1 SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INFO, LDA, LDB, N, NRHS
11 * ..
12 * .. Array Arguments ..
13 INTEGER IPIV( * )
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DSYTRS solves a system of linear equations A*X = B with a real
21 * symmetric matrix A using the factorization A = U*D*U**T or
22 * A = L*D*L**T computed by DSYTRF.
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**T;
31 * = 'L': Lower triangular, form is A = L*D*L**T.
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) DOUBLE PRECISION 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 DSYTRF.
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 DSYTRF.
50 *
51 * B (input/output) DOUBLE PRECISION 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 DOUBLE PRECISION ONE
66 PARAMETER ( ONE = 1.0D+0 )
67 * ..
68 * .. Local Scalars ..
69 LOGICAL UPPER
70 INTEGER J, K, KP
71 DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
72 * ..
73 * .. External Functions ..
74 LOGICAL LSAME
75 EXTERNAL LSAME
76 * ..
77 * .. External Subroutines ..
78 EXTERNAL DGEMV, DGER, DSCAL, DSWAP, XERBLA
79 * ..
80 * .. Intrinsic Functions ..
81 INTRINSIC MAX
82 * ..
83 * .. Executable Statements ..
84 *
85 INFO = 0
86 UPPER = LSAME( UPLO, 'U' )
87 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
88 INFO = -1
89 ELSE IF( N.LT.0 ) THEN
90 INFO = -2
91 ELSE IF( NRHS.LT.0 ) THEN
92 INFO = -3
93 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
94 INFO = -5
95 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
96 INFO = -8
97 END IF
98 IF( INFO.NE.0 ) THEN
99 CALL XERBLA( 'DSYTRS', -INFO )
100 RETURN
101 END IF
102 *
103 * Quick return if possible
104 *
105 IF( N.EQ.0 .OR. NRHS.EQ.0 )
106 $ RETURN
107 *
108 IF( UPPER ) THEN
109 *
110 * Solve A*X = B, where A = U*D*U**T.
111 *
112 * First solve U*D*X = B, overwriting B with X.
113 *
114 * K is the main loop index, decreasing from N to 1 in steps of
115 * 1 or 2, depending on the size of the diagonal blocks.
116 *
117 K = N
118 10 CONTINUE
119 *
120 * If K < 1, exit from loop.
121 *
122 IF( K.LT.1 )
123 $ GO TO 30
124 *
125 IF( IPIV( K ).GT.0 ) THEN
126 *
127 * 1 x 1 diagonal block
128 *
129 * Interchange rows K and IPIV(K).
130 *
131 KP = IPIV( K )
132 IF( KP.NE.K )
133 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
134 *
135 * Multiply by inv(U(K)), where U(K) is the transformation
136 * stored in column K of A.
137 *
138 CALL DGER( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
139 $ B( 1, 1 ), LDB )
140 *
141 * Multiply by the inverse of the diagonal block.
142 *
143 CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
144 K = K - 1
145 ELSE
146 *
147 * 2 x 2 diagonal block
148 *
149 * Interchange rows K-1 and -IPIV(K).
150 *
151 KP = -IPIV( K )
152 IF( KP.NE.K-1 )
153 $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
154 *
155 * Multiply by inv(U(K)), where U(K) is the transformation
156 * stored in columns K-1 and K of A.
157 *
158 CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
159 $ B( 1, 1 ), LDB )
160 CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
161 $ LDB, B( 1, 1 ), LDB )
162 *
163 * Multiply by the inverse of the diagonal block.
164 *
165 AKM1K = A( K-1, K )
166 AKM1 = A( K-1, K-1 ) / AKM1K
167 AK = A( K, K ) / AKM1K
168 DENOM = AKM1*AK - ONE
169 DO 20 J = 1, NRHS
170 BKM1 = B( K-1, J ) / AKM1K
171 BK = B( K, J ) / AKM1K
172 B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
173 B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
174 20 CONTINUE
175 K = K - 2
176 END IF
177 *
178 GO TO 10
179 30 CONTINUE
180 *
181 * Next solve U**T *X = B, overwriting B with X.
182 *
183 * K is the main loop index, increasing from 1 to N in steps of
184 * 1 or 2, depending on the size of the diagonal blocks.
185 *
186 K = 1
187 40 CONTINUE
188 *
189 * If K > N, exit from loop.
190 *
191 IF( K.GT.N )
192 $ GO TO 50
193 *
194 IF( IPIV( K ).GT.0 ) THEN
195 *
196 * 1 x 1 diagonal block
197 *
198 * Multiply by inv(U**T(K)), where U(K) is the transformation
199 * stored in column K of A.
