LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ ctbtrs()

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

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

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.

Definition at line 144 of file ctbtrs.f.

146 *
147 * -- LAPACK computational routine --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 *
151 * .. Scalar Arguments ..
152  CHARACTER DIAG, TRANS, UPLO
153  INTEGER INFO, KD, LDAB, LDB, N, NRHS
154 * ..
155 * .. Array Arguments ..
156  COMPLEX AB( LDAB, * ), B( LDB, * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  COMPLEX ZERO
163  parameter( zero = ( 0.0e+0, 0.0e+0 ) )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL NOUNIT, UPPER
167  INTEGER J
168 * ..
169 * .. External Functions ..
170  LOGICAL LSAME
171  EXTERNAL lsame
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL ctbsv, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC max
178 * ..
179 * .. Executable Statements ..
180 *
181 * Test the input parameters.
182 *
183  info = 0
184  nounit = lsame( diag, 'N' )
185  upper = lsame( uplo, 'U' )
186  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
187  info = -1
188  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
189  $ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
190  info = -2
191  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
192  info = -3
193  ELSE IF( n.LT.0 ) THEN
194  info = -4
195  ELSE IF( kd.LT.0 ) THEN
196  info = -5
197  ELSE IF( nrhs.LT.0 ) THEN
198  info = -6
199  ELSE IF( ldab.LT.kd+1 ) THEN
200  info = -8
201  ELSE IF( ldb.LT.max( 1, n ) ) THEN
202  info = -10
203  END IF
204  IF( info.NE.0 ) THEN
205  CALL xerbla( 'CTBTRS', -info )
206  RETURN
207  END IF
208 *
209 * Quick return if possible
210 *
211  IF( n.EQ.0 )
212  $ RETURN
213 *
214 * Check for singularity.
215 *
216  IF( nounit ) THEN
217  IF( upper ) THEN
218  DO 10 info = 1, n
219  IF( ab( kd+1, info ).EQ.zero )
220  $ RETURN
221  10 CONTINUE
222  ELSE
223  DO 20 info = 1, n
224  IF( ab( 1, info ).EQ.zero )
225  $ RETURN
226  20 CONTINUE
227  END IF
228  END IF
229  info = 0
230 *
231 * Solve A * X = B, A**T * X = B, or A**H * X = B.
232 *
233  DO 30 j = 1, nrhs
234  CALL ctbsv( uplo, trans, diag, n, kd, ab, ldab, b( 1, j ), 1 )
235  30 CONTINUE
236 *
237  RETURN
238 *
239 * End of CTBTRS
240 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ctbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBSV
Definition: ctbsv.f:189
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