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1.1 bertrand 1: SUBROUTINE ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INFO, LDA, LDB, N, NRHS
11: * ..
12: * .. Array Arguments ..
13: INTEGER IPIV( * )
14: COMPLEX*16 A( LDA, * ), B( LDB, * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZHETRS solves a system of linear equations A*X = B with a complex
21: * Hermitian matrix A using the factorization A = U*D*U**H or
22: * A = L*D*L**H computed by ZHETRF.
23: *
24: * Arguments
25: * =========
26: *
27: * UPLO (input) CHARACTER*1
28: * Specifies whether the details of the factorization are stored
29: * as an upper or lower triangular matrix.
30: * = 'U': Upper triangular, form is A = U*D*U**H;
31: * = 'L': Lower triangular, form is A = L*D*L**H.
32: *
33: * N (input) INTEGER
34: * The order of the matrix A. N >= 0.
35: *
36: * NRHS (input) INTEGER
37: * The number of right hand sides, i.e., the number of columns
38: * of the matrix B. NRHS >= 0.
39: *
40: * A (input) COMPLEX*16 array, dimension (LDA,N)
41: * The block diagonal matrix D and the multipliers used to
42: * obtain the factor U or L as computed by ZHETRF.
43: *
44: * LDA (input) INTEGER
45: * The leading dimension of the array A. LDA >= max(1,N).
46: *
47: * IPIV (input) INTEGER array, dimension (N)
48: * Details of the interchanges and the block structure of D
49: * as determined by ZHETRF.
50: *
51: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
52: * On entry, the right hand side matrix B.
53: * On exit, the solution matrix X.
54: *
55: * LDB (input) INTEGER
56: * The leading dimension of the array B. LDB >= max(1,N).
57: *
58: * INFO (output) INTEGER
59: * = 0: successful exit
60: * < 0: if INFO = -i, the i-th argument had an illegal value
61: *
62: * =====================================================================
63: *
64: * .. Parameters ..
65: COMPLEX*16 ONE
66: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
67: * ..
68: * .. Local Scalars ..
69: LOGICAL UPPER
70: INTEGER J, K, KP
71: DOUBLE PRECISION S
72: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
73: * ..
74: * .. External Functions ..
75: LOGICAL LSAME
76: EXTERNAL LSAME
77: * ..
78: * .. External Subroutines ..
79: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP
80: * ..
81: * .. Intrinsic Functions ..
82: INTRINSIC DBLE, DCONJG, MAX
83: * ..
84: * .. Executable Statements ..
85: *
86: INFO = 0
87: UPPER = LSAME( UPLO, 'U' )
88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
89: INFO = -1
90: ELSE IF( N.LT.0 ) THEN
91: INFO = -2
92: ELSE IF( NRHS.LT.0 ) THEN
93: INFO = -3
94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
95: INFO = -5
96: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
97: INFO = -8
98: END IF
99: IF( INFO.NE.0 ) THEN
100: CALL XERBLA( 'ZHETRS', -INFO )
101: RETURN
102: END IF
103: *
104: * Quick return if possible
105: *
106: IF( N.EQ.0 .OR. NRHS.EQ.0 )
107: $ RETURN
108: *
109: IF( UPPER ) THEN
110: *
111: * Solve A*X = B, where A = U*D*U'.
112: *
113: * First solve U*D*X = B, overwriting B with X.
114: *
115: * K is the main loop index, decreasing from N to 1 in steps of
116: * 1 or 2, depending on the size of the diagonal blocks.
117: *
118: K = N
119: 10 CONTINUE
120: *
121: * If K < 1, exit from loop.
122: *
123: IF( K.LT.1 )
124: $ GO TO 30
125: *
126: IF( IPIV( K ).GT.0 ) THEN
127: *
128: * 1 x 1 diagonal block
129: *
130: * Interchange rows K and IPIV(K).
131: *
132: KP = IPIV( K )
133: IF( KP.NE.K )
134: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
135: *
136: * Multiply by inv(U(K)), where U(K) is the transformation
137: * stored in column K of A.
138: *
139: CALL ZGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
140: $ B( 1, 1 ), LDB )
141: *
142: * Multiply by the inverse of the diagonal block.
143: *
144: S = DBLE( ONE ) / DBLE( A( K, K ) )
145: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
146: K = K - 1
147: ELSE
148: *
149: * 2 x 2 diagonal block
150: *
151: * Interchange rows K-1 and -IPIV(K).
152: *
153: KP = -IPIV( K )
154: IF( KP.NE.K-1 )
155: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
156: *
157: * Multiply by inv(U(K)), where U(K) is the transformation
158: * stored in columns K-1 and K of A.
159: *
160: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
161: $ B( 1, 1 ), LDB )
162: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
163: $ LDB, B( 1, 1 ), LDB )
164: *
165: * Multiply by the inverse of the diagonal block.
166: *
167: AKM1K = A( K-1, K )
168: AKM1 = A( K-1, K-1 ) / AKM1K
169: AK = A( K, K ) / DCONJG( AKM1K )
170: DENOM = AKM1*AK - ONE
171: DO 20 J = 1, NRHS
172: BKM1 = B( K-1, J ) / AKM1K
173: BK = B( K, J ) / DCONJG( AKM1K )
174: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
175: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
176: 20 CONTINUE
177: K = K - 2
178: END IF
179: *
180: GO TO 10
181: 30 CONTINUE
182: *
183: * Next solve U'*X = B, overwriting B with X.