200 *
201 CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
202 $ 1, ONE, B( K, 1 ), LDB )
203 *
204 * Interchange rows K and IPIV(K).
205 *
206 KP = IPIV( K )
207 IF( KP.NE.K )
208 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
209 K = K + 1
210 ELSE
211 *
212 * 2 x 2 diagonal block
213 *
214 * Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
215 * stored in columns K and K+1 of A.
216 *
217 CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
218 $ 1, ONE, B( K, 1 ), LDB )
219 CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
220 $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
221 *
222 * Interchange rows K and -IPIV(K).
223 *
224 KP = -IPIV( K )
225 IF( KP.NE.K )
226 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
227 K = K + 2
228 END IF
229 *
230 GO TO 40
231 50 CONTINUE
232 *
233 ELSE
234 *
235 * Solve A*X = B, where A = L*D*L**T.
236 *
237 * First solve L*D*X = B, overwriting B with X.
238 *
239 * K is the main loop index, increasing from 1 to N in steps of
240 * 1 or 2, depending on the size of the diagonal blocks.
241 *
242 K = 1
243 60 CONTINUE
244 *
245 * If K > N, exit from loop.
246 *
247 IF( K.GT.N )
248 $ GO TO 80
249 *
250 IF( IPIV( K ).GT.0 ) THEN
251 *
252 * 1 x 1 diagonal block
253 *
254 * Interchange rows K and IPIV(K).
255 *
256 KP = IPIV( K )
257 IF( KP.NE.K )
258 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
259 *
260 * Multiply by inv(L(K)), where L(K) is the transformation
261 * stored in column K of A.
262 *
263 IF( K.LT.N )
264 $ CALL DGER( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
265 $ LDB, B( K+1, 1 ), LDB )
266 *
267 * Multiply by the inverse of the diagonal block.
268 *
269 CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
270 K = K + 1
271 ELSE
272 *
273 * 2 x 2 diagonal block
274 *
275 * Interchange rows K+1 and -IPIV(K).
276 *
277 KP = -IPIV( K )
278 IF( KP.NE.K+1 )
279 $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
280 *
281 * Multiply by inv(L(K)), where L(K) is the transformation
282 * stored in columns K and K+1 of A.
283 *
284 IF( K.LT.N-1 ) THEN
285 CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
286 $ LDB, B( K+2, 1 ), LDB )
287 CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
288 $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
289 END IF
290 *
291 * Multiply by the inverse of the diagonal block.
292 *
293 AKM1K = A( K+1, K )
294 AKM1 = A( K, K ) / AKM1K
295 AK = A( K+1, K+1 ) / AKM1K
296 DENOM = AKM1*AK - ONE
297 DO 70 J = 1, NRHS
298 BKM1 = B( K, J ) / AKM1K
299 BK = B( K+1, J ) / AKM1K
300 B( K, J ) = ( AK*BKM1-BK ) / DENOM
301 B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
302 70 CONTINUE
303 K = K + 2
304 END IF
305 *
306 GO TO 60
307 80 CONTINUE
308 *
309 * Next solve L**T *X = B, overwriting B with X.
310 *
311 * K is the main loop index, decreasing from N to 1 in steps of
312 * 1 or 2, depending on the size of the diagonal blocks.
313 *
314 K = N
315 90 CONTINUE
316 *
317 * If K < 1, exit from loop.
318 *
319 IF( K.LT.1 )
320 $ GO TO 100
321 *
322 IF( IPIV( K ).GT.0 ) THEN
323 *
324 * 1 x 1 diagonal block
325 *
326 * Multiply by inv(L**T(K)), where L(K) is the transformation
327 * stored in column K of A.
328 *
329 IF( K.LT.N )
330 $ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
331 $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
332 *
333 * Interchange rows K and IPIV(K).
334 *
335 KP = IPIV( K )
336 IF( KP.NE.K )
337 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
338 K = K - 1
339 ELSE
340 *
341 * 2 x 2 diagonal block
342 *
343 * Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
344 * stored in columns K-1 and K of A.
345 *
346 IF( K.LT.N ) THEN
347 CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
348 $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
349 CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
350 $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
351 $ LDB )
352 END IF
353 *
354 * Interchange rows K and -IPIV(K).
355 *
356 KP = -IPIV( K )
357 IF( KP.NE.K )
358 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
359 K = K - 2
360 END IF
361 *
362 GO TO 90
363 100 CONTINUE
364 END IF
365 *
366 RETURN
367 *
368 * End of DSYTRS
369 *
370 END
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INFO, LDA, LDB, N, NRHS
11 * ..
