LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sgbtrs()

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

SGBTRS

Purpose:
``` SGBTRS 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 SGBTRF.```
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 REAL array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by SGBTRF. 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 REAL 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 sgbtrs.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 REAL AB( LDAB, * ), B( LDB, * )
150* ..
151*
152* =====================================================================
153*
154* .. Parameters ..
155 REAL ONE
156 parameter( one = 1.0e+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 sgemv, sger, sswap, stbsv, 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( 'SGBTRS', -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 sswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
224 CALL sger( 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 stbsv( '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 stbsv( '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 sgemv( '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 sswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
259 40 CONTINUE
260 END IF
261 END IF
262 RETURN
263*
264* End of SGBTRS
265*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine stbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBSV
Definition: stbsv.f:189
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:130
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:156
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