1 /* zhpmv.f -- translated by f2c (version 20100827).
2 You must link the resulting object file with libf2c:
3 on Microsoft Windows system, link with libf2c.lib;
4 on Linux or Unix systems, link with .../path/to/libf2c.a -lm
5 or, if you install libf2c.a in a standard place, with -lf2c -lm
6 -- in that order, at the end of the command line, as in
7 cc *.o -lf2c -lm
8 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
9
10 http://www.netlib.org/f2c/libf2c.zip
11 */
12
13 #include "datatypes.h"
14
zhpmv_(char * uplo,integer * n,doublecomplex * alpha,doublecomplex * ap,doublecomplex * x,integer * incx,doublecomplex * beta,doublecomplex * y,integer * incy,ftnlen uplo_len)15 /* Subroutine */ int zhpmv_(char *uplo, integer *n, doublecomplex *alpha,
16 doublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex *
17 beta, doublecomplex *y, integer *incy, ftnlen uplo_len)
18 {
19 /* System generated locals */
20 integer i__1, i__2, i__3, i__4, i__5;
21 doublereal d__1;
22 doublecomplex z__1, z__2, z__3, z__4;
23
24 /* Builtin functions */
25 void d_cnjg(doublecomplex *, doublecomplex *);
26
27 /* Local variables */
28 integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;
29 doublecomplex temp1, temp2;
30 extern logical lsame_(char *, char *, ftnlen, ftnlen);
31 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
32
33 /* .. Scalar Arguments .. */
34 /* .. */
35 /* .. Array Arguments .. */
36 /* .. */
37
38 /* Purpose */
39 /* ======= */
40
41 /* ZHPMV performs the matrix-vector operation */
42
43 /* y := alpha*A*x + beta*y, */
44
45 /* where alpha and beta are scalars, x and y are n element vectors and */
46 /* A is an n by n hermitian matrix, supplied in packed form. */
47
48 /* Arguments */
49 /* ========== */
50
51 /* UPLO - CHARACTER*1. */
52 /* On entry, UPLO specifies whether the upper or lower */
53 /* triangular part of the matrix A is supplied in the packed */
54 /* array AP as follows: */
55
56 /* UPLO = 'U' or 'u' The upper triangular part of A is */
57 /* supplied in AP. */
58
59 /* UPLO = 'L' or 'l' The lower triangular part of A is */
60 /* supplied in AP. */
61
62 /* Unchanged on exit. */
63
64 /* N - INTEGER. */
65 /* On entry, N specifies the order of the matrix A. */
66 /* N must be at least zero. */
67 /* Unchanged on exit. */
68
69 /* ALPHA - COMPLEX*16 . */
70 /* On entry, ALPHA specifies the scalar alpha. */
71 /* Unchanged on exit. */
72
73 /* AP - COMPLEX*16 array of DIMENSION at least */
74 /* ( ( n*( n + 1 ) )/2 ). */
75 /* Before entry with UPLO = 'U' or 'u', the array AP must */
76 /* contain the upper triangular part of the hermitian matrix */
77 /* packed sequentially, column by column, so that AP( 1 ) */
78 /* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */
79 /* and a( 2, 2 ) respectively, and so on. */
80 /* Before entry with UPLO = 'L' or 'l', the array AP must */
81 /* contain the lower triangular part of the hermitian matrix */
82 /* packed sequentially, column by column, so that AP( 1 ) */
83 /* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */
84 /* and a( 3, 1 ) respectively, and so on. */
85 /* Note that the imaginary parts of the diagonal elements need */
86 /* not be set and are assumed to be zero. */
87 /* Unchanged on exit. */
88
89 /* X - COMPLEX*16 array of dimension at least */
90 /* ( 1 + ( n - 1 )*abs( INCX ) ). */
91 /* Before entry, the incremented array X must contain the n */
92 /* element vector x. */
93 /* Unchanged on exit. */
94
95 /* INCX - INTEGER. */
96 /* On entry, INCX specifies the increment for the elements of */
97 /* X. INCX must not be zero. */
98 /* Unchanged on exit. */
99
100 /* BETA - COMPLEX*16 . */
101 /* On entry, BETA specifies the scalar beta. When BETA is */
102 /* supplied as zero then Y need not be set on input. */
103 /* Unchanged on exit. */
104
105 /* Y - COMPLEX*16 array of dimension at least */
106 /* ( 1 + ( n - 1 )*abs( INCY ) ). */
107 /* Before entry, the incremented array Y must contain the n */
108 /* element vector y. On exit, Y is overwritten by the updated */
109 /* vector y. */
110
111 /* INCY - INTEGER. */
112 /* On entry, INCY specifies the increment for the elements of */
113 /* Y. INCY must not be zero. */
114 /* Unchanged on exit. */
115
116 /* Further Details */
117 /* =============== */
118
119 /* Level 2 Blas routine. */
120
121 /* -- Written on 22-October-1986. */
