1.0d+0, 0.0d+0 ),
127 $ zero = ( 0.0d+0, 0.0d+0 ) )
128
129
130 LOGICAL UPPER
131 INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
132 DOUBLE PRECISION AK, AKP1, D, T
133 COMPLEX*16 AKKP1, TEMP
134
135
136 LOGICAL LSAME
137 COMPLEX*16 ZDOTC
139
140
142
143
144 INTRINSIC abs, dble, dconjg
145
146
147
148
149
150 info = 0
151 upper =
lsame( uplo,
'U' )
152 IF( .NOT.upper .AND. .NOT.
lsame( uplo,
'L' ) )
THEN
153 info = -1
154 ELSE IF( n.LT.0 ) THEN
155 info = -2
156 END IF
157 IF( info.NE.0 ) THEN
158 CALL xerbla(
'ZHPTRI', -info )
159 RETURN
160 END IF
161
162
163
164 IF( n.EQ.0 )
165 $ RETURN
166
167
168
169 IF( upper ) THEN
170
171
172
173 kp = n*( n+1 ) / 2
174 DO 10 info = n, 1, -1
175 IF( ipiv( info ).GT.0 .AND. ap( kp ).EQ.zero )
176 $ RETURN
177 kp = kp - info
178 10 CONTINUE
179 ELSE
180
181
182
183 kp = 1
184 DO 20 info = 1, n
185 IF( ipiv( info ).GT.0 .AND. ap( kp ).EQ.zero )
186 $ RETURN
187 kp = kp + n - info + 1
188 20 CONTINUE
189 END IF
190 info = 0
191
192 IF( upper ) THEN
193
194
195
196
197
198
199 k = 1
200 kc = 1
201 30 CONTINUE
202
203
204
205 IF( k.GT.n )
206 $ GO TO 50
207
208 kcnext = kc + k
209 IF( ipiv( k ).GT.0 ) THEN
210
211
212
213
214
215 ap( kc+k-1 ) = one / dble( ap( kc+k-1 ) )
216
217
218
219 IF( k.GT.1 ) THEN
220 CALL zcopy( k-1, ap( kc ), 1, work, 1 )
221 CALL zhpmv( uplo, k-1, -cone, ap, work, 1, zero,
222 $ ap( kc ), 1 )
223 ap( kc+k-1 ) = ap( kc+k-1 ) -
224 $ dble(
zdotc( k-1, work, 1, ap( kc ),
225 $ 1 ) )
226 END IF
227 kstep = 1
228 ELSE
229
230
231
232
233
234 t = abs( ap( kcnext+k-1 ) )
235 ak = dble( ap( kc+k-1 ) ) / t
236 akp1 = dble( ap( kcnext+k ) ) / t
237 akkp1 = ap( kcnext+k-1 ) / t
238 d = t*( ak*akp1-one )
239 ap( kc+k-1 ) = akp1 / d
240 ap( kcnext+k ) = ak / d
241 ap( kcnext+k-1 ) = -akkp1 / d
242
243
244
245 IF( k.GT.1 ) THEN
246 CALL zcopy( k-1, ap( kc ), 1, work, 1 )
247 CALL zhpmv( uplo, k-1, -cone, ap, work, 1, zero,
248 $ ap( kc ), 1 )
249 ap( kc+k-1 ) = ap( kc+k-1 ) -
250 $ dble(
zdotc( k-1, work, 1, ap( kc ),
251 $ 1 ) )
252 ap( kcnext+k-1 ) = ap( kcnext+k-1 ) -
253 $
zdotc( k-1, ap( kc ), 1,
254 $ ap( kcnext ),
255 $ 1 )
256 CALL zcopy( k-1, ap( kcnext ), 1, work, 1 )
257 CALL zhpmv( uplo, k-1, -cone, ap, work, 1, zero,
258 $ ap( kcnext ), 1 )
259 ap( kcnext+k ) = ap( kcnext+k ) -
260 $ dble(
zdotc( k-1, work, 1,
261 $ ap( kcnext ),
262 $ 1 ) )
263 END IF
264 kstep = 2
265 kcnext = kcnext + k + 1
266 END IF
267
268 kp = abs( ipiv( k ) )
269 IF( kp.NE.k ) THEN
270
271
272
273
274 kpc = ( kp-1 )*kp / 2 + 1
275 CALL zswap( kp-1, ap( kc ), 1, ap( kpc ), 1 )
276 kx = kpc + kp - 1
277 DO 40 j = kp + 1, k - 1
278 kx = kx + j - 1
279 temp = dconjg( ap( kc+j-1 ) )
280 ap( kc+j-1 ) = dconjg( ap( kx ) )
281 ap( kx ) = temp
282 40 CONTINUE
283 ap( kc+kp-1 ) = dconjg( ap( kc+kp-1 ) )
