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1.1 bertrand 1: SUBROUTINE ZSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
2: $ WORK, INFO )
3: *
4: * -- LAPACK PROTOTYPE routine (version 3.2.2) --
5: *
6: * -- Written by Julie Langou of the Univ. of TN --
7: * May 2010
8: *
9: * -- LAPACK is a software package provided by Univ. of Tennessee, --
10: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
11: *
12: * .. Scalar Arguments ..
13: CHARACTER UPLO
14: INTEGER INFO, LDA, LDB, N, NRHS
15: * ..
16: * .. Array Arguments ..
17: INTEGER IPIV( * )
18: DOUBLE COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
19: * ..
20: *
21: * Purpose
22: * =======
23: *
24: * ZSYTRS2 solves a system of linear equations A*X = B with a real
25: * symmetric matrix A using the factorization A = U*D*U**T or
26: * A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.
27: *
28: * Arguments
29: * =========
30: *
31: * UPLO (input) CHARACTER*1
32: * Specifies whether the details of the factorization are stored
33: * as an upper or lower triangular matrix.
34: * = 'U': Upper triangular, form is A = U*D*U**T;
35: * = 'L': Lower triangular, form is A = L*D*L**T.
36: *
37: * N (input) INTEGER
38: * The order of the matrix A. N >= 0.
39: *
40: * NRHS (input) INTEGER
41: * The number of right hand sides, i.e., the number of columns
42: * of the matrix B. NRHS >= 0.
43: *
44: * A (input) DOUBLE COMPLEX array, dimension (LDA,N)
45: * The block diagonal matrix D and the multipliers used to
46: * obtain the factor U or L as computed by ZSYTRF.
47: *
48: * LDA (input) INTEGER
49: * The leading dimension of the array A. LDA >= max(1,N).
50: *
51: * IPIV (input) INTEGER array, dimension (N)
52: * Details of the interchanges and the block structure of D
53: * as determined by ZSYTRF.
54: *
55: * B (input/output) DOUBLE COMPLEX array, dimension (LDB,NRHS)
56: * On entry, the right hand side matrix B.
57: * On exit, the solution matrix X.
58: *
59: * LDB (input) INTEGER
60: * The leading dimension of the array B. LDB >= max(1,N).
61: *
62: * WORK (workspace) REAL array, dimension (N)
63: *
64: * INFO (output) INTEGER
65: * = 0: successful exit
66: * < 0: if INFO = -i, the i-th argument had an illegal value
67: *
68: * =====================================================================
69: *
70: * .. Parameters ..
71: DOUBLE COMPLEX ONE
72: PARAMETER ( ONE = (1.0D+0,0.0D+0) )
73: * ..
74: * .. Local Scalars ..
75: LOGICAL UPPER
76: INTEGER I, IINFO, J, K, KP
77: DOUBLE COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM
78: * ..
79: * .. External Functions ..
80: LOGICAL LSAME
81: EXTERNAL LSAME
82: * ..
83: * .. External Subroutines ..
84: EXTERNAL ZSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA
85: * ..
86: * .. Intrinsic Functions ..
87: INTRINSIC MAX
88: * ..
89: * .. Executable Statements ..
90: *
91: INFO = 0
92: UPPER = LSAME( UPLO, 'U' )
93: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
94: INFO = -1
95: ELSE IF( N.LT.0 ) THEN
96: INFO = -2
97: ELSE IF( NRHS.LT.0 ) THEN
98: INFO = -3
99: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
100: INFO = -5
101: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
102: INFO = -8
103: END IF
104: IF( INFO.NE.0 ) THEN
105: CALL XERBLA( 'ZSYTRS2', -INFO )
106: RETURN
107: END IF
108: *
109: * Quick return if possible
110: *
111: IF( N.EQ.0 .OR. NRHS.EQ.0 )
112: $ RETURN
113: *
114: * Convert A
115: *
116: CALL ZSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
117: *
118: IF( UPPER ) THEN
119: *
120: * Solve A*X = B, where A = U*D*U'.
121: *
122: * P' * B
123: K=N
124: DO WHILE ( K .GE. 1 )
125: IF( IPIV( K ).GT.0 ) THEN
126: * 1 x 1 diagonal block
127: * Interchange rows K and IPIV(K).
128: KP = IPIV( K )
129: IF( KP.NE.K )
130: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
131: K=K-1
132: ELSE
133: * 2 x 2 diagonal block
134: * Interchange rows K-1 and -IPIV(K).
