1 SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
2 $ WORK, INFO )
3 *
4 * -- LAPACK PROTOTYPE routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * -- Written by Julie Langou of the Univ. of TN --
10 *
11 * .. Scalar Arguments ..
12 CHARACTER UPLO
13 INTEGER INFO, LDA, LDB, N, NRHS
14 * ..
15 * .. Array Arguments ..
16 INTEGER IPIV( * )
17 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
18 * ..
19 *
20 * Purpose
21 * =======
22 *
23 * DSYTRS2 solves a system of linear equations A*X = B with a real
24 * symmetric matrix A using the factorization A = U*D*U**T or
25 * A = L*D*L**T computed by DSYTRF and converted by DSYCONV.
26 *
27 * Arguments
28 * =========
29 *
30 * UPLO (input) CHARACTER*1
31 * Specifies whether the details of the factorization are stored
32 * as an upper or lower triangular matrix.
33 * = 'U': Upper triangular, form is A = U*D*U**T;
34 * = 'L': Lower triangular, form is A = L*D*L**T.
35 *
36 * N (input) INTEGER
37 * The order of the matrix A. N >= 0.
38 *
39 * NRHS (input) INTEGER
40 * The number of right hand sides, i.e., the number of columns
41 * of the matrix B. NRHS >= 0.
42 *
43 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
44 * The block diagonal matrix D and the multipliers used to
45 * obtain the factor U or L as computed by DSYTRF.
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= max(1,N).
49 *
50 * IPIV (input) INTEGER array, dimension (N)
51 * Details of the interchanges and the block structure of D
52 * as determined by DSYTRF.
53 *
54 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
55 * On entry, the right hand side matrix B.
56 * On exit, the solution matrix X.
57 *
58 * LDB (input) INTEGER
59 * The leading dimension of the array B. LDB >= max(1,N).
60 *
61 * WORK (workspace) REAL array, dimension (N)
62 *
63 * INFO (output) INTEGER
64 * = 0: successful exit
65 * < 0: if INFO = -i, the i-th argument had an illegal value
66 *
67 * =====================================================================
68 *
69 * .. Parameters ..
70 DOUBLE PRECISION ONE
71 PARAMETER ( ONE = 1.0D+0 )
72 * ..
73 * .. Local Scalars ..
74 LOGICAL UPPER
75 INTEGER I, IINFO, J, K, KP
76 DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
77 * ..
78 * .. External Functions ..
79 LOGICAL LSAME
80 EXTERNAL LSAME
81 * ..
82 * .. External Subroutines ..
83 EXTERNAL DSCAL, DSYCONV, DSWAP, DTRSM, XERBLA
84 * ..
85 * .. Intrinsic Functions ..
86 INTRINSIC MAX
87 * ..
88 * .. Executable Statements ..
89 *
90 INFO = 0
91 UPPER = LSAME( UPLO, 'U' )
92 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
93 INFO = -1
94 ELSE IF( N.LT.0 ) THEN
95 INFO = -2
96 ELSE IF( NRHS.LT.0 ) THEN
97 INFO = -3
98 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
99 INFO = -5
100 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
101 INFO = -8
102 END IF
103 IF( INFO.NE.0 ) THEN
104 CALL XERBLA( 'DSYTRS2', -INFO )
105 RETURN
106 END IF
107 *
108 * Quick return if possible
109 *
110 IF( N.EQ.0 .OR. NRHS.EQ.0 )
111 $ RETURN
112 *
113 * Convert A
114 *
115 CALL DSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
116 *
117 IF( UPPER ) THEN
118 *
119 * Solve A*X = B, where A = U*D*U**T.
120 *
121 * P**T * B
122 K=N
123 DO WHILE ( K .GE. 1 )
124 IF( IPIV( K ).GT.0 ) THEN
125 * 1 x 1 diagonal block
126 * Interchange rows K and IPIV(K).
127 KP = IPIV( K )
128 IF( KP.NE.K )
129 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
130 K=K-1
131 ELSE
132 * 2 x 2 diagonal block
133 * Interchange rows K-1 and -IPIV(K).
