LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dgbtrs()

 subroutine dgbtrs ( character TRANS, integer N, integer KL, integer KU, integer NRHS, double precision, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB, integer INFO )

DGBTRS

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Purpose:
``` DGBTRS solves a system of linear equations
A * X = B  or  A**T * X = B
with a general band matrix A using the LU factorization computed
by DGBTRF.```
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**T* X = B (Conjugate transpose = 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 DOUBLE PRECISION array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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 DOUBLE PRECISION 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```

Definition at line 136 of file dgbtrs.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  DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION ONE
156  parameter( one = 1.0d+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 dgemv, dger, dswap, dtbsv, xerbla
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( 'DGBTRS', -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 dswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
224  CALL dger( 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 dtbsv( 'Upper', 'No transpose', 'Non-unit', n, kl+ku,
234  \$ ab, ldab, b( 1, i ), 1 )
235  20 CONTINUE
236 *
237  ELSE
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 dtbsv( '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 dgemv( '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 dswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
259  40 CONTINUE
260  END IF
261  END IF
262  RETURN
263 *
264 * End of DGBTRS
265 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:130
subroutine dtbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBSV
Definition: dtbsv.f:189
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
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