itpack.h File Reference

Declarations of functions from itpack. More...

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Functions
int	jcg_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	jsi_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	sor_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	ssorcg_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	ssorsi_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	rscg_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	rssi_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, integer *iwksp, integer *nw, doublereal *wksp, integer *iparm, doublereal *rparm, integer *ierr)
int	itjcg_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *u1, doublereal *d__, doublereal *d1, doublereal *dtwd, doublereal *tri)
int	itjsi_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *u1, doublereal *d__, integer *icnt)
int	itsor_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *wk)
int	itsrcg_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *u1, doublereal *c__, doublereal *c1, doublereal *d__, doublereal *dl, doublereal *wk, doublereal *tri)
int	itsrsi_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *u1, doublereal *c__, doublereal *d__, doublereal *ctwd, doublereal *wk)
int	itrscg_ (integer *n, integer *nnb, integer *ia, integer *ja, doublereal *a, doublereal *ub, doublereal *ub1, doublereal *db, doublereal *db1, doublereal *wb, doublereal *tri)
int	itrssi_ (integer *n, integer *nnb, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *ub, doublereal *ub1, doublereal *db)
integer	bisrch_ (integer *n, integer *k, integer *l)
doublereal	cheby_ (doublereal *qa, doublereal *qt, doublereal *rrr, integer *ip, doublereal *cme, doublereal *sme)
int	chgcon_ (doublereal *tri, doublereal *gamold, doublereal *rhoold, integer *ibmth)
int	chgsi_ (doublereal *dtnrm, integer *ibmth)
logical	chgsme_ (doublereal *oldnrm, integer *icnt)
int	daxpy_ (integer *n, doublereal *da, doublereal *dx, integer *incx, doublereal *dy, integer *incy)
int	dcopy_ (integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy)
doublereal	ddot_ (integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy)
doublereal	determ_ (integer *n, doublereal *tri, doublereal *xlmda)
int	dfault_ (integer *iparm, doublereal *rparm)
int	echall_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, integer *iparm, doublereal *rparm, integer *icall)
int	echout_ (integer *iparm, doublereal *rparm, integer *imthd)
doublereal	eigvns_ (integer *n, doublereal *tri, doublereal *d__, doublereal *e2, integer *ier)
doublereal	eigvss_ (integer *n, doublereal *tri, doublereal *start, doublereal *zeta, integer *itmax, integer *ier)
int	eqrt1s_ (doublereal *d__, doublereal *e2, integer *nn, integer *m, integer *isw, integer *ierr)
integer	ipstr_ (doublereal *omega)
int	iterm_ (integer *nn, doublereal *a, doublereal *u, doublereal *wk, integer *imthdd)
int	ivfill_ (integer *n, integer *iv, integer *ival)
int	omeg_ (doublereal *dnrm, integer *iflag)
logical	omgchg_ (integer *ndummy)
logical	omgstr_ (integer *ndummy)
int	parcon_ (doublereal *dtnrm, doublereal *c1, doublereal *c2, doublereal *c3, doublereal *c4, doublereal *gamold, doublereal *rhotmp, integer *ibmth)
