.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.## Copyright © EDF 2002 - 2025

## ThermoSysPro Version 4.2

              

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;