284 temp = ap( kc+k-1 )
285 ap( kc+k-1 ) = ap( kpc+kp-1 )
286 ap( kpc+kp-1 ) = temp
287 IF( kstep.EQ.2 ) THEN
288 temp = ap( kc+k+k-1 )
289 ap( kc+k+k-1 ) = ap( kc+k+kp-1 )
290 ap( kc+k+kp-1 ) = temp
291 END IF
292 END IF
293
294 k = k + kstep
295 kc = kcnext
296 GO TO 30
297 50 CONTINUE
298
299 ELSE
300
301
302
303
304
305
306 npp = n*( n+1 ) / 2
307 k = n
308 kc = npp
309 60 CONTINUE
310
311
312
313 IF( k.LT.1 )
314 $ GO TO 80
315
316 kcnext = kc - ( n-k+2 )
317 IF( ipiv( k ).GT.0 ) THEN
318
319
320
321
322
323 ap( kc ) = one / dble( ap( kc ) )
324
325
326
327 IF( k.LT.n ) THEN
328 CALL zcopy( n-k, ap( kc+1 ), 1, work, 1 )
329 CALL zhpmv( uplo, n-k, -cone, ap( kc+n-k+1 ), work, 1,
330 $ zero, ap( kc+1 ), 1 )
331 ap( kc ) = ap( kc ) - dble(
zdotc( n-k, work, 1,
332 $ ap( kc+1 ), 1 ) )
333 END IF
334 kstep = 1
335 ELSE
336
337
338
339
340
341 t = abs( ap( kcnext+1 ) )
342 ak = dble( ap( kcnext ) ) / t
343 akp1 = dble( ap( kc ) ) / t
344 akkp1 = ap( kcnext+1 ) / t
345 d = t*( ak*akp1-one )
346 ap( kcnext ) = akp1 / d
347 ap( kc ) = ak / d
348 ap( kcnext+1 ) = -akkp1 / d
349
350
351
352 IF( k.LT.n ) THEN
353 CALL zcopy( n-k, ap( kc+1 ), 1, work, 1 )
354 CALL zhpmv( uplo, n-k, -cone, ap( kc+( n-k+1 ) ),
355 $ work,
356 $ 1, zero, ap( kc+1 ), 1 )
357 ap( kc ) = ap( kc ) - dble(
zdotc( n-k, work, 1,
358 $ ap( kc+1 ), 1 ) )
359 ap( kcnext+1 ) = ap( kcnext+1 ) -
360 $
zdotc( n-k, ap( kc+1 ), 1,
361 $ ap( kcnext+2 ), 1 )
362 CALL zcopy( n-k, ap( kcnext+2 ), 1, work, 1 )
363 CALL zhpmv( uplo, n-k, -cone, ap( kc+( n-k+1 ) ),
364 $ work,
365 $ 1, zero, ap( kcnext+2 ), 1 )
366 ap( kcnext ) = ap( kcnext ) -
367 $ dble(
zdotc( n-k, work, 1,
368 $ ap( kcnext+2 ),
369 $ 1 ) )
370 END IF
371 kstep = 2
372 kcnext = kcnext - ( n-k+3 )
373 END IF
374
375 kp = abs( ipiv( k ) )
376 IF( kp.NE.k ) THEN
377
378
379
380
381 kpc = npp - ( n-kp+1 )*( n-kp+2 ) / 2 + 1
382 IF( kp.LT.n )
383 $
CALL zswap( n-kp, ap( kc+kp-k+1 ), 1, ap( kpc+1 ), 1 )
384 kx = kc + kp - k
385 DO 70 j = k + 1, kp - 1
386 kx = kx + n - j + 1
387 temp = dconjg( ap( kc+j-k ) )
388 ap( kc+j-k ) = dconjg( ap( kx ) )
389 ap( kx ) = temp
390 70 CONTINUE
391 ap( kc+kp-k ) = dconjg( ap( kc+kp-k ) )
392 temp = ap( kc )
393 ap( kc ) = ap( kpc )
394 ap( kpc ) = temp
395 IF( kstep.EQ.2 ) THEN
396 temp = ap( kc-n+k-1 )
397 ap( kc-n+k-1 ) = ap( kc-n+kp-1 )
398 ap( kc-n+kp-1 ) = temp
399 END IF
400 END IF
401
402 k = k - kstep
403 kc = kcnext
404 GO TO 60
405 80 CONTINUE
406 END IF
407
408 RETURN
409
410
411
subroutine xerbla(srname, info)
subroutine zcopy(n, zx, incx, zy, incy)
ZCOPY
complex *16 function zdotc(n, zx, incx, zy, incy)
ZDOTC
subroutine zhpmv(uplo, n, alpha, ap, x, incx, beta, y, incy)
ZHPMV
logical function lsame(ca, cb)
LSAME
subroutine zswap(n, zx, incx, zy, incy)
ZSWAP