122 /* Jack Dongarra, Argonne National Lab. */
123 /* Jeremy Du Croz, Nag Central Office. */
124 /* Sven Hammarling, Nag Central Office. */
125 /* Richard Hanson, Sandia National Labs. */
126
127 /* ===================================================================== */
128
129 /* .. Parameters .. */
130 /* .. */
131 /* .. Local Scalars .. */
132 /* .. */
133 /* .. External Functions .. */
134 /* .. */
135 /* .. External Subroutines .. */
136 /* .. */
137 /* .. Intrinsic Functions .. */
138 /* .. */
139
140 /* Test the input parameters. */
141
142 /* Parameter adjustments */
143 --y;
144 --x;
145 --ap;
146
147 /* Function Body */
148 info = 0;
149 if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
150 ftnlen)1, (ftnlen)1)) {
151 info = 1;
152 } else if (*n < 0) {
153 info = 2;
154 } else if (*incx == 0) {
155 info = 6;
156 } else if (*incy == 0) {
157 info = 9;
158 }
159 if (info != 0) {
160 xerbla_("ZHPMV ", &info, (ftnlen)6);
161 return 0;
162 }
163
164 /* Quick return if possible. */
165
166 if (*n == 0 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
167 beta->i == 0.))) {
168 return 0;
169 }
170
171 /* Set up the start points in X and Y. */
172
173 if (*incx > 0) {
174 kx = 1;
175 } else {
176 kx = 1 - (*n - 1) * *incx;
177 }
178 if (*incy > 0) {
179 ky = 1;
180 } else {
181 ky = 1 - (*n - 1) * *incy;
182 }
183
184 /* Start the operations. In this version the elements of the array AP */
185 /* are accessed sequentially with one pass through AP. */
186
187 /* First form y := beta*y. */
188
189 if (beta->r != 1. || beta->i != 0.) {
190 if (*incy == 1) {
191 if (beta->r == 0. && beta->i == 0.) {
192 i__1 = *n;
193 for (i__ = 1; i__ <= i__1; ++i__) {
194 i__2 = i__;
195 y[i__2].r = 0., y[i__2].i = 0.;
196 /* L10: */
197 }
198 } else {
199 i__1 = *n;
200 for (i__ = 1; i__ <= i__1; ++i__) {
201 i__2 = i__;
202 i__3 = i__;
203 z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
204 z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
205 .r;
206 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
207 /* L20: */
208 }
209 }
210 } else {
211 iy = ky;
212 if (beta->r == 0. && beta->i == 0.) {
213 i__1 = *n;
214 for (i__ = 1; i__ <= i__1; ++i__) {
215 i__2 = iy;
216 y[i__2].r = 0., y[i__2].i = 0.;
217 iy += *incy;
218 /* L30: */
219 }
220 } else {
221 i__1 = *n;
222 for (i__ = 1; i__ <= i__1; ++i__) {
223 i__2 = iy;
224 i__3 = iy;
225 z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
226 z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
227 .r;
228 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
229 iy += *incy;
230 /* L40: */
231 }
232 }
233 }
234 }
235 if (alpha->r == 0. && alpha->i == 0.) {
236 return 0;
237 }
238 kk = 1;
239 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
240
241 /* Form y when AP contains the upper triangle. */
242
243 if (*incx == 1 && *incy == 1) {
244 i__1 = *n;
245 for (j = 1; j <= i__1; ++j) {
246 i__2 = j;
247 z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
248 alpha->r * x[i__2].i + alpha->i * x[i__2].r;
249 temp1.r = z__1.r, temp1.i = z__1.i;
250 temp2.r = 0., temp2.i = 0.;
251 k = kk;
252 i__2 = j - 1;
253 for (i__ = 1; i__ <= i__2; ++i__) {
254 i__3 = i__;
255 i__4 = i__;
256 i__5 = k;
257 z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
258 z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
259 .r;
260 z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
261 y[i__3].r = z__1.r, y[i__3].i = z__1.i;
262 d_cnjg(&z__3, &ap[k]);
263 i__3 = i__;
264 z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
265 z__3.r * x[i__3].i + z__3.i * x[i__3].r;
266 z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
267 temp2.r = z__1.r, temp2.i = z__1.i;
268 ++k;
269 /* L50: */
270 }
271 i__2 = j;
272 i__3 = j;
273 i__4 = kk + j - 1;
274 d__1 = ap[i__4].r;
275 z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
276 z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
277 z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
278 alpha->r * temp2.i + alpha->i * temp2.r;
279 z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
280 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
281 kk += j;
282 /* L60: */
283 }
284 } else {
285 jx = kx;
286 jy = ky;
287 i__1 = *n;
288 for (j = 1; j <= i__1; ++j) {
289 i__2 = jx;
290 z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