int	parsi_ (doublereal *c1, doublereal *c2, doublereal *c3, integer *ibmth)
doublereal	pbeta_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *v, doublereal *w1, doublereal *w2)
int	pbsor_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *rhs)
int	permat_ (integer *nn, integer *ia, integer *ja, doublereal *a, integer *p, integer *newia, integer *isym, integer *level, integer *nout, integer *ierr)
int	perror_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *w, doublereal *digtt1, doublereal *digtt2, integer *idgtts)
int	pervec_ (integer *n, doublereal *v, integer *p)
int	pfsor_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *rhs)
int	pfsor1_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *rhs)
int	pjac_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *rhs)
int	pmult_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *w)
int	prbndx_ (integer *nn, integer *nblack, integer *ia, integer *ja, integer *p, integer *ip, integer *level, integer *nout, integer *ier)
int	prsblk_ (integer *nnb, integer *nnr, integer *ia, integer *ja, doublereal *a, doublereal *ur, doublereal *vb)
int	prsred_ (integer *nnb, integer *nnr, integer *ia, integer *ja, doublereal *a, doublereal *ub, doublereal *vr)
int	pssor1_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *u, doublereal *rhs, doublereal *fr, doublereal *br)
int	pstop_ (integer *n, doublereal *u, doublereal *dnrm, doublereal *ccon, integer *iflag, logical *q1)
doublereal	pvtbv_ (integer *n, integer *ia, integer *ja, doublereal *a, doublereal *v)
int	qsort_ (integer *nn, integer *key, doublereal *data, integer *error)
int	sbagn_ (integer *n, integer *nz, integer *ia, integer *ja, doublereal *a, integer *iwork, integer *levell, integer *noutt, integer *ierr)
int	sbelm_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, integer *iw, doublereal *rw, doublereal *tol, integer *isym, integer *level, integer *nout, integer *ier)
int	sbend_ (integer *nn, integer *nz, integer *ia, integer *ja, doublereal *a, integer *iwork)
int	sbini_ (integer *nn, integer *nz, integer *ia, integer *ja, doublereal *a, integer *iwork)
int	sbsij_ (integer *nn, integer *nz, integer *ia, integer *ja, doublereal *a, integer *iwork, integer *ii, integer *jj, doublereal *vall, integer *mode, integer *levell, integer *noutt, integer *ierr)
int	scal_ (integer *nn, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *d__, integer *level, integer *nout, integer *ier)
int	sum3_ (integer *n, doublereal *c1, doublereal *x1, doublereal *c2, doublereal *x2, doublereal *c3, doublereal *x3)
doublereal	tau_ (integer *ii)
E_f	timer_ (real *timdmy)
logical	tstchg_ (integer *ibmth)
int	unscal_ (integer *n, integer *ia, integer *ja, doublereal *a, doublereal *rhs, doublereal *u, doublereal *d__)
int	vevmw_ (integer *n, doublereal *v, doublereal *w)
int	vevpw_ (integer *n, doublereal *v, doublereal *w)
int	vfill_ (integer *n, doublereal *v, doublereal *val)
int	vout_ (integer *n, doublereal *v, integer *iswt, integer *noutt)
int	wevmw_ (integer *n, doublereal *v, doublereal *w)
int	zbrent_ (integer *n, doublereal *tri, doublereal *eps, integer *nsig, doublereal *aa, doublereal *bb, integer *maxfnn, integer *ier)

