Annotation of rpl/lapack/lapack/zsptrs.f, revision 1.12
1.9 bertrand 1: *> \brief \b ZSPTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSPTRS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptrs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsptrs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsptrs.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * COMPLEX*16 AP( * ), B( LDB, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSPTRS solves a system of linear equations A*X = B with a complex
39: *> symmetric matrix A stored in packed format using the factorization
40: *> A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] UPLO
47: *> \verbatim
48: *> UPLO is CHARACTER*1
49: *> Specifies whether the details of the factorization are stored
50: *> as an upper or lower triangular matrix.
51: *> = 'U': Upper triangular, form is A = U*D*U**T;
52: *> = 'L': Lower triangular, form is A = L*D*L**T.
53: *> \endverbatim
54: *>
55: *> \param[in] N
56: *> \verbatim
57: *> N is INTEGER
58: *> The order of the matrix A. N >= 0.
59: *> \endverbatim
60: *>
61: *> \param[in] NRHS
62: *> \verbatim
63: *> NRHS is INTEGER
64: *> The number of right hand sides, i.e., the number of columns
65: *> of the matrix B. NRHS >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] AP
69: *> \verbatim
70: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
71: *> The block diagonal matrix D and the multipliers used to
72: *> obtain the factor U or L as computed by ZSPTRF, stored as a
73: *> packed triangular matrix.
74: *> \endverbatim
75: *>
76: *> \param[in] IPIV
77: *> \verbatim
78: *> IPIV is INTEGER array, dimension (N)
79: *> Details of the interchanges and the block structure of D
80: *> as determined by ZSPTRF.
81: *> \endverbatim
82: *>
83: *> \param[in,out] B
84: *> \verbatim
85: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
86: *> On entry, the right hand side matrix B.
87: *> On exit, the solution matrix X.
88: *> \endverbatim
89: *>
90: *> \param[in] LDB
91: *> \verbatim
92: *> LDB is INTEGER
93: *> The leading dimension of the array B. LDB >= max(1,N).
94: *> \endverbatim
95: *>
96: *> \param[out] INFO
97: *> \verbatim
98: *> INFO is INTEGER
99: *> = 0: successful exit
100: *> < 0: if INFO = -i, the i-th argument had an illegal value
101: *> \endverbatim
102: *
103: * Authors:
104: * ========
105: *
106: *> \author Univ. of Tennessee
107: *> \author Univ. of California Berkeley
108: *> \author Univ. of Colorado Denver
109: *> \author NAG Ltd.
110: *
111: *> \date November 2011
112: *
113: *> \ingroup complex16OTHERcomputational
114: *
115: * =====================================================================
1.1 bertrand 116: SUBROUTINE ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
117: *
1.9 bertrand 118: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 119: * -- LAPACK is a software package provided by Univ. of Tennessee, --
120: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 121: * November 2011
1.1 bertrand 122: *
123: * .. Scalar Arguments ..
124: CHARACTER UPLO
125: INTEGER INFO, LDB, N, NRHS
126: * ..
127: * .. Array Arguments ..
128: INTEGER IPIV( * )
129: COMPLEX*16 AP( * ), B( LDB, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: COMPLEX*16 ONE
136: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
137: * ..
138: * .. Local Scalars ..
139: LOGICAL UPPER
140: INTEGER J, K, KC, KP
141: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
142: * ..
143: * .. External Functions ..
144: LOGICAL LSAME
145: EXTERNAL LSAME
146: * ..
147: * .. External Subroutines ..
148: EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP
149: * ..
150: * .. Intrinsic Functions ..
151: INTRINSIC MAX
152: * ..
153: * .. Executable Statements ..
154: *
155: INFO = 0
156: UPPER = LSAME( UPLO, 'U' )
157: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
158: INFO = -1
159: ELSE IF( N.LT.0 ) THEN
160: INFO = -2
161: ELSE IF( NRHS.LT.0 ) THEN
162: INFO = -3
163: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
164: INFO = -7
165: END IF
166: IF( INFO.NE.0 ) THEN
167: CALL XERBLA( 'ZSPTRS', -INFO )
168: RETURN
169: END IF
170: *
171: * Quick return if possible
172: *
173: IF( N.EQ.0 .OR. NRHS.EQ.0 )
174: $ RETURN
175: *
176: IF( UPPER ) THEN
177: *
1.8 bertrand 178: * Solve A*X = B, where A = U*D*U**T.