291 alpha->r * x[i__2].i + alpha->i * x[i__2].r;
292 temp1.r = z__1.r, temp1.i = z__1.i;
293 temp2.r = 0., temp2.i = 0.;
294 ix = kx;
295 iy = ky;
296 i__2 = kk + j - 2;
297 for (k = kk; k <= i__2; ++k) {
298 i__3 = iy;
299 i__4 = iy;
300 i__5 = k;
301 z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
302 z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
303 .r;
304 z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
305 y[i__3].r = z__1.r, y[i__3].i = z__1.i;
306 d_cnjg(&z__3, &ap[k]);
307 i__3 = ix;
308 z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
309 z__3.r * x[i__3].i + z__3.i * x[i__3].r;
310 z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
311 temp2.r = z__1.r, temp2.i = z__1.i;
312 ix += *incx;
313 iy += *incy;
314 /* L70: */
315 }
316 i__2 = jy;
317 i__3 = jy;
318 i__4 = kk + j - 1;
319 d__1 = ap[i__4].r;
320 z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
321 z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
322 z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
323 alpha->r * temp2.i + alpha->i * temp2.r;
324 z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
325 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
326 jx += *incx;
327 jy += *incy;
328 kk += j;
329 /* L80: */
330 }
331 }
332 } else {
333
334 /* Form y when AP contains the lower triangle. */
335
336 if (*incx == 1 && *incy == 1) {
337 i__1 = *n;
338 for (j = 1; j <= i__1; ++j) {
339 i__2 = j;
340 z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
341 alpha->r * x[i__2].i + alpha->i * x[i__2].r;
342 temp1.r = z__1.r, temp1.i = z__1.i;
343 temp2.r = 0., temp2.i = 0.;
344 i__2 = j;
345 i__3 = j;
346 i__4 = kk;
347 d__1 = ap[i__4].r;
348 z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
349 z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
350 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
351 k = kk + 1;
352 i__2 = *n;
353 for (i__ = j + 1; i__ <= i__2; ++i__) {
354 i__3 = i__;
355 i__4 = i__;
356 i__5 = k;
357 z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
358 z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
359 .r;
360 z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
361 y[i__3].r = z__1.r, y[i__3].i = z__1.i;
362 d_cnjg(&z__3, &ap[k]);
363 i__3 = i__;
364 z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
365 z__3.r * x[i__3].i + z__3.i * x[i__3].r;
366 z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
367 temp2.r = z__1.r, temp2.i = z__1.i;
368 ++k;
369 /* L90: */
370 }
371 i__2 = j;
372 i__3 = j;
373 z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
374 alpha->r * temp2.i + alpha->i * temp2.r;
375 z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
376 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
377 kk += *n - j + 1;
378 /* L100: */
379 }
380 } else {
381 jx = kx;
382 jy = ky;
383 i__1 = *n;
384 for (j = 1; j <= i__1; ++j) {
385 i__2 = jx;
386 z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
387 alpha->r * x[i__2].i + alpha->i * x[i__2].r;
388 temp1.r = z__1.r, temp1.i = z__1.i;
389 temp2.r = 0., temp2.i = 0.;
390 i__2 = jy;
391 i__3 = jy;
392 i__4 = kk;
393 d__1 = ap[i__4].r;
394 z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
395 z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
396 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
397 ix = jx;
398 iy = jy;
399 i__2 = kk + *n - j;
400 for (k = kk + 1; k <= i__2; ++k) {
401 ix += *incx;
402 iy += *incy;
403 i__3 = iy;
404 i__4 = iy;
405 i__5 = k;
406 z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
407 z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
408 .r;
409 z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
410 y[i__3].r = z__1.r, y[i__3].i = z__1.i;
411 d_cnjg(&z__3, &ap[k]);
412 i__3 = ix;
413 z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
414 z__3.r * x[i__3].i + z__3.i * x[i__3].r;
415 z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
416 temp2.r = z__1.r, temp2.i = z__1.i;
417 /* L110: */
418 }
419 i__2 = jy;
420 i__3 = jy;
421 z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
422 alpha->r * temp2.i + alpha->i * temp2.r;
423 z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
424 y[i__2].r = z__1.r, y[i__2].i = z__1.i;
425 jx += *incx;
426 jy += *incy;
427 kk += *n - j + 1;
428 /* L120: */
429 }
430 }
431 }
432
433 return 0;
434
435 /* End of ZHPMV . */
436
437 } /* zhpmv_ */
438
439