Procedures

This routine computes an adjustment, LDIF, to the required integer storage space in IWK (sparse matrix work space).

This routine computes an adjustment, LDIF, to the required integer storage space in IWK (sparse matrix work space).

cdrv(3f) - [M_odepack ] driver for solving sparse non-symmetric systems of linear equations

cdrv(3f) - [M_odepack ] driver for solving sparse non-symmetric systems of linear equations

This routine counts the number of nonzero elements in the strict upper triangle of the matrix M + M(transpose), where the sparsity structure of M is given by pointer arrays IA and JA.

This routine counts the number of nonzero elements in the strict upper triangle of the matrix M + M(transpose), where the sparsity structure of M is given by pointer arrays IA and JA.

This subroutine computes the initial value of the vector YDOT satisfying

This subroutine computes the initial value of the vector YDOT satisfying

This subroutine computes the initial value of the vector YDOT satisfying

This subroutine computes the initial value of the vector YDOT satisfying

This subroutine computes the initial value of the vector YDOT satisfying

This subroutine computes the initial value of the vector YDOT satisfying

This routine computes the product

This routine computes the product

daxpy(3f) - [M_odepack::matrix] Compute a constant times a vector plus a vector.

daxpy(3f) - [M_odepack::matrix] Compute a constant times a vector plus a vector.

This function computes the norm of a banded N by N matrix, stored in the array A, that is consistent with the weighted max-norm on vectors, with weights stored in the array W. ML and MU are the lower and upper half-bandwidths of the matrix. NRA is the first dimension of the A array, NRA .ge. ML+MU+1. In terms of the matrix elements a(i,j), the norm is given by:

dcfode(3f) - [M_odepack] Set ODE integrator coefficients.

dcfode(3f) - [M_odepack] Set ODE integrator coefficients.

dcopy(3f) - [M_odepack::matrix] copy a vector

dcopy(3f) - [M_odepack::matrix] copy a vector

ddecbt(3f) -[M_odepack] Block-tridiagonal matrix decomposition routine.

ddot(3f) - [M_odepack::matrix] Compute the inner product of two vectors.

dewset(3f) - [M_odepack] Set error weight vector.

dewset(3f) - [M_odepack] Set error weight vector.

This function computes the norm of a full N by N matrix, stored in the array A, that is consistent with the weighted max-norm on vectors, with weights stored in the array W:

dgbfa(3f) - [M_odepack::matrix] Factor a band matrix using Gaussian elimination.

dgbsl(3f) - [M_odepack::Matrix] Solve the real band system AX=B or TRANS(A)X=B using the factors computed by DGBCO(3f) or DGBFA().

dgefa(3f) - [M_odepack::matrix] Factor a matrix using Gaussian elimination.

dgefa(3f) - [M_odepack::matrix] Factor a matrix using Gaussian elimination.

dgesl(3f) - [M_odepack::matrix] Solve the real system AX=B or TRANS(A)X=B using the factors computed by DGECO or DGEFA.

dgesl(3f) - [M_odepack::matrix] Solve the real system AX=B or TRANS(A)X=B using the factors computed by DGECO or DGEFA.

This routine is a modification of the LINPACK routine DGEFA and performs an LU decomposition of an upper Hessenberg matrix A. There are two options available:

This is part of the LINPACK routine DGESL with changes due to the fact that A is an upper Hessenberg matrix.

This routine performs a QR decomposition of an upper Hessenberg matrix A. There are two options available:

This is essentially the LINPACK routine DGESL except for changes due to the fact that A is an upper Hessenberg matrix.

DINTDY computes interpolated values of the K-th derivative of the dependent variable vector y, and stores it in DKY. This routine is called within the package with K = 0 and T = TOUT, but may also be called by the user for any K up to the current order. (See detailed instructions in the usage documentation.)

DINTDY computes interpolated values of the K-th derivative of the dependent variable vector y, and stores it in DKY. This routine is called within the package with K = 0 and T = TOUT, but may also be called by the user for any K up to the current order. (See detailed instructions in the usage documentation.)

