LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine zgbsv ( integer  N,
integer  KL,
integer  KU,
integer  NRHS,
complex*16, dimension( ldab, * )  AB,
integer  LDAB,
integer, dimension( * )  IPIV,
complex*16, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

ZGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

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

Purpose: 
 ZGBSV computes the solution to a complex system of linear equations
 A * X = B, where A is a band matrix of order N with KL subdiagonals
 and KU superdiagonals, and X and B are N-by-NRHS matrices.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as A = L * U, where L is a product of permutation
 and unit lower triangular matrices with KL subdiagonals, and U is
 upper triangular with KL+KU superdiagonals.  The factored form of A
 is then used to solve the system of equations A * X = B.
Parameters
[in]N
          N is INTEGER
          The number of linear equations, i.e., the order of the
          matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 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 matrix A in band storage, in rows KL+1 to
          2*KL+KU+1; rows 1 to KL of the array need not be set.
          The j-th column of A is stored in the j-th column of the
          array AB as follows:
          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
          On exit, details of the factorization: U is stored as an
          upper triangular band matrix with KL+KU superdiagonals in
          rows 1 to KL+KU+1, and the multipliers used during the
          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
          See below for further details.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i).
[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, U(i,i) is exactly zero.  The factorization
                has been completed, but the factor U is exactly
                singular, and the solution has not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Further Details: 
  The band storage scheme is illustrated by the following example, when
  M = N = 6, KL = 2, KU = 1:

  On entry:                       On exit:

      *    *    *    +    +    +       *    *    *   u14  u25  u36
      *    *    +    +    +    +       *    *   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
     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *

  Array elements marked * are not used by the routine; elements marked
  + need not be set on entry, but are required by the routine to store
  elements of U because of fill-in resulting from the row interchanges.

Definition at line 164 of file zgbsv.f.

164 *
165 * -- LAPACK driver routine (version 3.4.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * November 2011
169 *
170 * .. Scalar Arguments ..
171  INTEGER info, kl, ku, ldab, ldb, n, nrhs
172 * ..
173 * .. Array Arguments ..
174  INTEGER ipiv( * )
175  COMPLEX*16 ab( ldab, * ), b( ldb, * )
176 * ..
177 *
178 * =====================================================================
179 *
180 * .. External Subroutines ..
181  EXTERNAL xerbla, zgbtrf, zgbtrs
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC max
185 * ..
186 * .. Executable Statements ..
187 *
188 * Test the input parameters.
189 *
190  info = 0
191  IF( n.LT.0 ) THEN
192  info = -1
193  ELSE IF( kl.LT.0 ) THEN
194  info = -2
195  ELSE IF( ku.LT.0 ) THEN
196  info = -3
197  ELSE IF( nrhs.LT.0 ) THEN
198  info = -4
199  ELSE IF( ldab.LT.2*kl+ku+1 ) THEN
200  info = -6
201  ELSE IF( ldb.LT.max( n, 1 ) ) THEN
202  info = -9
203  END IF
204  IF( info.NE.0 ) THEN
205  CALL xerbla( 'ZGBSV ', -info )
206  RETURN
207  END IF
208 *
209 * Compute the LU factorization of the band matrix A.
210 *
211  CALL zgbtrf( n, n, kl, ku, ab, ldab, ipiv, info )
212  IF( info.EQ.0 ) THEN
213 *
214 * Solve the system A*X = B, overwriting B with X.
215 *
216  CALL zgbtrs( 'No transpose', n, kl, ku, nrhs, ab, ldab, ipiv,
217  $ b, ldb, info )
218  END IF
219  RETURN
220 *
221 * End of ZGBSV
222 *
zgbtrs
subroutine zgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
ZGBTRS
Definition: zgbtrs.f:140
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
zgbtrf
subroutine zgbtrf(M, N, KL, KU, AB, LDAB, IPIV, INFO)
ZGBTRF
Definition: zgbtrf.f:146

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