LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ 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

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.```

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)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ctbsv(uplo, trans, diag, n, k, a, lda, x, incx)
CTBSV
Definition ctbsv.f:189
Here is the call graph for this function:
Here is the caller graph for this function: