LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ zgbtrs()

subroutine zgbtrs ( character  trans,
integer  n,
integer  kl,
integer  ku,
integer  nrhs,
complex*16, dimension( ldab, * )  ab,
integer  ldab,
integer, dimension( * )  ipiv,
complex*16, dimension( ldb, * )  b,
integer  ldb,
integer  info 
)

ZGBTRS

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

Purpose:
 ZGBTRS solves a system of linear equations
    A * X = B,  A**T * X = B,  or  A**H * X = B
 with a general band matrix A using the LU factorization computed
 by ZGBTRF.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose)
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 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]AB
          AB is COMPLEX*16 array, dimension (LDAB,N)
          Details of the LU factorization of the band matrix A, as
          computed by ZGBTRF.  U is stored as an upper triangular band
          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
          the multipliers used during the factorization are stored in
          rows KL+KU+2 to 2*KL+KU+1.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= N, row i of the matrix was
          interchanged with row IPIV(i).
[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]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 136 of file zgbtrs.f.

138*
139* -- LAPACK computational routine --
140* -- LAPACK is a software package provided by Univ. of Tennessee, --
141* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142*
143* .. Scalar Arguments ..
144 CHARACTER TRANS
145 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
146* ..
147* .. Array Arguments ..
148 INTEGER IPIV( * )
149 COMPLEX*16 AB( LDAB, * ), B( LDB, * )
150* ..
151*
152* =====================================================================
153*
154* .. Parameters ..
155 COMPLEX*16 ONE
156 parameter( one = ( 1.0d+0, 0.0d+0 ) )
157* ..
158* .. Local Scalars ..
159 LOGICAL LNOTI, NOTRAN
160 INTEGER I, J, KD, L, LM
161* ..
162* .. External Functions ..
163 LOGICAL LSAME
164 EXTERNAL lsame
165* ..
166* .. External Subroutines ..
167 EXTERNAL xerbla, zgemv, zgeru, zlacgv, zswap, ztbsv
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC max, min
171* ..
172* .. Executable Statements ..
173*
174* Test the input parameters.
175*
176 info = 0
177 notran = lsame( trans, 'N' )
178 IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
179 $ lsame( trans, 'C' ) ) THEN
180 info = -1
181 ELSE IF( n.LT.0 ) THEN
182 info = -2
183 ELSE IF( kl.LT.0 ) THEN
184 info = -3
185 ELSE IF( ku.LT.0 ) THEN
186 info = -4
187 ELSE IF( nrhs.LT.0 ) THEN
188 info = -5
189 ELSE IF( ldab.LT.( 2*kl+ku+1 ) ) THEN
190 info = -7
191 ELSE IF( ldb.LT.max( 1, n ) ) THEN
192 info = -10
193 END IF
194 IF( info.NE.0 ) THEN
195 CALL xerbla( 'ZGBTRS', -info )
196 RETURN
197 END IF
198*
199* Quick return if possible
200*
201 IF( n.EQ.0 .OR. nrhs.EQ.0 )
202 $ RETURN
203*
204 kd = ku + kl + 1
205 lnoti = kl.GT.0
206*
207 IF( notran ) THEN
208*
209* Solve A*X = B.
210*
211* Solve L*X = B, overwriting B with X.
212*
213* L is represented as a product of permutations and unit lower
214* triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
215* where each transformation L(i) is a rank-one modification of
216* the identity matrix.
217*
218 IF( lnoti ) THEN
219 DO 10 j = 1, n - 1
220 lm = min( kl, n-j )
221 l = ipiv( j )
222 IF( l.NE.j )
223 $ CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
224 CALL zgeru( lm, nrhs, -one, ab( kd+1, j ), 1, b( j, 1 ),
225 $ ldb, b( j+1, 1 ), ldb )
226 10 CONTINUE
227 END IF
228*
229 DO 20 i = 1, nrhs
230*
231* Solve U*X = B, overwriting B with X.
232*
233 CALL ztbsv( 'Upper', 'No transpose', 'Non-unit', n, kl+ku,
234 $ ab, ldab, b( 1, i ), 1 )
235 20 CONTINUE
236*
237 ELSE IF( lsame( trans, 'T' ) ) THEN
238*
239* Solve A**T * X = B.
240*
241 DO 30 i = 1, nrhs
242*
243* Solve U**T * X = B, overwriting B with X.
244*
245 CALL ztbsv( 'Upper', 'Transpose', 'Non-unit', n, kl+ku, ab,
246 $ ldab, b( 1, i ), 1 )
247 30 CONTINUE
248*
249* Solve L**T * X = B, overwriting B with X.
250*
251 IF( lnoti ) THEN
252 DO 40 j = n - 1, 1, -1
253 lm = min( kl, n-j )
254 CALL zgemv( 'Transpose', lm, nrhs, -one, b( j+1, 1 ),
255 $ ldb, ab( kd+1, j ), 1, one, b( j, 1 ), ldb )
256 l = ipiv( j )
257 IF( l.NE.j )
258 $ CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
259 40 CONTINUE
260 END IF
261*
262 ELSE
263*
264* Solve A**H * X = B.
265*
266 DO 50 i = 1, nrhs
267*
268* Solve U**H * X = B, overwriting B with X.
269*
270 CALL ztbsv( 'Upper', 'Conjugate transpose', 'Non-unit', n,
271 $ kl+ku, ab, ldab, b( 1, i ), 1 )
272 50 CONTINUE
273*
274* Solve L**H * X = B, overwriting B with X.
275*
276 IF( lnoti ) THEN
277 DO 60 j = n - 1, 1, -1
278 lm = min( kl, n-j )
279 CALL zlacgv( nrhs, b( j, 1 ), ldb )
280 CALL zgemv( 'Conjugate transpose', lm, nrhs, -one,
281 $ b( j+1, 1 ), ldb, ab( kd+1, j ), 1, one,
282 $ b( j, 1 ), ldb )
283 CALL zlacgv( nrhs, b( j, 1 ), ldb )
284 l = ipiv( j )
285 IF( l.NE.j )
286 $ CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
287 60 CONTINUE
288 END IF
289 END IF
290 RETURN
291*
292* End of ZGBTRS
293*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zgemv
subroutine zgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZGEMV
Definition zgemv.f:160
zgeru
subroutine zgeru(m, n, alpha, x, incx, y, incy, a, lda)
ZGERU
Definition zgeru.f:130
zlacgv
subroutine zlacgv(n, x, incx)
ZLACGV conjugates a complex vector.
Definition zlacgv.f:74
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
zswap
subroutine zswap(n, zx, incx, zy, incy)
ZSWAP
Definition zswap.f:81
ztbsv
subroutine ztbsv(uplo, trans, diag, n, k, a, lda, x, incx)
ZTBSV
Definition ztbsv.f:189
Here is the call graph for this function:
Here is the caller graph for this function: