LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
chetrs2.f
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1 *> \brief \b CHETRS2
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CHETRS2( 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 * COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CHETRS2 solves a system of linear equations A*X = B with a complex
40 *> Hermitian matrix A using the factorization A = U*D*U**H or
41 *> A = L*D*L**H computed by CHETRF and converted by CSYCONV.
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**H;
53 *> = 'L': Lower triangular, form is A = L*D*L**H.
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] A
70 *> \verbatim
71 *> A is COMPLEX 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 CHETRF.
74 *> \endverbatim
75 *>
76 *> \param[in] LDA
77 *> \verbatim
78 *> LDA is INTEGER
79 *> The leading dimension of the array A. LDA >= max(1,N).
80 *> \endverbatim
81 *>
82 *> \param[in] IPIV
83 *> \verbatim
84 *> IPIV is INTEGER array, dimension (N)
85 *> Details of the interchanges and the block structure of D
86 *> as determined by CHETRF.
87 *> \endverbatim
88 *>
89 *> \param[in,out] B
90 *> \verbatim
91 *> B is COMPLEX array, dimension (LDB,NRHS)
92 *> On entry, the right hand side matrix B.
93 *> On exit, the solution matrix X.
94 *> \endverbatim
95 *>
96 *> \param[in] LDB
97 *> \verbatim
98 *> LDB is INTEGER
99 *> The leading dimension of the array B. LDB >= max(1,N).
100 *> \endverbatim
101 *>
102 *> \param[out] WORK
103 *> \verbatim
104 *> WORK is COMPLEX array, dimension (N)
105 *> \endverbatim
106 *>
107 *> \param[out] INFO
108 *> \verbatim
109 *> INFO is INTEGER
110 *> = 0: successful exit
111 *> < 0: if INFO = -i, the i-th argument had an illegal value
112 *> \endverbatim
113 *
114 * Authors:
115 * ========
116 *
117 *> \author Univ. of Tennessee
118 *> \author Univ. of California Berkeley
119 *> \author Univ. of Colorado Denver
120 *> \author NAG Ltd.
121 *
122 *> \ingroup complexHEcomputational
123 *
124 * =====================================================================
125  SUBROUTINE chetrs2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
126  $ WORK, INFO )
127 *
128 * -- LAPACK computational routine --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 *
132 * .. Scalar Arguments ..
133  CHARACTER UPLO
134  INTEGER INFO, LDA, LDB, N, NRHS
135 * ..
136 * .. Array Arguments ..
137  INTEGER IPIV( * )
138  COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  COMPLEX ONE
145  parameter( one = (1.0e+0,0.0e+0) )
146 * ..
147 * .. Local Scalars ..
148  LOGICAL UPPER
149  INTEGER I, IINFO, J, K, KP
150  REAL S
151  COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM
152 * ..
153 * .. External Functions ..
154  LOGICAL LSAME
155  EXTERNAL lsame
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL csscal, csyconv, cswap, ctrsm, xerbla
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC conjg, max, real
162 * ..
163 * .. Executable Statements ..
164 *
165  info = 0
166  upper = lsame( uplo, 'U' )
167  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
168  info = -1
169  ELSE IF( n.LT.0 ) THEN
170  info = -2
171  ELSE IF( nrhs.LT.0 ) THEN
172  info = -3
173  ELSE IF( lda.LT.max( 1, n ) ) THEN
174  info = -5
175  ELSE IF( ldb.LT.max( 1, n ) ) THEN
176  info = -8
177  END IF
178  IF( info.NE.0 ) THEN
179  CALL xerbla( 'CHETRS2', -info )
180  RETURN
181  END IF
182 *
183 * Quick return if possible
184 *
185  IF( n.EQ.0 .OR. nrhs.EQ.0 )
186  $ RETURN
187 *
188 * Convert A
189 *
190  CALL csyconv( uplo, 'C', n, a, lda, ipiv, work, iinfo )
191 *
192  IF( upper ) THEN
193 *
194 * Solve A*X = B, where A = U*D*U**H.
195 *
196 * P**T * B
197  k=n
198  DO WHILE ( k .GE. 1 )
199  IF( ipiv( k ).GT.0 ) THEN
200 * 1 x 1 diagonal block
201 * Interchange rows K and IPIV(K).
202  kp = ipiv( k )
203  IF( kp.NE.k )
204  $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
205  k=k-1
206  ELSE
207 * 2 x 2 diagonal block
208 * Interchange rows K-1 and -IPIV(K).
