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

CPBTRS

Purpose:
``` CPBTRS solves a system of linear equations A*X = B with a Hermitian
positive definite band matrix A using the Cholesky factorization
A = U**H*U or A = L*L**H computed by CPBTRF.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. 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 triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).``` [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, 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```
Date
November 2011

Definition at line 123 of file cpbtrs.f.

123 *
124 * -- LAPACK computational routine (version 3.4.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * November 2011
128 *
129 * .. Scalar Arguments ..
130  CHARACTER uplo
131  INTEGER info, kd, ldab, ldb, n, nrhs
132 * ..
133 * .. Array Arguments ..
134  COMPLEX ab( ldab, * ), b( ldb, * )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Local Scalars ..
140  LOGICAL upper
141  INTEGER j
142 * ..
143 * .. External Functions ..
144  LOGICAL lsame
145  EXTERNAL lsame
146 * ..
147 * .. External Subroutines ..
148  EXTERNAL ctbsv, xerbla
149 * ..
150 * .. Intrinsic Functions ..
151  INTRINSIC max
152 * ..
153 * .. Executable Statements ..
154 *
155 * Test the input parameters.
156 *
157  info = 0
158  upper = lsame( uplo, 'U' )
159  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
160  info = -1
161  ELSE IF( n.LT.0 ) THEN
162  info = -2
163  ELSE IF( kd.LT.0 ) THEN
164  info = -3
165  ELSE IF( nrhs.LT.0 ) THEN
166  info = -4
167  ELSE IF( ldab.LT.kd+1 ) THEN
168  info = -6
169  ELSE IF( ldb.LT.max( 1, n ) ) THEN
170  info = -8
171  END IF
172  IF( info.NE.0 ) THEN
173  CALL xerbla( 'CPBTRS', -info )
174  RETURN
175  END IF
176 *
177 * Quick return if possible
178 *
179  IF( n.EQ.0 .OR. nrhs.EQ.0 )
180  \$ RETURN
181 *
182  IF( upper ) THEN
183 *
184 * Solve A*X = B where A = U**H *U.
185 *
186  DO 10 j = 1, nrhs
187 *
188 * Solve U**H *X = B, overwriting B with X.
189 *
190  CALL ctbsv( 'Upper', 'Conjugate transpose', 'Non-unit', n,
191  \$ kd, ab, ldab, b( 1, j ), 1 )
192 *
193 * Solve U*X = B, overwriting B with X.
194 *
195  CALL ctbsv( 'Upper', 'No transpose', 'Non-unit', n, kd, ab,
196  \$ ldab, b( 1, j ), 1 )
197  10 CONTINUE
198  ELSE
199 *
200 * Solve A*X = B where A = L*L**H.
201 *
202  DO 20 j = 1, nrhs
203 *
204 * Solve L*X = B, overwriting B with X.
205 *
206  CALL ctbsv( 'Lower', 'No transpose', 'Non-unit', n, kd, ab,
207  \$ ldab, b( 1, j ), 1 )
208 *
209 * Solve L**H *X = B, overwriting B with X.
210 *
211  CALL ctbsv( 'Lower', 'Conjugate transpose', 'Non-unit', n,
212  \$ kd, ab, ldab, b( 1, j ), 1 )
213  20 CONTINUE
214  END IF
215 *
216  RETURN
217 *
218 * End of CPBTRS
219 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ctbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBSV
Definition: ctbsv.f:191
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

Here is the call graph for this function:

Here is the caller graph for this function: