LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zhetrs2()

subroutine zhetrs2 ( character  UPLO,
integer  N,
integer  NRHS,
complex*16, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( * )  WORK,
integer  INFO 
)

ZHETRS2

Download ZHETRS2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZHETRS2 solves a system of linear equations A*X = B with a complex
 Hermitian matrix A using the factorization A = U*D*U**H or
 A = L*D*L**H computed by ZHETRF and converted by ZSYCONV.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are stored
          as an upper or lower triangular matrix.
          = 'U':  Upper triangular, form is A = U*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*L**H.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZHETRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZHETRF.
[in,out]B
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is COMPLEX*16 array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 125 of file zhetrs2.f.

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*16 A( LDA, * ), B( LDB, * ), WORK( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  COMPLEX*16 ONE
145  parameter( one = (1.0d+0,0.0d+0) )
146 * ..
147 * .. Local Scalars ..
148  LOGICAL UPPER
149  INTEGER I, IINFO, J, K, KP
150  DOUBLE PRECISION S
151  COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
152 * ..
153 * .. External Functions ..
154  LOGICAL LSAME
155  EXTERNAL lsame
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL zdscal, zsyconv, zswap, ztrsm, xerbla
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC dble, dconjg, max
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( 'ZHETRS2', -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 zsyconv( 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 zswap( 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 zswap( 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 ztrsm('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 = dble( one ) / dble( a( i, i ) )
226  CALL zdscal( 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 ) / dconjg( akm1k )
232  denom = akm1*ak - one
233  DO 15 j = 1, nrhs
234  bkm1 = b( i-1, j ) / akm1k
235  bk = b( i, j ) / dconjg( 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 ztrsm('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 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 .LT. n .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  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 zswap( 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 zswap( 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 ztrsm('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 = dble( one ) / dble( a( i, i ) )
304  CALL zdscal( nrhs, s, b( i, 1 ), ldb )
305  ELSE
306  akm1k = work(i)
307  akm1 = a( i, i ) / dconjg( 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 ) / dconjg( 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 ztrsm('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 zswap( 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 zswap( 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 zsyconv( uplo, 'R', n, a, lda, ipiv, work, iinfo )
351 *
352  RETURN
353 *
354 * End of ZHETRS2
355 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine zsyconv(UPLO, WAY, N, A, LDA, IPIV, E, INFO)
ZSYCONV
Definition: zsyconv.f:114
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