This routine serves as an interface between the driver and Subroutine DPREP. It is called only if MITER is 1 or 2. Tasks performed here are:

This routine serves as an interface between the driver and Subroutine DPREP. It is called only if MITER is 1 or 2. Tasks performed here are:

This routine serves as an interface between the driver and Subroutine DPREPI. Tasks performed here are:

This routine serves as an interface between the driver and Subroutine DPREPI. Tasks performed here are:

dlhin(3f) - [M_odepack] compute step size H0 to be attempted on the first step, when the user supplied value is absent

dlhin(3f) - [M_odepack] compute step size H0 to be attempted on the first step, when the user supplied value is absent

DLSODA solves the initial value problem for stiff or nonstiff systems of first order ODEs of the form

DLSODA solves the initial value problem for stiff or nonstiff systems of first order ODEs of the form

DLSODAR solves the initial value problem for stiff or nonstiff systems of first order ODEs of the form

DLSODAR solves the initial value problem for stiff or nonstiff systems of first order ODEs of the form

DLSODE solves the initial-value problem for stiff or nonstiff systems of first-order ODE’s,

DLSODE solves the initial-value problem for stiff or nonstiff systems of first-order ODE’s,

DLSODES solves the initial value problem for stiff or nonstiff systems of first order ODEs,

DLSODES solves the initial value problem for stiff or nonstiff systems of first order ODEs,

DLSODI solves the initial value problem for linearly implicit systems of first order ODEs,

DLSODI solves the initial value problem for linearly implicit systems of first order ODEs,

DLSODIS solves the initial value problem for linearly implicit systems of first order ODEs,

DLSODIS solves the initial value problem for linearly implicit systems of first order ODEs,

DLSODKR: Livermore Solver for Ordinary Differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with Rootfinding.

DLSODKR: Livermore Solver for Ordinary Differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with Rootfinding.

DLSODPK: Livermore Solver for Ordinary Differential equations, with Preconditioned Krylov iteration methods for the Newton correction linear systems.

DLSODPK: Livermore Solver for Ordinary Differential equations, with Preconditioned Krylov iteration methods for the Newton correction linear systems.

DLSOIBT: Livermore Solver for Ordinary differential equations given in Implicit form, with Block-Tridiagonal Jacobian treatment.

DLSOIBT: Livermore Solver for Ordinary differential equations given in Implicit form, with Block-Tridiagonal Jacobian treatment.

This function routine computes the weighted max-norm of the vector of length N contained in the array V, with weights contained in the array w of length N: DMNORM = MAX(i=1,…,N) ABS(V(i))*W(i)

This function routine computes the weighted max-norm of the vector of length N contained in the array V, with weights contained in the array w of length N: DMNORM = MAX(i=1,…,N) ABS(V(i))*W(i)

dnrm2(3f) - [M_odepack::matrix] Compute the Euclidean length (L2 norm) of a vector.

This routine orthogonalizes the vector VNEW against the previous KMP vectors in the V array. It uses a modified Gram-Schmidt orthogonalization procedure with conditional reorthogonalization. This is the version of 28 may 1986.

This routine computes the solution to the system A*x = b using a preconditioned version of the Conjugate Gradient algorithm. It is assumed here that the matrix A and the preconditioner matrix M are symmetric positive definite or nearly so.

This routine computes the solution to the system A*x = b using a scaled preconditioned version of the Conjugate Gradient algorithm.

DPJIBT is called by DSTODI to compute and process the matrix P = A - HEL(1)J, where J is an approximation to the Jacobian dr/dy, and r = g(t,y) - A(t,y)*s.

DPJIBT is called by DSTODI to compute and process the matrix P = A - HEL(1)J, where J is an approximation to the Jacobian dr/dy, and r = g(t,y) - A(t,y)*s.

DPKSET is called by DSTODPK to interface with the user-supplied routine JAC, to compute and process relevant parts of the matrix P = I - HEL(1)J, where J is the Jacobian df/dy, as need for preconditioning matrix operations later.

This routine performs preprocessing related to the sparse linear systems that must be solved if MITER = 1 or 2.

This routine performs preprocessing related to the sparse linear systems that must be solved if MITER = 1 or 2.

This routine performs preprocessing related to the sparse linear systems that must be solved.

This routine performs preprocessing related to the sparse linear systems that must be solved.

DPREPJ is called by DSTODE to compute and process the matrix P = I - hel(1)J , where J is an approximation to the Jacobian.

