LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
•All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Modules Pages

◆ zgbsv()

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.
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 159 of file zgbsv.f.

161*
162* -- LAPACK driver routine --
163* -- LAPACK is a software package provided by Univ. of Tennessee, --
164* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165*
166* .. Scalar Arguments ..
167 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
168* ..
169* .. Array Arguments ..
170 INTEGER IPIV( * )
171 COMPLEX*16 AB( LDAB, * ), B( LDB, * )
172* ..
173*
174* =====================================================================
175*
176* .. External Subroutines ..
177 EXTERNAL xerbla, zgbtrf, zgbtrs
178* ..
179* .. Intrinsic Functions ..
180 INTRINSIC max
181* ..
182* .. Executable Statements ..
183*
184* Test the input parameters.
185*
186 info = 0
187 IF( n.LT.0 ) THEN
188 info = -1
189 ELSE IF( kl.LT.0 ) THEN
190 info = -2
191 ELSE IF( ku.LT.0 ) THEN
192 info = -3
193 ELSE IF( nrhs.LT.0 ) THEN
194 info = -4
195 ELSE IF( ldab.LT.2*kl+ku+1 ) THEN
196 info = -6
197 ELSE IF( ldb.LT.max( n, 1 ) ) THEN
198 info = -9
199 END IF
200 IF( info.NE.0 ) THEN
201 CALL xerbla( 'ZGBSV ', -info )
202 RETURN
203 END IF
204*
205* Compute the LU factorization of the band matrix A.
206*
207 CALL zgbtrf( n, n, kl, ku, ab, ldab, ipiv, info )
208 IF( info.EQ.0 ) THEN
209*
210* Solve the system A*X = B, overwriting B with X.
211*
212 CALL zgbtrs( 'No transpose', n, kl, ku, nrhs, ab, ldab,
213 $ ipiv,
214 $ b, ldb, info )
215 END IF
216 RETURN
217*
218* End of ZGBSV
219*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zgbtrf
subroutine zgbtrf(m, n, kl, ku, ab, ldab, ipiv, info)
ZGBTRF
Definition zgbtrf.f:142
zgbtrs
subroutine zgbtrs(trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
ZGBTRS
Definition zgbtrs.f:137
Here is the call graph for this function:
Here is the caller graph for this function: