LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zpbsv()

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

ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

Download ZPBSV + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZPBSV computes the solution to a complex system of linear equations
    A * X = B,
 where A is an N-by-N Hermitian positive definite band matrix and X
 and B are N-by-NRHS matrices.

 The Cholesky decomposition is used to factor A as
    A = U**H * U,  if UPLO = 'U', or
    A = L * L**H,  if UPLO = 'L',
 where U is an upper triangular band matrix, and L is a lower
 triangular band matrix, with the same number of superdiagonals or
 subdiagonals as A.  The factored form of A is then used to solve the
 system of equations A * X = B.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
[in]N
          N is INTEGER
          The number of linear equations, i.e., 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,out]AB
          AB is COMPLEX*16 array, dimension (LDAB,N)
          On entry, the upper or lower triangle of the Hermitian band
          matrix A, stored in the first KD+1 rows of the array.  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).
          See below for further details.

          On exit, if INFO = 0, the triangular factor U or L from the
          Cholesky factorization A = U**H *U or A = L*L**H of the band
          matrix A, in the same storage format as A.
[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 N-by-NRHS right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS 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 leading minor of order i of A is not
                positive definite, so the factorization could not be
                completed, and the solution has not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016
Further Details:
  The band storage scheme is illustrated by the following example, when
  N = 6, KD = 2, and UPLO = 'U':

  On entry:                       On exit:

      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66

  Similarly, if UPLO = 'L' the format of A is as follows:

  On entry:                       On exit:

     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *

  Array elements marked * are not used by the routine.

Definition at line 166 of file zpbsv.f.

166 *
167 * -- LAPACK driver routine (version 3.7.0) --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170 * December 2016
171 *
172 * .. Scalar Arguments ..
173  CHARACTER uplo
174  INTEGER info, kd, ldab, ldb, n, nrhs
175 * ..
176 * .. Array Arguments ..
177  COMPLEX*16 ab( ldab, * ), b( ldb, * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. External Functions ..
183  LOGICAL lsame
184  EXTERNAL lsame
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL xerbla, zpbtrf, zpbtrs
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC max
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  info = 0
197  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
198  info = -1
199  ELSE IF( n.LT.0 ) THEN
200  info = -2
201  ELSE IF( kd.LT.0 ) THEN
202  info = -3
203  ELSE IF( nrhs.LT.0 ) THEN
204  info = -4
205  ELSE IF( ldab.LT.kd+1 ) THEN
206  info = -6
207  ELSE IF( ldb.LT.max( 1, n ) ) THEN
208  info = -8
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'ZPBSV ', -info )
212  RETURN
213  END IF
214 *
215 * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
216 *
217  CALL zpbtrf( uplo, n, kd, ab, ldab, info )
218  IF( info.EQ.0 ) THEN
219 *
220 * Solve the system A*X = B, overwriting B with X.
221 *
222  CALL zpbtrs( uplo, n, kd, nrhs, ab, ldab, b, ldb, info )
223 *
224  END IF
225  RETURN
226 *
227 * End of ZPBSV
228 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zpbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
ZPBTRS
Definition: zpbtrs.f:123
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zpbtrf(UPLO, N, KD, AB, LDAB, INFO)
ZPBTRF
Definition: zpbtrf.f:144
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