LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine ctbtrs ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  KD,
integer  NRHS,
complex, dimension( ldab, * )  AB,
integer  LDAB,
complex, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

CTBTRS

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Purpose: 
 CTBTRS solves a triangular system of the form

    A * X = B,  A**T * X = B,  or  A**H * X = B,

 where A is a triangular band matrix of order N, and B is an
 N-by-NRHS matrix.  A check is made to verify that A is nonsingular.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.
[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]DIAG
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 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 array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of AB.  The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in,out]B
          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, if INFO = 0, 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
          > 0:  if INFO = i, the i-th diagonal element of A is zero,
                indicating that the matrix is singular and the
                solutions X have not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 148 of file ctbtrs.f.

148 *
149 * -- LAPACK computational routine (version 3.4.0) --
150 * -- LAPACK is a software package provided by Univ. of Tennessee, --
151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152 * November 2011
153 *
154 * .. Scalar Arguments ..
155  CHARACTER diag, trans, uplo
156  INTEGER info, kd, ldab, ldb, n, nrhs
157 * ..
158 * .. Array Arguments ..
159  COMPLEX ab( ldab, * ), b( ldb, * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  COMPLEX zero
166  parameter ( zero = ( 0.0e+0, 0.0e+0 ) )
167 * ..
168 * .. Local Scalars ..
169  LOGICAL nounit, upper
170  INTEGER j
171 * ..
172 * .. External Functions ..
173  LOGICAL lsame
174  EXTERNAL lsame
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL ctbsv, xerbla
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC max
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187  nounit = lsame( diag, 'N' )
188  upper = lsame( uplo, 'U' )
189  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
190  info = -1
191  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
192  $ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
193  info = -2
194  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
195  info = -3
196  ELSE IF( n.LT.0 ) THEN
197  info = -4
198  ELSE IF( kd.LT.0 ) THEN
199  info = -5
200  ELSE IF( nrhs.LT.0 ) THEN
201  info = -6
202  ELSE IF( ldab.LT.kd+1 ) THEN
203  info = -8
204  ELSE IF( ldb.LT.max( 1, n ) ) THEN
205  info = -10
206  END IF
207  IF( info.NE.0 ) THEN
208  CALL xerbla( 'CTBTRS', -info )
209  RETURN
210  END IF
211 *
212 * Quick return if possible
213 *
214  IF( n.EQ.0 )
215  $ RETURN
216 *
217 * Check for singularity.
218 *
219  IF( nounit ) THEN
220  IF( upper ) THEN
221  DO 10 info = 1, n
222  IF( ab( kd+1, info ).EQ.zero )
223  $ RETURN
224  10 CONTINUE
225  ELSE
226  DO 20 info = 1, n
227  IF( ab( 1, info ).EQ.zero )
228  $ RETURN
229  20 CONTINUE
230  END IF
231  END IF
232  info = 0
233 *
234 * Solve A * X = B, A**T * X = B, or A**H * X = B.
235 *
236  DO 30 j = 1, nrhs
237  CALL ctbsv( uplo, trans, diag, n, kd, ab, ldab, b( 1, j ), 1 )
238  30 CONTINUE
239 *
240  RETURN
241 *
242 * End of CTBTRS
243 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
ctbsv
subroutine ctbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBSV
Definition: ctbsv.f:191
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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