1: *> \brief \b ZSYTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
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13: *> [ZIP]</a>
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15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * COMPLEX*16 A( LDA, * ), B( LDB, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSYTRS solves a system of linear equations A*X = B with a complex
39: *> symmetric matrix A using the factorization A = U*D*U**T or
40: *> A = L*D*L**T computed by ZSYTRF.
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] A
69: *> \verbatim
70: *> A is COMPLEX*16 array, dimension (LDA,N)
71: *> The block diagonal matrix D and the multipliers used to
72: *> obtain the factor U or L as computed by ZSYTRF.
73: *> \endverbatim
74: *>
75: *> \param[in] LDA
76: *> \verbatim
77: *> LDA is INTEGER
78: *> The leading dimension of the array A. LDA >= max(1,N).
79: *> \endverbatim
80: *>
81: *> \param[in] IPIV
82: *> \verbatim
83: *> IPIV is INTEGER array, dimension (N)
84: *> Details of the interchanges and the block structure of D
85: *> as determined by ZSYTRF.
86: *> \endverbatim
87: *>
88: *> \param[in,out] B
89: *> \verbatim
90: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
91: *> On entry, the right hand side matrix B.
92: *> On exit, the solution matrix X.
93: *> \endverbatim
94: *>
95: *> \param[in] LDB
96: *> \verbatim
97: *> LDB is INTEGER
98: *> The leading dimension of the array B. LDB >= max(1,N).
99: *> \endverbatim
100: *>
101: *> \param[out] INFO
102: *> \verbatim
103: *> INFO is INTEGER
104: *> = 0: successful exit
105: *> < 0: if INFO = -i, the i-th argument had an illegal value
106: *> \endverbatim
107: *
108: * Authors:
109: * ========
110: *
111: *> \author Univ. of Tennessee
112: *> \author Univ. of California Berkeley
113: *> \author Univ. of Colorado Denver
114: *> \author NAG Ltd.
115: *
116: *> \ingroup complex16SYcomputational
117: *
118: * =====================================================================
119: SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
120: *
121: * -- LAPACK computational routine --
122: * -- LAPACK is a software package provided by Univ. of Tennessee, --
123: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124: *
125: * .. Scalar Arguments ..
126: CHARACTER UPLO
127: INTEGER INFO, LDA, LDB, N, NRHS
128: * ..
129: * .. Array Arguments ..
130: INTEGER IPIV( * )
131: COMPLEX*16 A( LDA, * ), B( LDB, * )
132: * ..
133: *
134: * =====================================================================
135: *
136: * .. Parameters ..
137: COMPLEX*16 ONE
138: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
139: * ..
140: * .. Local Scalars ..
141: LOGICAL UPPER
142: INTEGER J, K, KP
143: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
144: * ..
145: * .. External Functions ..
146: LOGICAL LSAME
147: EXTERNAL LSAME
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP
151: * ..
152: * .. Intrinsic Functions ..
153: INTRINSIC MAX
154: * ..
155: * .. Executable Statements ..
156: *
157: INFO = 0
158: UPPER = LSAME( UPLO, 'U' )
159: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
160: INFO = -1
161: ELSE IF( N.LT.0 ) THEN
162: INFO = -2
163: ELSE IF( NRHS.LT.0 ) THEN
164: INFO = -3
165: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
166: INFO = -5
167: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
168: INFO = -8
169: END IF
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'ZSYTRS', -INFO )
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: IF( N.EQ.0 .OR. NRHS.EQ.0 )
178: $ RETURN
179: *
180: IF( UPPER ) THEN
181: *
182: * Solve A*X = B, where A = U*D*U**T.
183: *
184: * First solve U*D*X = B, overwriting B with X.
185: *
186: * K is the main loop index, decreasing from N to 1 in steps of
187: * 1 or 2, depending on the size of the diagonal blocks.
188: *
189: K = N
190: 10 CONTINUE
191: *
192: * If K < 1, exit from loop.
193: *
194: IF( K.LT.1 )
195: $ GO TO 30
196: *
197: IF( IPIV( K ).GT.0 ) THEN
198: *
199: * 1 x 1 diagonal block
200: *
201: * Interchange rows K and IPIV(K).
202: *
203: KP = IPIV( K )
204: IF( KP.NE.K )
205: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
206: *
207: * Multiply by inv(U(K)), where U(K) is the transformation
208: * stored in column K of A.
209: *
210: CALL ZGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
211: $ B( 1, 1 ), LDB )
212: *
213: * Multiply by the inverse of the diagonal block.
214: *
215: CALL ZSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
216: K = K - 1
217: ELSE
218: *
219: * 2 x 2 diagonal block
220: *
221: * Interchange rows K-1 and -IPIV(K).
222: *
223: KP = -IPIV( K )
224: IF( KP.NE.K-1 )
225: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
226: *
227: * Multiply by inv(U(K)), where U(K) is the transformation
228: * stored in columns K-1 and K of A.
229: *
230: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
231: $ B( 1, 1 ), LDB )
232: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
233: $ LDB, B( 1, 1 ), LDB )
234: *
235: * Multiply by the inverse of the diagonal block.
236: *
237: AKM1K = A( K-1, K )
238: AKM1 = A( K-1, K-1 ) / AKM1K
239: AK = A( K, K ) / AKM1K
240: DENOM = AKM1*AK - ONE
241: DO 20 J = 1, NRHS
242: BKM1 = B( K-1, J ) / AKM1K
243: BK = B( K, J ) / AKM1K
244: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
245: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
246: 20 CONTINUE
247: K = K - 2
248: END IF
249: *
250: GO TO 10
251: 30 CONTINUE
252: *
253: * Next solve U**T *X = B, overwriting B with X.
254: *
255: * K is the main loop index, increasing from 1 to N in steps of
256: * 1 or 2, depending on the size of the diagonal blocks.
257: *
258: K = 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: *
270: * Multiply by inv(U**T(K)), where U(K) is the transformation
271: * stored in column K of A.
272: *
273: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
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: K = K + 1
282: ELSE
283: *
284: * 2 x 2 diagonal block
285: *
286: * Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
287: * stored in columns K and K+1 of A.
288: *
289: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
290: $ 1, ONE, B( K, 1 ), LDB )
291: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
292: $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
293: *
294: * Interchange rows K and -IPIV(K).
295: *
296: KP = -IPIV( K )
297: IF( KP.NE.K )
298: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
299: K = K + 2
300: END IF
301: *
302: GO TO 40
303: 50 CONTINUE
304: *
305: ELSE
306: *
307: * Solve A*X = B, where A = L*D*L**T.
308: *
309: * First solve L*D*X = B, overwriting B with X.
310: *
311: * K is the main loop index, increasing from 1 to N in steps of
312: * 1 or 2, depending on the size of the diagonal blocks.
313: *
314: K = 1
315: 60 CONTINUE
316: *
317: * If K > N, exit from loop.
318: *
319: IF( K.GT.N )
320: $ GO TO 80
321: *
322: IF( IPIV( K ).GT.0 ) THEN
323: *
324: * 1 x 1 diagonal block
325: *
326: * Interchange rows K and IPIV(K).
327: *
328: KP = IPIV( K )
329: IF( KP.NE.K )
330: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
331: *
332: * Multiply by inv(L(K)), where L(K) is the transformation
333: * stored in column K of A.
334: *
335: IF( K.LT.N )
336: $ CALL ZGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
337: $ LDB, B( K+1, 1 ), LDB )
338: *
339: * Multiply by the inverse of the diagonal block.
340: *
341: CALL ZSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
342: K = K + 1
343: ELSE
344: *
345: * 2 x 2 diagonal block
346: *
347: * Interchange rows K+1 and -IPIV(K).
348: *
349: KP = -IPIV( K )
350: IF( KP.NE.K+1 )
351: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
352: *
353: * Multiply by inv(L(K)), where L(K) is the transformation
354: * stored in columns K and K+1 of A.
355: *
356: IF( K.LT.N-1 ) THEN
357: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
358: $ LDB, B( K+2, 1 ), LDB )
359: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
360: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
361: END IF
362: *
363: * Multiply by the inverse of the diagonal block.
364: *
365: AKM1K = A( K+1, K )
366: AKM1 = A( K, K ) / AKM1K
367: AK = A( K+1, K+1 ) / AKM1K
368: DENOM = AKM1*AK - ONE
369: DO 70 J = 1, NRHS
370: BKM1 = B( K, J ) / AKM1K
371: BK = B( K+1, J ) / AKM1K
372: B( K, J ) = ( AK*BKM1-BK ) / DENOM
373: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
374: 70 CONTINUE
375: K = K + 2
376: END IF
377: *
378: GO TO 60
379: 80 CONTINUE
380: *
381: * Next solve L**T *X = B, overwriting B with X.
382: *
383: * K is the main loop index, decreasing from N to 1 in steps of
384: * 1 or 2, depending on the size of the diagonal blocks.
385: *
386: K = N
387: 90 CONTINUE
388: *
389: * If K < 1, exit from loop.
390: *
391: IF( K.LT.1 )
392: $ GO TO 100
393: *
394: IF( IPIV( K ).GT.0 ) THEN
395: *
396: * 1 x 1 diagonal block
397: *
398: * Multiply by inv(L**T(K)), where L(K) is the transformation
399: * stored in column K of A.
400: *
401: IF( K.LT.N )
402: $ CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
403: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
404: *
405: * Interchange rows K and IPIV(K).
406: *
407: KP = IPIV( K )
408: IF( KP.NE.K )
409: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
410: K = K - 1
411: ELSE
412: *
413: * 2 x 2 diagonal block
414: *
415: * Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
416: * stored in columns K-1 and K of A.
417: *
418: IF( K.LT.N ) THEN
419: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
420: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
421: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
422: $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
423: $ LDB )
424: END IF
425: *
426: * Interchange rows K and -IPIV(K).
427: *
428: KP = -IPIV( K )
429: IF( KP.NE.K )
430: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
431: K = K - 2
432: END IF
433: *
434: GO TO 90
435: 100 CONTINUE
436: END IF
437: *
438: RETURN
439: *
440: * End of ZSYTRS
441: *
442: END
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