1.1 bertrand 179: *
180: * First solve U*D*X = B, overwriting B with X.
181: *
182: * K is the main loop index, decreasing from N to 1 in steps of
183: * 1 or 2, depending on the size of the diagonal blocks.
184: *
185: K = N
186: KC = N*( N+1 ) / 2 + 1
187: 10 CONTINUE
188: *
189: * If K < 1, exit from loop.
190: *
191: IF( K.LT.1 )
192: $ GO TO 30
193: *
194: KC = KC - K
195: IF( IPIV( K ).GT.0 ) THEN
196: *
197: * 1 x 1 diagonal block
198: *
199: * Interchange rows K and IPIV(K).
200: *
201: KP = IPIV( K )
202: IF( KP.NE.K )
203: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
204: *
205: * Multiply by inv(U(K)), where U(K) is the transformation
206: * stored in column K of A.
207: *
208: CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
209: $ B( 1, 1 ), LDB )
210: *
211: * Multiply by the inverse of the diagonal block.
212: *
213: CALL ZSCAL( NRHS, ONE / AP( KC+K-1 ), B( K, 1 ), LDB )
214: K = K - 1
215: ELSE
216: *
217: * 2 x 2 diagonal block
218: *
219: * Interchange rows K-1 and -IPIV(K).
220: *
221: KP = -IPIV( K )
222: IF( KP.NE.K-1 )
223: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
224: *
225: * Multiply by inv(U(K)), where U(K) is the transformation
226: * stored in columns K-1 and K of A.
227: *
228: CALL ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
229: $ B( 1, 1 ), LDB )
230: CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1,
231: $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB )
232: *
233: * Multiply by the inverse of the diagonal block.
234: *
235: AKM1K = AP( KC+K-2 )
236: AKM1 = AP( KC-1 ) / AKM1K
237: AK = AP( KC+K-1 ) / AKM1K
238: DENOM = AKM1*AK - ONE
239: DO 20 J = 1, NRHS
240: BKM1 = B( K-1, J ) / AKM1K
241: BK = B( K, J ) / AKM1K
242: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
243: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
244: 20 CONTINUE
245: KC = KC - K + 1
246: K = K - 2
247: END IF
248: *
249: GO TO 10
250: 30 CONTINUE
251: *
1.8 bertrand 252: * Next solve U**T*X = B, overwriting B with X.
1.1 bertrand 253: *
254: * K is the main loop index, increasing from 1 to N in steps of
255: * 1 or 2, depending on the size of the diagonal blocks.
256: *
257: K = 1
258: KC = 1
259: 40 CONTINUE
260: *
261: * If K > N, exit from loop.
262: *
263: IF( K.GT.N )
264: $ GO TO 50
265: *
266: IF( IPIV( K ).GT.0 ) THEN
267: *
268: * 1 x 1 diagonal block
269: *
1.8 bertrand 270: * Multiply by inv(U**T(K)), where U(K) is the transformation
1.1 bertrand 271: * stored in column K of A.
272: *
273: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
274: $ 1, ONE, B( K, 1 ), LDB )
275: *
276: * Interchange rows K and IPIV(K).
277: *
278: KP = IPIV( K )
279: IF( KP.NE.K )
280: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
281: KC = KC + K
282: K = K + 1
283: ELSE
284: *
285: * 2 x 2 diagonal block
286: *
1.8 bertrand 287: * Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
1.1 bertrand 288: * stored in columns K and K+1 of A.
289: *
290: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
291: $ 1, ONE, B( K, 1 ), LDB )
292: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
293: $ AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB )
294: *
295: * Interchange rows K and -IPIV(K).
296: *
297: KP = -IPIV( K )
298: IF( KP.NE.K )
299: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
300: KC = KC + 2*K + 1
301: K = K + 2
302: END IF
303: *
304: GO TO 40
305: 50 CONTINUE
306: *
307: ELSE
308: *
1.8 bertrand 309: * Solve A*X = B, where A = L*D*L**T.
1.1 bertrand 310: *
311: * First solve L*D*X = B, overwriting B with X.
