 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ sgbsv()

 subroutine sgbsv ( integer N, integer KL, integer KU, integer NRHS, real, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB, integer INFO )

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

Purpose:
SGBSV computes the solution to a real 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 REAL 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 REAL 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.
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 161 of file sgbsv.f.

162 *
163 * -- LAPACK driver routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
169 * ..
170 * .. Array Arguments ..
171  INTEGER IPIV( * )
172  REAL AB( LDAB, * ), B( LDB, * )
173 * ..
174 *
175 * =====================================================================
176 *
177 * .. External Subroutines ..
178  EXTERNAL sgbtrf, sgbtrs, xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max
182 * ..
183 * .. Executable Statements ..
184 *
185 * Test the input parameters.
186 *
187  info = 0
188  IF( n.LT.0 ) THEN
189  info = -1
190  ELSE IF( kl.LT.0 ) THEN
191  info = -2
192  ELSE IF( ku.LT.0 ) THEN
193  info = -3
194  ELSE IF( nrhs.LT.0 ) THEN
195  info = -4
196  ELSE IF( ldab.LT.2*kl+ku+1 ) THEN
197  info = -6
198  ELSE IF( ldb.LT.max( n, 1 ) ) THEN
199  info = -9
200  END IF
201  IF( info.NE.0 ) THEN
202  CALL xerbla( 'SGBSV ', -info )
203  RETURN
204  END IF
205 *
206 * Compute the LU factorization of the band matrix A.
207 *
208  CALL sgbtrf( n, n, kl, ku, ab, ldab, ipiv, info )
209  IF( info.EQ.0 ) THEN
210 *
211 * Solve the system A*X = B, overwriting B with X.
212 *
213  CALL sgbtrs( 'No transpose', n, kl, ku, nrhs, ab, ldab, ipiv,
214  \$ b, ldb, info )
215  END IF
216  RETURN
217 *
218 * End of SGBSV
219 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
SGBTRS
Definition: sgbtrs.f:138
subroutine sgbtrf(M, N, KL, KU, AB, LDAB, IPIV, INFO)
SGBTRF
Definition: sgbtrf.f:144
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