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DGBFA Class

***PURPOSE Factor a band matrix using Gaussian elimination. ***CATEGORY D2A2 ***TYPE DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C) ***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION ***AUTHOR Moler, C. B., (U. of New Mexico) ***DESCRIPTION DGBFA factors a double precision band matrix by elimination. DGBFA is usually called by DGBCO, but it can be called directly with a saving in time if RCOND is not needed. On Entry ABD DOUBLE PRECISION(LDA, N) contains the matrix in band storage. The columns of the matrix are stored in the columns of ABD and the diagonals of the matrix are stored in rows ML+1 through 2*ML+MU+1 of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. 2*ML + MU + 1 . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. 0 .LE. ML .LT. N . MU INTEGER number of diagonals above the main diagonal. 0 .LE. MU .LT. N . More efficient if ML .LE. MU . On Return ABD an upper triangular matrix in band storage and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if U(K,K) .EQ. 0.0 . This is not an error condition for this subroutine, but it does indicate that DGBSL will divide by zero if called. Use RCOND in DGBCO for a reliable indication of singularity. Band Storage If A is a band matrix, the following program segment will set up the input. ML = (band width below the diagonal) MU = (band width above the diagonal) M = ML + MU + 1 DO 20 J = 1, N I1 = MAX(1, J-MU) I2 = MIN(N, J+ML) DO 10 I = I1, I2 K = I - J + M ABD(K,J) = A(I,J) 10 CONTINUE 20 CONTINUE This uses rows ML+1 through 2*ML+MU+1 of ABD . In addition, the first ML rows in ABD are used for elements generated during the triangularization. The total number of rows needed in ABD is 2*ML+MU+1 . The ML+MU by ML+MU upper left triangle and the ML by ML lower right triangle are not referenced. ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979. ***ROUTINES CALLED DAXPY, DSCAL, IDAMAX ***REVISION HISTORY (YYMMDD) 780814 DATE WRITTEN 890531 Changed all specific intrinsics to generic. (WRB) 890831 Modified array declarations. (WRB) 890831 REVISION DATE from Version 3.2 891214 Prologue converted to Version 4.0 format. (BAB) 900326 Removed duplicate information from DESCRIPTION section. (WRB) 920501 Reformatted the REFERENCES section. (WRB) ***END PROLOGUE DGBFA
Inheritance Hierarchy
SystemObject
  Altaxo.Calc.Ode.Obsolete.DVodeDGBFA

Namespace: Altaxo.Calc.Ode.Obsolete.DVode
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
public class DGBFA

The DGBFA type exposes the following members.

Constructors
 NameDescription
Public methodDGBFAInitializes a new instance of the DGBFA class
Public methodDGBFA(IDAMAX, DSCAL, DAXPY)Initializes a new instance of the DGBFA class
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Methods
 NameDescription
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodRun ***PURPOSE Factor a band matrix using Gaussian elimination. ***CATEGORY D2A2 ***TYPE DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C) ***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION ***AUTHOR Moler, C. B., (U. of New Mexico) ***DESCRIPTION DGBFA factors a double precision band matrix by elimination. DGBFA is usually called by DGBCO, but it can be called directly with a saving in time if RCOND is not needed. On Entry ABD DOUBLE PRECISION(LDA, N) contains the matrix in band storage. The columns of the matrix are stored in the columns of ABD and the diagonals of the matrix are stored in rows ML+1 through 2*ML+MU+1 of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. 2*ML + MU + 1 . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. 0 .LE. ML .LT. N . MU INTEGER number of diagonals above the main diagonal. 0 .LE. MU .LT. N . More efficient if ML .LE. MU . On Return ABD an upper triangular matrix in band storage and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if U(K,K) .EQ. 0.0 . This is not an error condition for this subroutine, but it does indicate that DGBSL will divide by zero if called. Use RCOND in DGBCO for a reliable indication of singularity. Band Storage If A is a band matrix, the following program segment will set up the input. ML = (band width below the diagonal) MU = (band width above the diagonal) M = ML + MU + 1 DO 20 J = 1, N I1 = MAX(1, J-MU) I2 = MIN(N, J+ML) DO 10 I = I1, I2 K = I - J + M ABD(K,J) = A(I,J) 10 CONTINUE 20 CONTINUE This uses rows ML+1 through 2*ML+MU+1 of ABD . In addition, the first ML rows in ABD are used for elements generated during the triangularization. The total number of rows needed in ABD is 2*ML+MU+1 . The ML+MU by ML+MU upper left triangle and the ML by ML lower right triangle are not referenced. ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979. ***ROUTINES CALLED DAXPY, DSCAL, IDAMAX ***REVISION HISTORY (YYMMDD) 780814 DATE WRITTEN 890531 Changed all specific intrinsics to generic. (WRB) 890831 Modified array declarations. (WRB) 890831 REVISION DATE from Version 3.2 891214 Prologue converted to Version 4.0 format. (BAB) 900326 Removed duplicate information from DESCRIPTION section. (WRB) 920501 Reformatted the REFERENCES section. (WRB) ***END PROLOGUE DGBFA
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
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See Also