312: *
313: * K is the main loop index, increasing from 1 to N in steps of
314: * 1 or 2, depending on the size of the diagonal blocks.
315: *
316: K = 1
317: KC = 1
318: 60 CONTINUE
319: *
320: * If K > N, exit from loop.
321: *
322: IF( K.GT.N )
323: $ GO TO 80
324: *
325: IF( IPIV( K ).GT.0 ) THEN
326: *
327: * 1 x 1 diagonal block
328: *
329: * Interchange rows K and IPIV(K).
330: *
331: KP = IPIV( K )
332: IF( KP.NE.K )
333: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
334: *
335: * Multiply by inv(L(K)), where L(K) is the transformation
336: * stored in column K of A.
337: *
338: IF( K.LT.N )
339: $ CALL ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ),
340: $ LDB, B( K+1, 1 ), LDB )
341: *
342: * Multiply by the inverse of the diagonal block.
343: *
344: CALL ZSCAL( NRHS, ONE / AP( KC ), B( K, 1 ), LDB )
345: KC = KC + N - K + 1
346: K = K + 1
347: ELSE
348: *
349: * 2 x 2 diagonal block
350: *
351: * Interchange rows K+1 and -IPIV(K).
352: *
353: KP = -IPIV( K )
354: IF( KP.NE.K+1 )
355: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
356: *
357: * Multiply by inv(L(K)), where L(K) is the transformation
358: * stored in columns K and K+1 of A.
359: *
360: IF( K.LT.N-1 ) THEN
361: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ),
362: $ LDB, B( K+2, 1 ), LDB )
363: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1,
364: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
365: END IF
366: *
367: * Multiply by the inverse of the diagonal block.
368: *
369: AKM1K = AP( KC+1 )
370: AKM1 = AP( KC ) / AKM1K
371: AK = AP( KC+N-K+1 ) / AKM1K
372: DENOM = AKM1*AK - ONE
373: DO 70 J = 1, NRHS
374: BKM1 = B( K, J ) / AKM1K
375: BK = B( K+1, J ) / AKM1K
376: B( K, J ) = ( AK*BKM1-BK ) / DENOM
377: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
378: 70 CONTINUE
379: KC = KC + 2*( N-K ) + 1
380: K = K + 2
381: END IF
382: *
383: GO TO 60
384: 80 CONTINUE
385: *
1.8 bertrand 386: * Next solve L**T*X = B, overwriting B with X.
1.1 bertrand 387: *
388: * K is the main loop index, decreasing from N to 1 in steps of
389: * 1 or 2, depending on the size of the diagonal blocks.
390: *
391: K = N
392: KC = N*( N+1 ) / 2 + 1
393: 90 CONTINUE
394: *
395: * If K < 1, exit from loop.
396: *
397: IF( K.LT.1 )
398: $ GO TO 100
399: *
400: KC = KC - ( N-K+1 )
401: IF( IPIV( K ).GT.0 ) THEN
402: *
403: * 1 x 1 diagonal block
404: *
1.8 bertrand 405: * Multiply by inv(L**T(K)), where L(K) is the transformation
1.1 bertrand 406: * stored in column K of A.
407: *
408: IF( K.LT.N )
409: $ CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
410: $ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
411: *
412: * Interchange rows K and IPIV(K).
413: *
414: KP = IPIV( K )
415: IF( KP.NE.K )
416: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
417: K = K - 1
418: ELSE
419: *
420: * 2 x 2 diagonal block
421: *
1.8 bertrand 422: * Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
1.1 bertrand 423: * stored in columns K-1 and K of A.
424: *
425: IF( K.LT.N ) THEN
426: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
427: $ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
428: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
429: $ LDB, AP( KC-( N-K ) ), 1, ONE, B( K-1, 1 ),
430: $ LDB )
431: END IF
432: *
433: * Interchange rows K and -IPIV(K).
434: *
435: KP = -IPIV( K )
436: IF( KP.NE.K )
437: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
438: KC = KC - ( N-K+2 )
439: K = K - 2
440: END IF
441: *
442: GO TO 90
443: 100 CONTINUE
444: END IF
445: *
446: RETURN
447: *
448: * End of ZSPTRS
449: *
450: END
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