LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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ssytrs2.f
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1*> \brief \b SSYTRS2
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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15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
22* WORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, LDA, LDB, N, NRHS
27* ..
28* .. Array Arguments ..
29* INTEGER IPIV( * )
30* REAL A( LDA, * ), B( LDB, * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SSYTRS2 solves a system of linear equations A*X = B with a real
40*> symmetric matrix A using the factorization A = U*D*U**T or
41*> A = L*D*L**T computed by SSYTRF and converted by SSYCONV.
42*> \endverbatim
43*
44* Arguments:
45* ==========
46*
47*> \param[in] UPLO
48*> \verbatim
49*> UPLO is CHARACTER*1
50*> Specifies whether the details of the factorization are stored
51*> as an upper or lower triangular matrix.
52*> = 'U': Upper triangular, form is A = U*D*U**T;
53*> = 'L': Lower triangular, form is A = L*D*L**T.
54*> \endverbatim
55*>
56*> \param[in] N
57*> \verbatim
58*> N is INTEGER
59*> The order of the matrix A. N >= 0.
60*> \endverbatim
61*>
62*> \param[in] NRHS
63*> \verbatim
64*> NRHS is INTEGER
65*> The number of right hand sides, i.e., the number of columns
66*> of the matrix B. NRHS >= 0.
67*> \endverbatim
68*>
69*> \param[in,out] A
70*> \verbatim
71*> A is REAL array, dimension (LDA,N)
72*> The block diagonal matrix D and the multipliers used to
73*> obtain the factor U or L as computed by SSYTRF.
74*> Note that A is input / output. This might be counter-intuitive,
75*> and one may think that A is input only. A is input / output. This
76*> is because, at the start of the subroutine, we permute A in a
77*> "better" form and then we permute A back to its original form at
78*> the end.
79*> \endverbatim
80*>
81*> \param[in] LDA
82*> \verbatim
83*> LDA is INTEGER
84*> The leading dimension of the array A. LDA >= max(1,N).
85*> \endverbatim
86*>
87*> \param[in] IPIV
88*> \verbatim
89*> IPIV is INTEGER array, dimension (N)
90*> Details of the interchanges and the block structure of D
91*> as determined by SSYTRF.
92*> \endverbatim
93*>
94*> \param[in,out] B
95*> \verbatim
96*> B is REAL array, dimension (LDB,NRHS)
97*> On entry, the right hand side matrix B.
98*> On exit, the solution matrix X.
99*> \endverbatim
100*>
101*> \param[in] LDB
102*> \verbatim
103*> LDB is INTEGER
104*> The leading dimension of the array B. LDB >= max(1,N).
105*> \endverbatim
106*>
107*> \param[out] WORK
108*> \verbatim
109*> WORK is REAL array, dimension (N)
110*> \endverbatim
111*>
112*> \param[out] INFO
113*> \verbatim
114*> INFO is INTEGER
115*> = 0: successful exit
116*> < 0: if INFO = -i, the i-th argument had an illegal value
117*> \endverbatim
118*
119* Authors:
120* ========
121*
122*> \author Univ. of Tennessee
123*> \author Univ. of California Berkeley
124*> \author Univ. of Colorado Denver
125*> \author NAG Ltd.
126*
127*> \ingroup hetrs2
128*
129* =====================================================================
130 SUBROUTINE ssytrs2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
131 \$ WORK, INFO )
132*
133* -- LAPACK computational routine --
134* -- LAPACK is a software package provided by Univ. of Tennessee, --
135* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136*
137* .. Scalar Arguments ..
138 CHARACTER UPLO
139 INTEGER INFO, LDA, LDB, N, NRHS
140* ..
141* .. Array Arguments ..
142 INTEGER IPIV( * )
143 REAL A( LDA, * ), B( LDB, * ), WORK( * )
144* ..
145*
146* =====================================================================
147*
148* .. Parameters ..
149 REAL ONE
150 parameter( one = 1.0e+0 )
151* ..
152* .. Local Scalars ..
153 LOGICAL UPPER
154 INTEGER I, IINFO, J, K, KP
155 REAL AK, AKM1, AKM1K, BK, BKM1, DENOM
156* ..
157* .. External Functions ..
158 LOGICAL LSAME
159 EXTERNAL lsame
160* ..
161* .. External Subroutines ..
162 EXTERNAL sscal, ssyconv, sswap, strsm, xerbla
163* ..
164* .. Intrinsic Functions ..
165 INTRINSIC max
166* ..
167* .. Executable Statements ..
168*
169 info = 0
170 upper = lsame( uplo, 'U' )
171 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
172 info = -1
173 ELSE IF( n.LT.0 ) THEN
174 info = -2
175 ELSE IF( nrhs.LT.0 ) THEN
176 info = -3
177 ELSE IF( lda.LT.max( 1, n ) ) THEN
178 info = -5
179 ELSE IF( ldb.LT.max( 1, n ) ) THEN
180 info = -8
181 END IF
182 IF( info.NE.0 ) THEN
183 CALL xerbla( 'SSYTRS2', -info )
184 RETURN
185 END IF
186*
187* Quick return if possible
188*
189 IF( n.EQ.0 .OR. nrhs.EQ.0 )
190 \$ RETURN
191*
192* Convert A
193*
194 CALL ssyconv( uplo, 'C', n, a, lda, ipiv, work, iinfo )
195*
196 IF( upper ) THEN
197*
198* Solve A*X = B, where A = U*D*U**T.
199*
200* P**T * B
201 k=n
202 DO WHILE ( k .GE. 1 )
203 IF( ipiv( k ).GT.0 ) THEN
204* 1 x 1 diagonal block
205* Interchange rows K and IPIV(K).
