.ThermoSysPro.Properties.WaterSteam.IF97_packages.IF97_wAJ.Spline_Utilities.Modelica_Interpolation.Utilities.dgbsv

Information

Lapack documentation:
Purpose
=======
DGBSV 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.
Arguments
=========
N       (input) INTEGER
        The number of linear equations, i.e., the order of the
        matrix A.  N >= 0.
KL      (input) INTEGER
        The number of subdiagonals within the band of A.  KL >= 0.
KU      (input) INTEGER
        The number of superdiagonals within the band of A.  KU >= 0.
NRHS    (input) INTEGER
        The number of right hand sides, i.e., the number of columns
        of the matrix B.  NRHS >= 0.
AB      (input/output) DOUBLE PRECISION 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.
LDAB    (input) INTEGER
        The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
IPIV    (output) INTEGER array, dimension (N)
        The pivot indices that define the permutation matrix P;
        row i of the matrix was interchanged with row IPIV(i).
B       (input/output) DOUBLE PRECISION 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.
LDB     (input) INTEGER
        The leading dimension of the array B.  LDB >= max(1,N).
INFO    (output) 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.

Interface

function dgbsv
  extends Modelica.Icons.Function;
  input Integer n "Number of equations";
  input Integer kLower "Number of lower bands";
  input Integer kUpper "Number of upper bands";
  input Real A[2*kLower + kUpper + 1, n];
  input Real B[n, :];
  output Real X[n, size(B, 2)] = B;
  output Integer info;
end dgbsv;