134 KP = -IPIV( K )
135 IF( KP.EQ.-IPIV( K-1 ) )
136 $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
137 K=K-2
138 END IF
139 END DO
140 *
141 * Compute (U \P**T * B) -> B [ (U \P**T * B) ]
142 *
143 CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
144 *
145 * Compute D \ B -> B [ D \ (U \P**T * B) ]
146 *
147 I=N
148 DO WHILE ( I .GE. 1 )
149 IF( IPIV(I) .GT. 0 ) THEN
150 CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
151 ELSEIF ( I .GT. 1) THEN
152 IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
153 AKM1K = WORK(I)
154 AKM1 = A( I-1, I-1 ) / AKM1K
155 AK = A( I, I ) / AKM1K
156 DENOM = AKM1*AK - ONE
157 DO 15 J = 1, NRHS
158 BKM1 = B( I-1, J ) / AKM1K
159 BK = B( I, J ) / AKM1K
160 B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
161 B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
162 15 CONTINUE
163 I = I - 1
164 ENDIF
165 ENDIF
166 I = I - 1
167 END DO
168 *
169 * Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ]
170 *
171 CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
172 *
173 * P * B [ P * (U**T \ (D \ (U \P**T * B) )) ]
174 *
175 K=1
176 DO WHILE ( K .LE. N )
177 IF( IPIV( K ).GT.0 ) THEN
178 * 1 x 1 diagonal block
179 * Interchange rows K and IPIV(K).
180 KP = IPIV( K )
181 IF( KP.NE.K )
182 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
183 K=K+1
184 ELSE
185 * 2 x 2 diagonal block
186 * Interchange rows K-1 and -IPIV(K).
187 KP = -IPIV( K )
188 IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
189 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
190 K=K+2
191 ENDIF
192 END DO
193 *
194 ELSE
195 *
196 * Solve A*X = B, where A = L*D*L**T.
197 *
198 * P**T * B
199 K=1
200 DO WHILE ( K .LE. N )
201 IF( IPIV( K ).GT.0 ) THEN
202 * 1 x 1 diagonal block
203 * Interchange rows K and IPIV(K).
204 KP = IPIV( K )
205 IF( KP.NE.K )
206 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
207 K=K+1
208 ELSE
209 * 2 x 2 diagonal block
210 * Interchange rows K and -IPIV(K+1).
211 KP = -IPIV( K+1 )
212 IF( KP.EQ.-IPIV( K ) )
213 $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
214 K=K+2
215 ENDIF
216 END DO
217 *
218 * Compute (L \P**T * B) -> B [ (L \P**T * B) ]
219 *
220 CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
221 *
222 * Compute D \ B -> B [ D \ (L \P**T * B) ]
223 *
224 I=1
225 DO WHILE ( I .LE. N )
226 IF( IPIV(I) .GT. 0 ) THEN
227 CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
228 ELSE
229 AKM1K = WORK(I)
230 AKM1 = A( I, I ) / AKM1K
231 AK = A( I+1, I+1 ) / AKM1K
232 DENOM = AKM1*AK - ONE
233 DO 25 J = 1, NRHS
234 BKM1 = B( I, J ) / AKM1K
235 BK = B( I+1, J ) / AKM1K
236 B( I, J ) = ( AK*BKM1-BK ) / DENOM
237 B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
238 25 CONTINUE
239 I = I + 1
240 ENDIF
241 I = I + 1
242 END DO
243 *
244 * Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ]
245 *
246 CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
247 *
248 * P * B [ P * (L**T \ (D \ (L \P**T * B) )) ]
249 *
250 K=N
251 DO WHILE ( K .GE. 1 )
252 IF( IPIV( K ).GT.0 ) THEN
253 * 1 x 1 diagonal block
254 * Interchange rows K and IPIV(K).
255 KP = IPIV( K )
256 IF( KP.NE.K )
257 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
258 K=K-1
259 ELSE
260 * 2 x 2 diagonal block
261 * Interchange rows K-1 and -IPIV(K).
262 KP = -IPIV( K )
263 IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
264 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
265 K=K-2
266 ENDIF
267 END DO
268 *
269 END IF
270 *
271 * Revert A
272 *
273 CALL DSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
274 *
275 RETURN
276 *
277 * End of DSYTRS2
278 *
279 END
2 $ WORK, INFO )
3 *
4 * -- LAPACK PROTOTYPE routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * -- Written by Julie Langou of the Univ. of TN --
10 *
11 * .. Scalar Arguments ..
