 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ztbtrs()

 subroutine ztbtrs ( character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO )

ZTBTRS

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Purpose:
``` ZTBTRS 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*16 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*16 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.```

Definition at line 144 of file ztbtrs.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*16 AB( LDAB, * ), B( LDB, * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  COMPLEX*16 ZERO
163  parameter( zero = ( 0.0d+0, 0.0d+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 xerbla, ztbsv
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( 'ZTBTRS', -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 ztbsv( uplo, trans, diag, n, kd, ab, ldab, b( 1, j ), 1 )
235  30 CONTINUE
236 *
237  RETURN
238 *
239 * End of ZTBTRS
240 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBSV
Definition: ztbsv.f:189
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