209  kp = -ipiv( k )
210  IF( kp.EQ.-ipiv( k-1 ) )
211  $ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
212  k=k-2
213  END IF
214  END DO
215 *
216 * Compute (U \P**T * B) -> B [ (U \P**T * B) ]
217 *
218  CALL ctrsm('L','U','N','U',n,nrhs,one,a,lda,b,ldb)
219 *
220 * Compute D \ B -> B [ D \ (U \P**T * B) ]
221 *
222  i=n
223  DO WHILE ( i .GE. 1 )
224  IF( ipiv(i) .GT. 0 ) THEN
225  s = real( one ) / real( a( i, i ) )
226  CALL csscal( nrhs, s, b( i, 1 ), ldb )
227  ELSEIF ( i .GT. 1) THEN
228  IF ( ipiv(i-1) .EQ. ipiv(i) ) THEN
229  akm1k = work(i)
230  akm1 = a( i-1, i-1 ) / akm1k
231  ak = a( i, i ) / conjg( akm1k )
232  denom = akm1*ak - one
233  DO 15 j = 1, nrhs
234  bkm1 = b( i-1, j ) / akm1k
235  bk = b( i, j ) / conjg( akm1k )
236  b( i-1, j ) = ( ak*bkm1-bk ) / denom
237  b( i, j ) = ( akm1*bk-bkm1 ) / denom
238  15 CONTINUE
239  i = i - 1
240  ENDIF
241  ENDIF
242  i = i - 1
243  END DO
244 *
245 * Compute (U**H \ B) -> B [ U**H \ (D \ (U \P**T * B) ) ]
246 *
247  CALL ctrsm('L','U','C','U',n,nrhs,one,a,lda,b,ldb)
248 *
249 * P * B [ P * (U**H \ (D \ (U \P**T * B) )) ]
250 *
251  k=1
252  DO WHILE ( k .LE. n )
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 cswap( 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 .LT. n .AND. kp.EQ.-ipiv( k+1 ) )
265  $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
266  k=k+2
267  ENDIF
268  END DO
269 *
270  ELSE
271 *
272 * Solve A*X = B, where A = L*D*L**H.
273 *
274 * P**T * B
275  k=1
276  DO WHILE ( k .LE. n )
277  IF( ipiv( k ).GT.0 ) THEN
278 * 1 x 1 diagonal block
279 * Interchange rows K and IPIV(K).
280  kp = ipiv( k )
281  IF( kp.NE.k )
282  $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
283  k=k+1
284  ELSE
285 * 2 x 2 diagonal block
286 * Interchange rows K and -IPIV(K+1).
287  kp = -ipiv( k+1 )
288  IF( kp.EQ.-ipiv( k ) )
289  $ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
290  k=k+2
291  ENDIF
292  END DO
293 *
294 * Compute (L \P**T * B) -> B [ (L \P**T * B) ]
295 *
296  CALL ctrsm('L','L','N','U',n,nrhs,one,a,lda,b,ldb)
297 *
298 * Compute D \ B -> B [ D \ (L \P**T * B) ]
299 *
300  i=1
301  DO WHILE ( i .LE. n )
302  IF( ipiv(i) .GT. 0 ) THEN
303  s = real( one ) / real( a( i, i ) )
304  CALL csscal( nrhs, s, b( i, 1 ), ldb )
305  ELSE
306  akm1k = work(i)
307  akm1 = a( i, i ) / conjg( akm1k )
308  ak = a( i+1, i+1 ) / akm1k
309  denom = akm1*ak - one
310  DO 25 j = 1, nrhs
311  bkm1 = b( i, j ) / conjg( akm1k )
312  bk = b( i+1, j ) / akm1k
313  b( i, j ) = ( ak*bkm1-bk ) / denom
314  b( i+1, j ) = ( akm1*bk-bkm1 ) / denom
315  25 CONTINUE
316  i = i + 1
317  ENDIF
318  i = i + 1
319  END DO
320 *
321 * Compute (L**H \ B) -> B [ L**H \ (D \ (L \P**T * B) ) ]
322 *
323  CALL ctrsm('L','L','C','U',n,nrhs,one,a,lda,b,ldb)
324 *
325 * P * B [ P * (L**H \ (D \ (L \P**T * B) )) ]
326 *
327  k=n
328  DO WHILE ( k .GE. 1 )
329  IF( ipiv( k ).GT.0 ) THEN
330 * 1 x 1 diagonal block
331 * Interchange rows K and IPIV(K).
332  kp = ipiv( k )
333  IF( kp.NE.k )
334  $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
335  k=k-1
336  ELSE
337 * 2 x 2 diagonal block
338 * Interchange rows K-1 and -IPIV(K).
339  kp = -ipiv( k )
340  IF( k.GT.1 .AND. kp.EQ.-ipiv( k-1 ) )
341  $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
342  k=k-2
343  ENDIF
344  END DO
345 *
346  END IF
347 *
348 * Revert A
349 *
350  CALL csyconv( uplo, 'R', n, a, lda, ipiv, work, iinfo )
351 *
352  RETURN
353 *
354 * End of CHETRS2
355 *
356  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine cswap(N, CX, INCX, CY, INCY)
CSWAP
Definition: cswap.f:81
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine chetrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
CHETRS2
Definition: chetrs2.f:127
subroutine csyconv(UPLO, WAY, N, A, LDA, IPIV, E, INFO)
CSYCONV
Definition: csyconv.f:114