12 * .. Array Arguments ..
13 INTEGER IPIV( * )
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DSYTRS solves a system of linear equations A*X = B with a real
21 * symmetric matrix A using the factorization A = U*D*U**T or
22 * A = L*D*L**T computed by DSYTRF.
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**T;
31 * = 'L': Lower triangular, form is A = L*D*L**T.
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) DOUBLE PRECISION 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 DSYTRF.
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 DSYTRF.
50 *
51 * B (input/output) DOUBLE PRECISION 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 DOUBLE PRECISION ONE
66 PARAMETER ( ONE = 1.0D+0 )
67 * ..
68 * .. Local Scalars ..
69 LOGICAL UPPER
70 INTEGER J, K, KP
71 DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
72 * ..
73 * .. External Functions ..
74 LOGICAL LSAME
75 EXTERNAL LSAME
76 * ..
77 * .. External Subroutines ..
78 EXTERNAL DGEMV, DGER, DSCAL, DSWAP, XERBLA
79 * ..
80 * .. Intrinsic Functions ..
81 INTRINSIC MAX
82 * ..
83 * .. Executable Statements ..
84 *
85 INFO = 0
86 UPPER = LSAME( UPLO, 'U' )
87 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
88 INFO = -1
89 ELSE IF( N.LT.0 ) THEN
90 INFO = -2
91 ELSE IF( NRHS.LT.0 ) THEN
92 INFO = -3
93 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
94 INFO = -5
95 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
96 INFO = -8
97 END IF
98 IF( INFO.NE.0 ) THEN
99 CALL XERBLA( 'DSYTRS', -INFO )
100 RETURN
101 END IF
102 *
103 * Quick return if possible
104 *
105 IF( N.EQ.0 .OR. NRHS.EQ.0 )
106 $ RETURN
107 *
108 IF( UPPER ) THEN
109 *
110 * Solve A*X = B, where A = U*D*U**T.
111 *
112 * First solve U*D*X = B, overwriting B with X.
113 *
114 * K is the main loop index, decreasing from N to 1 in steps of
115 * 1 or 2, depending on the size of the diagonal blocks.
116 *
117 K = N
118 10 CONTINUE
119 *
120 * If K < 1, exit from loop.
121 *
122 IF( K.LT.1 )
123 $ GO TO 30
124 *
125 IF( IPIV( K ).GT.0 ) THEN
126 *
127 * 1 x 1 diagonal block
128 *
129 * Interchange rows K and IPIV(K).
130 *
131 KP = IPIV( K )
132 IF( KP.NE.K )
133 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
134 *
135 * Multiply by inv(U(K)), where U(K) is the transformation
136 * stored in column K of A.
137 *
138 CALL DGER( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
139 $ B( 1, 1 ), LDB )
140 *
141 * Multiply by the inverse of the diagonal block.
142 *
143 CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
144 K = K - 1
145 ELSE
146 *
147 * 2 x 2 diagonal block
148 *
149 * Interchange rows K-1 and -IPIV(K).
150 *
151 KP = -IPIV( K )
152 IF( KP.NE.K-1 )
153 $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
154 *
155 * Multiply by inv(U(K)), where U(K) is the transformation
156 * stored in columns K-1 and K of A.
157 *
158 CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
159 $ B( 1, 1 ), LDB )
160 CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
161 $ LDB, B( 1, 1 ), LDB )
162 *
163 * Multiply by the inverse of the diagonal block.
164 *
165 AKM1K = A( K-1, K )
166 AKM1 = A( K-1, K-1 ) / AKM1K
167 AK = A( K, K ) / AKM1K
168 DENOM = AKM1*AK - ONE
169 DO 20 J = 1, NRHS
170 BKM1 = B( K-1, J ) / AKM1K
171 BK = B( K, J ) / AKM1K
172 B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
173 B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
174 20 CONTINUE
175 K = K - 2
176 END IF
177 *
178 GO TO 10
179 30 CONTINUE
180 *
181 * Next solve U**T *X = B, overwriting B with X.
182 *
183 * K is the main loop index, increasing from 1 to N in steps of
184 * 1 or 2, depending on the size of the diagonal blocks.
185 *
186 K = 1
187 40 CONTINUE
188 *
189 * If K > N, exit from loop.
190 *
191 IF( K.GT.N )
192 $ GO TO 50
193 *
194 IF( IPIV( K ).GT.0 ) THEN
195 *
196 * 1 x 1 diagonal block
197 *
198 * Multiply by inv(U**T(K)), where U(K) is the transformation
199 * stored in column K of A.