12 CHARACTER UPLO
13 INTEGER INFO, LDA, LDB, N, NRHS
14 * ..
15 * .. Array Arguments ..
16 INTEGER IPIV( * )
17 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
18 * ..
19 *
20 * Purpose
21 * =======
22 *
23 * DSYTRS2 solves a system of linear equations A*X = B with a real
24 * symmetric matrix A using the factorization A = U*D*U**T or
25 * A = L*D*L**T computed by DSYTRF and converted by DSYCONV.
26 *
27 * Arguments
28 * =========
29 *
30 * UPLO (input) CHARACTER*1
31 * Specifies whether the details of the factorization are stored
32 * as an upper or lower triangular matrix.
33 * = 'U': Upper triangular, form is A = U*D*U**T;
34 * = 'L': Lower triangular, form is A = L*D*L**T.
35 *
36 * N (input) INTEGER
37 * The order of the matrix A. N >= 0.
38 *
39 * NRHS (input) INTEGER
40 * The number of right hand sides, i.e., the number of columns
41 * of the matrix B. NRHS >= 0.
42 *
43 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
44 * The block diagonal matrix D and the multipliers used to
45 * obtain the factor U or L as computed by DSYTRF.
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= max(1,N).
49 *
50 * IPIV (input) INTEGER array, dimension (N)
51 * Details of the interchanges and the block structure of D
52 * as determined by DSYTRF.
53 *
54 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
55 * On entry, the right hand side matrix B.
56 * On exit, the solution matrix X.
57 *
58 * LDB (input) INTEGER
59 * The leading dimension of the array B. LDB >= max(1,N).
60 *
61 * WORK (workspace) REAL array, dimension (N)
62 *
63 * INFO (output) INTEGER
64 * = 0: successful exit
65 * < 0: if INFO = -i, the i-th argument had an illegal value
66 *
67 * =====================================================================
68 *
69 * .. Parameters ..
70 DOUBLE PRECISION ONE
71 PARAMETER ( ONE = 1.0D+0 )
72 * ..
73 * .. Local Scalars ..
74 LOGICAL UPPER
75 INTEGER I, IINFO, J, K, KP
76 DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
77 * ..
78 * .. External Functions ..
79 LOGICAL LSAME
80 EXTERNAL LSAME
81 * ..
82 * .. External Subroutines ..
83 EXTERNAL DSCAL, DSYCONV, DSWAP, DTRSM, XERBLA
84 * ..
85 * .. Intrinsic Functions ..
86 INTRINSIC MAX
87 * ..
88 * .. Executable Statements ..
89 *
90 INFO = 0
91 UPPER = LSAME( UPLO, 'U' )
92 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
93 INFO = -1
94 ELSE IF( N.LT.0 ) THEN
95 INFO = -2
96 ELSE IF( NRHS.LT.0 ) THEN
97 INFO = -3
98 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
99 INFO = -5
100 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
101 INFO = -8
102 END IF
103 IF( INFO.NE.0 ) THEN
104 CALL XERBLA( 'DSYTRS2', -INFO )
105 RETURN
106 END IF
107 *
108 * Quick return if possible
109 *
110 IF( N.EQ.0 .OR. NRHS.EQ.0 )
111 $ RETURN
112 *
113 * Convert A
114 *
115 CALL DSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
116 *
117 IF( UPPER ) THEN
118 *
119 * Solve A*X = B, where A = U*D*U**T.
120 *
121 * P**T * B
122 K=N
123 DO WHILE ( K .GE. 1 )
124 IF( IPIV( K ).GT.0 ) THEN
125 * 1 x 1 diagonal block
126 * Interchange rows K and IPIV(K).
127 KP = IPIV( K )
128 IF( KP.NE.K )
129 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
130 K=K-1
131 ELSE
132 * 2 x 2 diagonal block
133 * Interchange rows K-1 and -IPIV(K).
134 KP = -IPIV( K )
135 IF( KP.EQ.-IPIV( K-1 ) )
136 $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
137 K=K-2
138 END IF
139 END DO
140 *
141 * Compute (U \P**T * B) -> B [ (U \P**T * B) ]
142 *
143 CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
144 *
145 * Compute D \ B -> B [ D \ (U \P**T * B) ]
146 *
147 I=N
148 DO WHILE ( I .GE. 1 )
149 IF( IPIV(I) .GT. 0 ) THEN
150 CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
151 ELSEIF ( I .GT. 1) THEN
152 IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
153 AKM1K = WORK(I)
154 AKM1 = A( I-1, I-1 ) / AKM1K
155 AK = A( I, I ) / AKM1K
156 DENOM = AKM1*AK - ONE
157 DO 15 J = 1, NRHS
158 BKM1 = B( I-1, J ) / AKM1K
159 BK = B( I, J ) / AKM1K
160 B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
161 B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
162 15 CONTINUE
163 I = I - 1
164 ENDIF
165 ENDIF
166 I = I - 1
167 END DO
168 *
169 * Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ]
170 *
171 CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
172 *
173 * P * B [ P * (U**T \ (D \ (U \P**T * B) )) ]
174 *
175 K=1
176 DO WHILE ( K .LE. N )
177 IF( IPIV( K ).GT.0 ) THEN
178 * 1 x 1 diagonal block
179 * Interchange rows K and IPIV(K).
180 KP = IPIV( K )
181 IF( KP.NE.K )
182 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
183 K=K+1
184 ELSE
185 * 2 x 2 diagonal block
186 * Interchange rows K-1 and -IPIV(K).
187 KP = -IPIV( K )
188 IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
189 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
190 K=K+2
191 ENDIF
192 END DO
193 *
194 ELSE
195 *
196 * Solve A*X = B, where A = L*D*L**T.
197 *
198 * P**T * B
199 K=1
200 DO WHILE ( K .LE. N )
201 IF( IPIV( K ).GT.0 ) THEN
202 * 1 x 1 diagonal block
203 * Interchange rows K and IPIV(K).
204 KP = IPIV( K )
205 IF( KP.NE.K )
206 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
207 K=K+1
208 ELSE
209 * 2 x 2 diagonal block
210 * Interchange rows K and -IPIV(K+1).
211 KP = -IPIV( K+1 )
212 IF( KP.EQ.-IPIV( K ) )
213 $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
214 K=K+2
215 ENDIF
216 END DO
217 *
218 * Compute (L \P**T * B) -> B [ (L \P**T * B) ]
219 *
220 CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
221 *
222 * Compute D \ B -> B [ D \ (L \P**T * B) ]
223 *
224 I=1
225 DO WHILE ( I .LE. N )
226 IF( IPIV(I) .GT. 0 ) THEN
227 CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
228 ELSE
229 AKM1K = WORK(I)
230 AKM1 = A( I, I ) / AKM1K
231 AK = A( I+1, I+1 ) / AKM1K
232 DENOM = AKM1*AK - ONE
233 DO 25 J = 1, NRHS
234 BKM1 = B( I, J ) / AKM1K
235 BK = B( I+1, J ) / AKM1K
236 B( I, J ) = ( AK*BKM1-BK ) / DENOM
237 B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
238 25 CONTINUE
239 I = I + 1
240 ENDIF
241 I = I + 1
242 END DO
243 *
244 * Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ]
245 *
246 CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
247 *
248 * P * B [ P * (L**T \ (D \ (L \P**T * B) )) ]
249 *
250 K=N
251 DO WHILE ( K .GE. 1 )
252 IF( IPIV( K ).GT.0 ) THEN
253 * 1 x 1 diagonal block
254 * Interchange rows K and IPIV(K).
255 KP = IPIV( K )
256 IF( KP.NE.K )
257 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
258 K=K-1
259 ELSE
260 * 2 x 2 diagonal block
261 * Interchange rows K-1 and -IPIV(K).
262 KP = -IPIV( K )
263 IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
264 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
265 K=K-2
266 ENDIF
267 END DO
268 *
269 END IF
270 *
271 * Revert A
272 *
273 CALL DSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
274 *
275 RETURN
276 *
277 * End of DSYTRS2
278 *
279 END