135: KP = -IPIV( K )
136: IF( KP.EQ.-IPIV( K-1 ) )
137: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
138: K=K-2
139: END IF
140: END DO
141: *
142: * Compute (U \P' * B) -> B [ (U \P' * B) ]
143: *
144: CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N)
145: *
146: * Compute D \ B -> B [ D \ (U \P' * B) ]
147: *
148: I=N
149: DO WHILE ( I .GE. 1 )
150: IF( IPIV(I) .GT. 0 ) THEN
151: CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )
152: ELSEIF ( I .GT. 1) THEN
153: IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
154: AKM1K = WORK(I)
155: AKM1 = A( I-1, I-1 ) / AKM1K
156: AK = A( I, I ) / AKM1K
157: DENOM = AKM1*AK - ONE
158: DO 15 J = 1, NRHS
159: BKM1 = B( I-1, J ) / AKM1K
160: BK = B( I, J ) / AKM1K
161: B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
162: B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
163: 15 CONTINUE
164: I = I - 1
165: ENDIF
166: ENDIF
167: I = I - 1
168: END DO
169: *
170: * Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ]
171: *
172: CALL ZTRSM('L','U','T','U',N,NRHS,ONE,A,N,B,N)
173: *
174: * P * B [ P * (U' \ (D \ (U \P' * B) )) ]
175: *
176: K=1
177: DO WHILE ( K .LE. N )
178: IF( IPIV( K ).GT.0 ) THEN
179: * 1 x 1 diagonal block
180: * Interchange rows K and IPIV(K).
181: KP = IPIV( K )
182: IF( KP.NE.K )
183: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
184: K=K+1
185: ELSE
186: * 2 x 2 diagonal block
187: * Interchange rows K-1 and -IPIV(K).
188: KP = -IPIV( K )
189: IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
190: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
191: K=K+2
192: ENDIF
193: END DO
194: *
195: ELSE
196: *
197: * Solve A*X = B, where A = L*D*L'.
198: *
199: * P' * B
200: K=1
201: DO WHILE ( K .LE. N )
202: IF( IPIV( K ).GT.0 ) THEN
203: * 1 x 1 diagonal block
204: * Interchange rows K and IPIV(K).
205: KP = IPIV( K )
206: IF( KP.NE.K )
207: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
208: K=K+1
209: ELSE
210: * 2 x 2 diagonal block
211: * Interchange rows K and -IPIV(K+1).
212: KP = -IPIV( K+1 )
213: IF( KP.EQ.-IPIV( K ) )
214: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
215: K=K+2
216: ENDIF
217: END DO
218: *
219: * Compute (L \P' * B) -> B [ (L \P' * B) ]
220: *
221: CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N)
222: *
223: * Compute D \ B -> B [ D \ (L \P' * B) ]
224: *
225: I=1
226: DO WHILE ( I .LE. N )
227: IF( IPIV(I) .GT. 0 ) THEN
228: CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )
229: ELSE
230: AKM1K = WORK(I)
231: AKM1 = A( I, I ) / AKM1K
232: AK = A( I+1, I+1 ) / AKM1K
233: DENOM = AKM1*AK - ONE
234: DO 25 J = 1, NRHS
235: BKM1 = B( I, J ) / AKM1K
236: BK = B( I+1, J ) / AKM1K
237: B( I, J ) = ( AK*BKM1-BK ) / DENOM
238: B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
239: 25 CONTINUE
240: I = I + 1
241: ENDIF
242: I = I + 1
243: END DO
244: *
245: * Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ]
246: *
247: CALL ZTRSM('L','L','T','U',N,NRHS,ONE,A,N,B,N)
248: *
249: * P * B [ P * (L' \ (D \ (L \P' * B) )) ]
250: *
251: K=N
252: DO WHILE ( K .GE. 1 )
253: IF( IPIV( K ).GT.0 ) THEN
254: * 1 x 1 diagonal block
255: * Interchange rows K and IPIV(K).
256: KP = IPIV( K )
257: IF( KP.NE.K )
258: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
259: K=K-1
260: ELSE
261: * 2 x 2 diagonal block
262: * Interchange rows K-1 and -IPIV(K).
263: KP = -IPIV( K )
264: IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
265: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
266: K=K-2
267: ENDIF
268: END DO
269: *
270: END IF
271: *
272: * Revert A
273: *
274: CALL ZSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
275: *
276: RETURN
277: *
278: * End of ZSYTRS2
279: *
280: END