200 *
201 CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
202 $ 1, ONE, B( K, 1 ), LDB )
203 *
204 * Interchange rows K and IPIV(K).
205 *
206 KP = IPIV( K )
207 IF( KP.NE.K )
208 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
209 K = K + 1
210 ELSE
211 *
212 * 2 x 2 diagonal block
213 *
214 * Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
215 * stored in columns K and K+1 of A.
216 *
217 CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
218 $ 1, ONE, B( K, 1 ), LDB )
219 CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
220 $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
221 *
222 * Interchange rows K and -IPIV(K).
223 *
224 KP = -IPIV( K )
225 IF( KP.NE.K )
226 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
227 K = K + 2
228 END IF
229 *
230 GO TO 40
231 50 CONTINUE
232 *
233 ELSE
234 *
235 * Solve A*X = B, where A = L*D*L**T.
236 *
237 * First solve L*D*X = B, overwriting B with X.
238 *
239 * K is the main loop index, increasing from 1 to N in steps of
240 * 1 or 2, depending on the size of the diagonal blocks.
241 *
242 K = 1
243 60 CONTINUE
244 *
245 * If K > N, exit from loop.
246 *
247 IF( K.GT.N )
248 $ GO TO 80
249 *
250 IF( IPIV( K ).GT.0 ) THEN
251 *
252 * 1 x 1 diagonal block
253 *
254 * Interchange rows K and IPIV(K).
255 *
256 KP = IPIV( K )
257 IF( KP.NE.K )
258 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
259 *
260 * Multiply by inv(L(K)), where L(K) is the transformation
261 * stored in column K of A.
262 *
263 IF( K.LT.N )
264 $ CALL DGER( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
265 $ LDB, B( K+1, 1 ), LDB )
266 *
267 * Multiply by the inverse of the diagonal block.
268 *
269 CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
270 K = K + 1
271 ELSE
272 *
273 * 2 x 2 diagonal block
274 *
275 * Interchange rows K+1 and -IPIV(K).
276 *
277 KP = -IPIV( K )
278 IF( KP.NE.K+1 )
279 $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
280 *
281 * Multiply by inv(L(K)), where L(K) is the transformation
282 * stored in columns K and K+1 of A.
283 *
284 IF( K.LT.N-1 ) THEN
285 CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
286 $ LDB, B( K+2, 1 ), LDB )
287 CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
288 $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
289 END IF
290 *
291 * Multiply by the inverse of the diagonal block.
292 *
293 AKM1K = A( K+1, K )
294 AKM1 = A( K, K ) / AKM1K
295 AK = A( K+1, K+1 ) / AKM1K
296 DENOM = AKM1*AK - ONE
297 DO 70 J = 1, NRHS
298 BKM1 = B( K, J ) / AKM1K
299 BK = B( K+1, J ) / AKM1K
300 B( K, J ) = ( AK*BKM1-BK ) / DENOM
301 B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
302 70 CONTINUE
303 K = K + 2
304 END IF
305 *
306 GO TO 60
307 80 CONTINUE
308 *
309 * Next solve L**T *X = B, overwriting B with X.
310 *
311 * K is the main loop index, decreasing from N to 1 in steps of
312 * 1 or 2, depending on the size of the diagonal blocks.
313 *
314 K = N
315 90 CONTINUE
316 *
317 * If K < 1, exit from loop.
318 *
319 IF( K.LT.1 )
320 $ GO TO 100
321 *
322 IF( IPIV( K ).GT.0 ) THEN
323 *
324 * 1 x 1 diagonal block
325 *
326 * Multiply by inv(L**T(K)), where L(K) is the transformation
327 * stored in column K of A.
328 *
329 IF( K.LT.N )
330 $ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
331 $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
332 *
333 * Interchange rows K and IPIV(K).
334 *
335 KP = IPIV( K )
336 IF( KP.NE.K )
337 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
338 K = K - 1
339 ELSE
340 *
341 * 2 x 2 diagonal block
342 *
343 * Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
344 * stored in columns K-1 and K of A.
345 *
346 IF( K.LT.N ) THEN
347 CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
348 $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
349 CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
350 $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
351 $ LDB )
352 END IF
353 *
354 * Interchange rows K and -IPIV(K).
355 *
356 KP = -IPIV( K )
357 IF( KP.NE.K )
358 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
359 K = K - 2
360 END IF
361 *
362 GO TO 90
363 100 CONTINUE
364 END IF
365 *
366 RETURN
367 *
368 * End of DSYTRS
369 *
370 END