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Detailed Description

Declarations of functions from itpack.

The following are the common parameters that are used when calling functions. Note: Variables names are consistent with itpack to prevent confusion.

nn Order of linear system a Row pointers used in compressed row storage format m ja Column indices used in compressed row storage format

Parameters:

	a	Nonzero entries in compressed row storage format
	rhs	Right hand side of linear system
	u	Initial guess of solution. holds solution on output
	iwksp	Vector of length 3*nn. on output: holds permutation vector, its inverse, and integer workspace
	nw	On input: length of wksp, on output: actual amount used
	wksp	Vector used for real working space. must be at least nw in length
	iparm	Vector of length 12 used to initialize various parameters on input
	rparm	Vector of length 12 used to initialize various parameters on input
	ierr	Error flag, on output: zero=no error, non-zero=error condition
	nz	Number of non-zero entries in matrix
	iwork	Vector of length nz. matrix creation workspace
	i	Matrix index
	j	Matrix index
	value	Matrix entry
	mode	Type of matrix building
	level	Error reporting flag
	nout	Error reporting location
	ier	Error flag for matrix building

Definition in file itpack.h.

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Function Documentation

integer bisrch_ (  integer *  n, integer *  k, integer *  l )

Function which uses a bisection search to find the entry j in the array k such that the value l is greater than or equal to k[j] and strictly less than k[j+1] Parameters: n  since of array k  integer array to search l  searching criterion

doublereal cheby_ (  doublereal *  qa, doublereal *  qt, doublereal *  rrr, integer *  ip, doublereal *  cme, doublereal *  sme )

Computes the solution to the chebyshev equation Parameters: qa  ratio of pseudo-residuals qt  virtual spectral radius rrr  adaptive parameter ip  number of iterations since last change of parameters cme  estimate for largest eigen-value of iteration matrix sme  estimate for smallest eigen-value of iteration matrix

int chgcon_ (  doublereal *  tri, doublereal *  gamold, doublereal *  rhoold, integer *  ibmth )

Computes estimate for largest eigenvalue for conjugate gradient acceleration Parameters: tri  tridiagonal matrix associated with the eigenvalues of the conjugate gradient polynomial gamold  previous value of acceleration parameters rhoold  previous value of acceleration parameters ibmth  flag indicating method being accelerated by conjugate gradient 1 - jacobian 2 - reduced system 3 - ssor

int chgsi_ (  doublereal *  dtnrm, integer *  ibmth )

Computes new chebyshev acceleration parameters adaptively Parameters: dtnrm  numerator or rayleigh quotient ibmth  indicator of basic method being accelerated by si 1 = jacobi 2 = reduced system 3 = symmetric sor

logical chgsme_ (  doublereal *  oldnrm, integer *  icnt )

Tests for jacobi si whether sme should be changed when caseII = false if the test is positive, the new value of sme is computed Parameters: oldnrm  square of the norm of the pseudo-residual at the last iteration icnt  number of iterations since last change of parameters

int daxpy_ (  integer *  n, doublereal *  da, doublereal *  dx, integer *  incx, doublereal *  dy, integer *  incy )

Overwrite double precision dy with double precision da*dx + dy Parameters: n  length of da da  array of da values dx  array of dx values incx  increment size for dx array dy  array of dy values incy  increment size for dy array

int dcopy_ (  integer *  n, doublereal *  dx, integer *  incx, doublereal *  dy, integer *  incy )

Copy dx to dy Parameters: n  length of dx dx  array of values incx  increment size for dx array dy  array of values incy  increment size for dy array

doublereal ddot_ (  integer *  n, doublereal *  dx, integer *  incx, doublereal *  dy, integer *  incy )

Returns dot product of dx and dy Parameters: n  length of dx dx  array of values incx  increment size for dx array dy  array of values incy  increment size for dy array

doublereal determ_ (  integer *  n, doublereal *  tri, doublereal *  xlmda )

Subroutine that computes the determinant of a symmetric tridiagonal matrix given by tri. det(tri - xlmda*i) = 0 Parameters: n  order of tridiagonal system tri  symmetric tridiagonal matrix of order n xlmda  argument for characteristic equation

int dfault_ (  integer *  iparm, doublereal *  rparm )

Obtain default parameters Parameters: iparm  array of 12 integer parameters rparm  array of 12 double parameters

int echall_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, integer *  iparm, doublereal *  rparm, integer *  icall )

This routine initializes the itpack common blocks from the information contained in IPARM and RPARM. echall_ also prints the values of all the parameters in IPARM and RPARM Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system iparm  integer array of parameters rparm  doublereal array of parameters icall  indicator of which parameters are being printed Note: in this implementation...all printing is disabled

int echout_ (  integer *  iparm, doublereal *  rparm, integer *  imthd )

This routine initiazes the itpack common blocks from IPARM and RPARM Parameters: iparm  integer array of parameters rparm  doublereal array of parameters imthd  indicator of method 1 = jcg 2 = jsi 3 = sor 4 = ssorcg 5 = ssorsi 6 = rscg 7 = rssi

doublereal eigvns_ (  integer *  n, doublereal *  tri, doublereal *  d__, doublereal *  e2, integer *  ier )

Computes the largest eigenvalue of symmetric tridiagnoncal matrix for conjugate gradient acceleration Parameters: n  order of tridiagonal system tri  symmetric tridiagonal matrix of order n d__  array of eqrt1s (negative diagonal elements) e2  array of eqrt1s (super diagonal elements) ier  error flag (0 = success)

doublereal eigvss_ (  integer *  n, doublereal *  tri, doublereal *  start, doublereal *  zeta, integer *  itmax, integer *  ier )

