LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cpbtrs()

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

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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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 120 of file cpbtrs.f.

121 *
122 * -- LAPACK computational routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  CHARACTER UPLO
128  INTEGER INFO, KD, LDAB, LDB, N, NRHS
129 * ..
130 * .. Array Arguments ..
131  COMPLEX AB( LDAB, * ), B( LDB, * )
132 * ..
133 *
134 * =====================================================================
135 *
136 * .. Local Scalars ..
137  LOGICAL UPPER
138  INTEGER J
139 * ..
140 * .. External Functions ..
141  LOGICAL LSAME
142  EXTERNAL lsame
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL ctbsv, xerbla
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC max
149 * ..
150 * .. Executable Statements ..
151 *
152 * Test the input parameters.
153 *
154  info = 0
155  upper = lsame( uplo, 'U' )
156  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
157  info = -1
158  ELSE IF( n.LT.0 ) THEN
159  info = -2
160  ELSE IF( kd.LT.0 ) THEN
161  info = -3
162  ELSE IF( nrhs.LT.0 ) THEN
163  info = -4
164  ELSE IF( ldab.LT.kd+1 ) THEN
165  info = -6
166  ELSE IF( ldb.LT.max( 1, n ) ) THEN
167  info = -8
168  END IF
169  IF( info.NE.0 ) THEN
170  CALL xerbla( 'CPBTRS', -info )
171  RETURN
172  END IF
173 *
174 * Quick return if possible
175 *
176  IF( n.EQ.0 .OR. nrhs.EQ.0 )
177  $ RETURN
178 *
179  IF( upper ) THEN
180 *
181 * Solve A*X = B where A = U**H *U.
182 *
183  DO 10 j = 1, nrhs
184 *
185 * Solve U**H *X = B, overwriting B with X.
186 *
187  CALL ctbsv( 'Upper', 'Conjugate transpose', 'Non-unit', n,
188  $ kd, ab, ldab, b( 1, j ), 1 )
189 *
190 * Solve U*X = B, overwriting B with X.
191 *
192  CALL ctbsv( 'Upper', 'No transpose', 'Non-unit', n, kd, ab,
193  $ ldab, b( 1, j ), 1 )
194  10 CONTINUE
195  ELSE
196 *
197 * Solve A*X = B where A = L*L**H.
198 *
199  DO 20 j = 1, nrhs
200 *
201 * Solve L*X = B, overwriting B with X.
202 *
203  CALL ctbsv( 'Lower', 'No transpose', 'Non-unit', n, kd, ab,
204  $ ldab, b( 1, j ), 1 )
205 *
206 * Solve L**H *X = B, overwriting B with X.
207 *
208  CALL ctbsv( 'Lower', 'Conjugate transpose', 'Non-unit', n,
209  $ kd, ab, ldab, b( 1, j ), 1 )
210  20 CONTINUE
211  END IF
212 *
213  RETURN
214 *
215 * End of CPBTRS
216 *
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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