184: *
185: * K is the main loop index, increasing from 1 to N in steps of
186: * 1 or 2, depending on the size of the diagonal blocks.
187: *
188: K = 1
189: 40 CONTINUE
190: *
191: * If K > N, exit from loop.
192: *
193: IF( K.GT.N )
194: $ GO TO 50
195: *
196: IF( IPIV( K ).GT.0 ) THEN
197: *
198: * 1 x 1 diagonal block
199: *
200: * Multiply by inv(U'(K)), where U(K) is the transformation
201: * stored in column K of A.
202: *
203: IF( K.GT.1 ) THEN
204: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
205: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
206: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
207: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
208: END IF
209: *
210: * Interchange rows K and IPIV(K).
211: *
212: KP = IPIV( K )
213: IF( KP.NE.K )
214: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
215: K = K + 1
216: ELSE
217: *
218: * 2 x 2 diagonal block
219: *
220: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation
221: * stored in columns K and K+1 of A.
222: *
223: IF( K.GT.1 ) THEN
224: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
225: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
226: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
227: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
228: *
229: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
230: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
231: $ LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
232: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
233: END IF
234: *
235: * Interchange rows K and -IPIV(K).
236: *
237: KP = -IPIV( K )
238: IF( KP.NE.K )
239: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
240: K = K + 2
241: END IF
242: *
243: GO TO 40
244: 50 CONTINUE
245: *
246: ELSE
247: *
248: * Solve A*X = B, where A = L*D*L'.
249: *
250: * First solve L*D*X = B, overwriting B with X.
251: *
252: * K is the main loop index, increasing from 1 to N in steps of
253: * 1 or 2, depending on the size of the diagonal blocks.
254: *
255: K = 1
256: 60 CONTINUE
257: *
258: * If K > N, exit from loop.
259: *
260: IF( K.GT.N )
261: $ GO TO 80
262: *
263: IF( IPIV( K ).GT.0 ) THEN
264: *
265: * 1 x 1 diagonal block
266: *
267: * Interchange rows K and IPIV(K).
268: *
269: KP = IPIV( K )
270: IF( KP.NE.K )
271: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
272: *
273: * Multiply by inv(L(K)), where L(K) is the transformation
274: * stored in column K of A.
275: *
276: IF( K.LT.N )
277: $ CALL ZGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
278: $ LDB, B( K+1, 1 ), LDB )
279: *
280: * Multiply by the inverse of the diagonal block.
281: *
282: S = DBLE( ONE ) / DBLE( A( K, K ) )
283: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
284: K = K + 1
285: ELSE
286: *
287: * 2 x 2 diagonal block
288: *
289: * Interchange rows K+1 and -IPIV(K).
290: *
291: KP = -IPIV( K )
292: IF( KP.NE.K+1 )
293: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
294: *
295: * Multiply by inv(L(K)), where L(K) is the transformation
296: * stored in columns K and K+1 of A.
297: *
298: IF( K.LT.N-1 ) THEN
299: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
300: $ LDB, B( K+2, 1 ), LDB )
301: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
302: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
303: END IF
304: *
305: * Multiply by the inverse of the diagonal block.
306: *
307: AKM1K = A( K+1, K )
308: AKM1 = A( K, K ) / DCONJG( AKM1K )
309: AK = A( K+1, K+1 ) / AKM1K
310: DENOM = AKM1*AK - ONE
311: DO 70 J = 1, NRHS
312: BKM1 = B( K, J ) / DCONJG( AKM1K )
313: BK = B( K+1, J ) / AKM1K
314: B( K, J ) = ( AK*BKM1-BK ) / DENOM
315: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
316: 70 CONTINUE
317: K = K + 2
318: END IF
319: *
320: GO TO 60
321: 80 CONTINUE
322: *
323: * Next solve L'*X = B, overwriting B with X.
324: *
325: * K is the main loop index, decreasing from N to 1 in steps of
326: * 1 or 2, depending on the size of the diagonal blocks.
327: *
328: K = N
329: 90 CONTINUE
330: *
331: * If K < 1, exit from loop.
332: *
333: IF( K.LT.1 )
334: $ GO TO 100
335: *
336: IF( IPIV( K ).GT.0 ) THEN
337: *
338: * 1 x 1 diagonal block
339: *
340: * Multiply by inv(L'(K)), where L(K) is the transformation
341: * stored in column K of A.
342: *
343: IF( K.LT.N ) THEN
344: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
345: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
346: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
347: $ B( K, 1 ), LDB )
348: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
349: END IF
350: *
351: * Interchange rows K and IPIV(K).
352: *
353: KP = IPIV( K )
354: IF( KP.NE.K )
355: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
356: K = K - 1
357: ELSE
358: *
359: * 2 x 2 diagonal block
360: *
361: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation
362: * stored in columns K-1 and K of A.
363: *
364: IF( K.LT.N ) THEN
365: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
366: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
367: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
368: $ B( K, 1 ), LDB )
369: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
370: *
371: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
372: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
373: $ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE,
374: $ B( K-1, 1 ), LDB )
375: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
376: END IF
377: *
378: * Interchange rows K and -IPIV(K).
379: *
380: KP = -IPIV( K )
381: IF( KP.NE.K )
382: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
383: K = K - 2
384: END IF
385: *
386: GO TO 90
387: 100 CONTINUE
388: END IF
389: *
390: RETURN
391: *
392: * End of ZHETRS
393: *
394: END