Computes the largest eigenvalue of a symmetric tridiagonal matrix for conjugate gradient acceleration modified imsl routine zbrent is used Parameters: n  order of tridiagonal system tri  symmetric tridiagonal matrix of order n start  initial lower bound of interval containing root zeta  stopping criteria itmax  maximum number of iterations ier  error flag (0 = success)

int eqrt1s_ (  doublereal *  d__, doublereal *  e2, integer *  nn, integer *  m, integer *  isw, integer *  ierr )

Smallest or largest m eigenvalue of a symmetric tridiagonal matrix Parameters: d__  input vector of lenght n, contains diagonal elements of matrix the computed eigenvalues replace the first m components e2  input vector of lenght n containing the squares of the off-diagonal elements of the matrix nn  order of the matrix m  number of smallest eigenvalues desired isw  positive definite flag (0 = not pd, 1 = pd) ierr  error flag (601 = interates not monotone increasing, 602 = not really pd)

integer ipstr_ (  doublereal *  omega  )

Finds the smallest integer, ipstr, greater than 5 such that ipstr * (omega-1)**(ipstr-1) <= 0.5 Parameters: omega  relaxation factor for sor method

int iterm_ (  integer *  nn, doublereal *  a, doublereal *  u, doublereal *  wk, integer *  imthdd )

This routine produces teh iteration summary line at the end of each iteration if level = 5, the latest approx to the solution is printed Parameters: nn  order of system a  iteration matrix u  solution estimate wk  work array of length nn imthdd  indicator of method 1 = jcg 2 = jsi 3 = sor 4 = ssorcg 5 = ssorsi 6 = rscg 7 = rssi

int itjcg_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  u1, doublereal *  d__, doublereal *  d1, doublereal *  dtwd, doublereal *  tri )

Performs one iteration of the jacobian conjugate gradiant method Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values u  input version of solution vector u1  value of solution vector at the end of the in-1 iteration, gets filled with newest estimate d__  solution vector, gets filled with pseudo-residual vector after in iterations d1  pseudo-residual vector after in-1 iterations, gets filled with newest pseudo-residual vector dtwd  used in computation of acceleration parameeter gamma and the pseudo-residual tri  stores the tridiagonal matrix associated with the eigenvalues of the conjugate gradient ploynomial

int itjsi_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  u1, doublereal *  d__, integer *  icnt )

Performs one iteration of the jacobian semi-iteration method Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of linear system u  solution estimate at in iterations u1  value of solution vector at the end of the in-1 iteration, gets filled with newest estimate d__  solution vector, gets filled with pseudo-residual vector after in iterations icnt  number of iterations since last change in solution estimate

int itrscg_ (  integer *  n, integer *  nnb, integer *  ia, integer *  ja, doublereal *  a, doublereal *  ub, doublereal *  ub1, doublereal *  db, doublereal *  db1, doublereal *  wb, doublereal *  tri )

Performs one iteration of the reduced system conjugate gradient method Parameters: n  Order of linear system nnb  Number of black points ia  array of row offsets ja  array of column indices a  array of matrix values ub  estimate for the solution of black points after in iterations ub1  estimate for the solution of black points after in-1 iterations, filled with in+1 values db  pseudo-residual of black points after in iterations db1  pseudo-residual of black points after in-1 iterations, filled with in+1 values wb  used in computation involving black vector tri  stores the tridiagonal matrix associated with the eigenvalues of the conjugate gradient ploynomial

int itrssi_ (  integer *  n, integer *  nnb, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  ub, doublereal *  ub1, doublereal *  db )

Performs one iteration of the reduced system semi-iteration method Parameters: n  Order of linear system nnb  Number of black points ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of linear system ub  estimate for the solution of black points after in iterations ub1  pseudo-residual of black points after in-1 iterations, filled with in+1 values db  current residual

int itsor_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  wk )

Performs one iteration of the successive overrelaxation method Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of linear system u  solution estimate array wk  work array of length nn

int itsrcg_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  u1, doublereal *  c__, doublereal *  c1, doublereal *  d__, doublereal *  dl, doublereal *  wk, doublereal *  tri )