206 kp = ipiv( k )
207 IF( kp.NE.k )
208 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
209 k=k-1
210 ELSE
211* 2 x 2 diagonal block
212* Interchange rows K-1 and -IPIV(K).
213 kp = -ipiv( k )
214 IF( kp.EQ.-ipiv( k-1 ) )
215 \$ CALL sswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
216 k=k-2
217 END IF
218 END DO
219*
220* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
221*
222 CALL strsm('L','U','N','U',n,nrhs,one,a,lda,b,ldb)
223*
224* Compute D \ B -> B [ D \ (U \P**T * B) ]
225*
226 i=n
227 DO WHILE ( i .GE. 1 )
228 IF( ipiv(i) .GT. 0 ) THEN
229 CALL sscal( nrhs, one / a( i, i ), b( i, 1 ), ldb )
230 ELSEIF ( i .GT. 1) THEN
231 IF ( ipiv(i-1) .EQ. ipiv(i) ) THEN
232 akm1k = work(i)
233 akm1 = a( i-1, i-1 ) / akm1k
234 ak = a( i, i ) / akm1k
235 denom = akm1*ak - one
236 DO 15 j = 1, nrhs
237 bkm1 = b( i-1, j ) / akm1k
238 bk = b( i, j ) / akm1k
239 b( i-1, j ) = ( ak*bkm1-bk ) / denom
240 b( i, j ) = ( akm1*bk-bkm1 ) / denom
241 15 CONTINUE
242 i = i - 1
243 ENDIF
244 ENDIF
245 i = i - 1
246 END DO
247*
248* Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ]
249*
250 CALL strsm('L','U','T','U',n,nrhs,one,a,lda,b,ldb)
251*
252* P * B [ P * (U**T \ (D \ (U \P**T * B) )) ]
253*
254 k=1
255 DO WHILE ( k .LE. n )
256 IF( ipiv( k ).GT.0 ) THEN
257* 1 x 1 diagonal block
258* Interchange rows K and IPIV(K).
259 kp = ipiv( k )
260 IF( kp.NE.k )
261 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
262 k=k+1
263 ELSE
264* 2 x 2 diagonal block
265* Interchange rows K-1 and -IPIV(K).
266 kp = -ipiv( k )
267 IF( k .LT. n .AND. kp.EQ.-ipiv( k+1 ) )
268 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
269 k=k+2
270 ENDIF
271 END DO
272*
273 ELSE
274*
275* Solve A*X = B, where A = L*D*L**T.
276*
277* P**T * B
278 k=1
279 DO WHILE ( k .LE. n )
280 IF( ipiv( k ).GT.0 ) THEN
281* 1 x 1 diagonal block
282* Interchange rows K and IPIV(K).
283 kp = ipiv( k )
284 IF( kp.NE.k )
285 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
286 k=k+1
287 ELSE
288* 2 x 2 diagonal block
289* Interchange rows K and -IPIV(K+1).
290 kp = -ipiv( k+1 )
291 IF( kp.EQ.-ipiv( k ) )
292 \$ CALL sswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
293 k=k+2
294 ENDIF
295 END DO
296*
297* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
298*
299 CALL strsm('L','L','N','U',n,nrhs,one,a,lda,b,ldb)
300*
301* Compute D \ B -> B [ D \ (L \P**T * B) ]
302*
303 i=1
304 DO WHILE ( i .LE. n )
305 IF( ipiv(i) .GT. 0 ) THEN
306 CALL sscal( nrhs, one / a( i, i ), b( i, 1 ), ldb )
307 ELSE
308 akm1k = work(i)
309 akm1 = a( i, i ) / akm1k
310 ak = a( i+1, i+1 ) / akm1k
311 denom = akm1*ak - one
312 DO 25 j = 1, nrhs
313 bkm1 = b( i, j ) / akm1k
314 bk = b( i+1, j ) / akm1k
315 b( i, j ) = ( ak*bkm1-bk ) / denom
316 b( i+1, j ) = ( akm1*bk-bkm1 ) / denom
317 25 CONTINUE
318 i = i + 1
319 ENDIF
320 i = i + 1
321 END DO
322*
323* Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ]
324*
325 CALL strsm('L','L','T','U',n,nrhs,one,a,lda,b,ldb)
326*
327* P * B [ P * (L**T \ (D \ (L \P**T * B) )) ]
328*
329 k=n
330 DO WHILE ( k .GE. 1 )
331 IF( ipiv( k ).GT.0 ) THEN
332* 1 x 1 diagonal block
333* Interchange rows K and IPIV(K).
334 kp = ipiv( k )
335 IF( kp.NE.k )
336 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
337 k=k-1
338 ELSE
339* 2 x 2 diagonal block
340* Interchange rows K-1 and -IPIV(K).
341 kp = -ipiv( k )
342 IF( k.GT.1 .AND. kp.EQ.-ipiv( k-1 ) )
343 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
344 k=k-2
345 ENDIF
346 END DO
347*
348 END IF
349*
350* Revert A
351*
352 CALL ssyconv( uplo, 'R', n, a, lda, ipiv, work, iinfo )
353*
354 RETURN
355*
356* End of SSYTRS2
357*
358 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssytrs2(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)
SSYTRS2
Definition ssytrs2.f:132
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
subroutine sswap(n, sx, incx, sy, incy)
SSWAP
Definition sswap.f:82
subroutine ssyconv(uplo, way, n, a, lda, ipiv, e, info)
SSYCONV
Definition ssyconv.f:114
subroutine strsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
STRSM
Definition strsm.f:181