DPREPJ is called by DSTODE to compute and process the matrix P = I - hel(1)J , where J is an approximation to the Jacobian.

DPREPJI is called by DSTODI to compute and process the matrix P = A - HEL(1)J, where J is an approximation to the Jacobian dr/dy, where r = g(t,y) - A(t,y)*s.

DPREPJI is called by DSTODI to compute and process the matrix P = A - HEL(1)J, where J is an approximation to the Jacobian dr/dy, where r = g(t,y) - A(t,y)*s.

DPRJA is called by DSTODA to compute and process the matrix P = I - HEL(1)J, where J is an approximation to the Jacobian.

DPRJA is called by DSTODA to compute and process the matrix P = I - HEL(1)J, where J is an approximation to the Jacobian.

DPRJIS is called to compute and process the matrix P = A - HEL(1)J, where J is an approximation to the Jacobian dr/dy, where r = g(t,y) - A(t,y)*s.

DPRJIS is called to compute and process the matrix P = A - HEL(1)J, where J is an approximation to the Jacobian dr/dy, where r = g(t,y) - A(t,y)*s.

DPRJS is called to compute and process the matrix P = I - HEL(1)J, where J is an approximation to the Jacobian. J is computed by columns, either by the user-supplied routine JAC if MITER = 1, or by finite differencing if MITER = 2.

DPRJS is called to compute and process the matrix P = I - HEL(1)J, where J is an approximation to the Jacobian. J is computed by columns, either by the user-supplied routine JAC if MITER = 1, or by finite differencing if MITER = 2.

This routine checks for the presence of a root in the vicinity of the current T, in a manner depending on the input flag JOB. It calls Subroutine DROOTS to locate the root as precisely as possible.

This routine checks for the presence of a root in the vicinity of the current T, in a manner depending on the input flag JOB. It calls Subroutine DROOTS to locate the root as precisely as possible.

This subroutine finds the leftmost root of a set of arbitrary functions gi(x) (i = 1,…,NG) in an interval (X0,X1). Only roots of odd multiplicity (i.e. changes of sign of the gi) are found. Here the sign of X1 - X0 is arbitrary, but is constant for a given problem, and -leftmost- means nearest to X0. The values of the vector-valued function g(x) = (gi, i=1…NG) are communicated through the call sequence of DROOTS. The method used is the Illinois algorithm.

dscal(3f) - [M_odepack::matrix] Multiply a vector by a constant.

dscal(3f) - [M_odepack::matrix] Multiply a vector by a constant.

DSETPK is called by DSTOKA to interface with the user-supplied routine JAC, to compute and process relevant parts of the matrix P = I - HEL(1)J, where J is the Jacobian df/dy, as need for preconditioning matrix operations later.

This routine acts as an interface between the core integrator routine and the DSOLBT routine for the solution of the linear system arising from chord iteration. Communication with DSLSBT uses the following variables:

This routine acts as an interface between the core integrator routine and the DSOLBT routine for the solution of the linear system arising from chord iteration. Communication with DSLSBT uses the following variables:

Solution of block-tridiagonal linear system. Coefficient matrix must have been previously processed by DDECBT. M, N, A,B,C, and IP must not have been changed since call to DDECBT. Written by A. C. Hindmarsh.

This routine interfaces to one of DSPIOM, DSPIGMR, DPCG, DPCGS, or DUSOL, for the solution of the linear system arising from a Newton iteration. It is called if MITER .ne. 0. In addition to variables described elsewhere, communication with DSOLPK uses the following variables:

This routine manages the solution of the linear system arising from a chord iteration. It is called if MITER .ne. 0.

This routine manages the solution of the linear system arising from a chord iteration. It is called if MITER .ne. 0.

This routine manages the solution of the linear system arising from a chord iteration. It is called if MITER .ne. 0.

This routine manages the solution of the linear system arising from a chord iteration. It is called if MITER .ne. 0.

This routine solves the linear system A * x = b using a scaled preconditioned version of the Generalized Minimal Residual method. An initial guess of x = 0 is assumed.

