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

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```

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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