This routine solves the linear system A * x = b using a scaled preconditioned version of the Incomplete Orthogonalization Method. An initial guess of x = 0 is assumed.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, type(dlsa01)::DLSA, DLSR01, which are used internally by one or more ODEPACK solvers.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, type(dlsa01)::DLSA, DLSR01, which are used internally by one or more ODEPACK solvers.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, DLSR01, DLPK01, which are used internally by the DLSODKR solver.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, DLSR01, DLPK01, which are used internally by the DLSODKR solver.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, type(DLSA01)::DLSA, which are used internally by one or more ODEPACK solvers.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, type(DLSA01)::DLSA, which are used internally by one or more ODEPACK solvers.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, DLSS01, which are used internally by one or more ODEPACK solvers.

This routine saves or restores (depending on JOB) the contents of the Common blocks DLS001, DLSS01, which are used internally by one or more ODEPACK solvers.

dsrcom(3f) - [M_odepack] Save/restore ODEPACK COMMON blocks.

dsrcom(3f) - [M_odepack] Save/restore ODEPACK COMMON blocks.

This routine saves or restores (depending on JOB) the contents of the internal types used internally by the DLSODPK solver.

This routine saves or restores (depending on JOB) the contents of the internal types used internally by the DLSODPK solver.

DSTODA performs one step of the integration of an initial value problem for a system of ordinary differential equations.

DSTODA performs one step of the integration of an initial value problem for a system of ordinary differential equations.

dstode(3f) - [M_odepack] Performs one step of an ODEPACK integration.

dstode(3f) - [M_odepack] Performs one step of an ODEPACK integration.

DSTODI performs one step of the integration of an initial value problem for a system of Ordinary Differential Equations.

DSTODI performs one step of the integration of an initial value problem for a system of Ordinary Differential Equations.

DSTODPK performs one step of the integration of an initial value problem for a system of Ordinary Differential Equations.

DSTODPK performs one step of the integration of an initial value problem for a system of Ordinary Differential Equations.

DSTOKA performs one step of the integration of an initial value problem for a system of Ordinary Differential Equations.

DSTOKA performs one step of the integration of an initial value problem for a system of Ordinary Differential Equations.

This routine solves the linear system A * x = b using only a call to the user-supplied routine PSOL (no Krylov iteration). If the norm of the right-hand side vector b is smaller than DELTA, the vector X returned is X = b (if MNEWT = 0) or X = 0 otherwise. PSOL is called with an LR argument of 0.

dvnorm(3f) - [M_odepack] Weighted root-mean-square vector norm.

dvnorm(3f) - [M_odepack] Weighted root-mean-square vector norm.

idamax(3f) - [M_odepack::matrix] Find the smallest index of that component of a vector having the maximum magnitude.

ixsav(3f) - [M_odesave::matrix] Save and recall error message control parameters.

This subroutine constructs groupings of the column indices of the Jacobian matrix, used in the numerical evaluation of the Jacobian by finite differences.

This subroutine constructs groupings of the column indices of the Jacobian matrix, used in the numerical evaluation of the Jacobian by finite differences.

md – minimum degree algorithm (based on element model)

mdi – initialization

mdm – form element from uneliminated neighbors of vk

mdp – purge inactive elements and do mass elimination

mdu – update degrees of uneliminated vertices in ek

nnfc(3f) - [M_odepack] numerical LDU-factorization of sparse nonsymmetric matrix

numeric solution of the transpose of a sparse nonsymmetric system of linear equations given lu-factorization (compressed pointer storage)

nia - p - at the kth step, p is a linked list of the reordered - column indices of the kth row of a. p(n+1) points - to the first entry in the list. - size = n+1. nia - jar - at the kth step,jar contains the elements of the - reordered column indices of a. - size = n. fia - ar - at the kth step, ar contains the elements of the - reordered row of a. - size = n.

odrv(3f) [M_odepack] - driver for sparse matrix reordering routines

odrv(3f) [M_odepack] - driver for sparse matrix reordering routines

sro – symmetric reordering of sparse symmetric matrix

xerrwd(3f) - [M_odepack::Matrix] Write error message with values.

xerrwd(3f) - [M_odepack::Matrix] Write error message with values.

xsetf(3f) - [M_odepack::matrix] Reset the error print control flag.

xsetf(3f) - [M_odepack::matrix] Reset the error print control flag.

xsetun(3f) - [M_odepack::matrix] Reset the logical unit number for error messages.

xsetun(3f) - [M_odepack::matrix] Reset the logical unit number for error messages.