Performs one iteration of the symmetric successive overrelaxation conjugate gradient method Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of linear system u  solution estimate at in iterations, u1  value of solution vector at the end of the in-1 iteration, gets filled with newest estimate c__  forward residual after in iterations c1  forward residual after in-1 iterations, filled with in+1 values d__  used to compute backward pseudo-residual for current iteration dl  used in computation of acceleration parameters wk  work array of length nn tri  stores the tridiagonal matrix associated with the eigenvalues of the conjugate gradient ploynomial

int itsrsi_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  u1, doublereal *  c__, doublereal *  d__, doublereal *  ctwd, doublereal *  wk )

Performs one iteration of the symmetric successive overrelaxation semi-iteration method Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of linear system u  solution estimate at in-1 iterations u1  value of solution vector at the end of the in-1 iteration, gets filled with newest estimate c__  used to compute forward pseudo-residual vector d__  used to compute backward pseudo-residual vector ctwd  used in computation of acceleration parameters wk  work array of length nn

int ivfill_ (  integer *  n, integer *  iv, integer *  ival )

Fill integer array with a value Parameters: n  number of elements in array iv  pointer to integer array ival  value to fill array with

int jcg_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Jacobian conjugate gradient Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int jsi_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Jacobian semi-iteration Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int omeg_ (  doublereal *  dnrm, integer *  iflag )

logical omgchg_ (  integer *  ndummy  )

logical omgstr_ (  integer *  ndummy  )

int parcon_ (  doublereal *  dtnrm, doublereal *  c1, doublereal *  c2, doublereal *  c3, doublereal *  c4, doublereal *  gamold, doublereal *  rhotmp, integer *  ibmth )

int parsi_ (  doublereal *  c1, doublereal *  c2, doublereal *  c3, integer *  ibmth )

doublereal pbeta_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  v, doublereal *  w1, doublereal *  w2 )

int pbsor_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  rhs )

int permat_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, integer *  p, integer *  newia, integer *  isym, integer *  level, integer *  nout, integer *  ierr )

int perror_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  w, doublereal *  digtt1, doublereal *  digtt2, integer *  idgtts )

int pervec_ (  integer *  n, doublereal *  v, integer *  p )

int pfsor1_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  rhs )

int pfsor_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  rhs )

int pjac_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  rhs )

int pmult_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  w )

int prbndx_ (  integer *  nn, integer *  nblack, integer *  ia, integer *  ja, integer *  p, integer *  ip, integer *  level, integer *  nout, integer *  ier )

int prsblk_ (  integer *  nnb, integer *  nnr, integer *  ia, integer *  ja, doublereal *  a, doublereal *  ur, doublereal *  vb )

int prsred_ (  integer *  nnb, integer *  nnr, integer *  ia, integer *  ja, doublereal *  a, doublereal *  ub, doublereal *  vr )

int pssor1_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  u, doublereal *  rhs, doublereal *  fr, doublereal *  br )

int pstop_ (  integer *  n, doublereal *  u, doublereal *  dnrm, doublereal *  ccon, integer *  iflag, logical *  q1 )

doublereal pvtbv_ (  integer *  n, integer *  ia, integer *  ja, doublereal *  a, doublereal *  v )

int qsort_ (  integer *  nn, integer *  key, doublereal *  data, integer *  error )

int rscg_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Reduced system conjugate gradient Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int rssi_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Reduced system semi-iteration Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int sbagn_ (  integer *  n, integer *  nz, integer *  ia, integer *  ja, doublereal *  a, integer *  iwork, integer *  levell, integer *  noutt, integer *  ierr )

Convert compressed row matrix back to linked-list representation used for adding entires

int sbelm_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, integer *  iw, doublereal *  rw, doublereal *  tol, integer *  isym, integer *  level, integer *  nout, integer *  ier )

int sbend_ (  integer *  nn, integer *  nz, integer *  ia, integer *  ja, doublereal *  a, integer *  iwork )

Finalize matrix storage format Parameters: nn  order of matrix nz  maximum number of non-zero values ia  array of row offsets ja  array of column indices a  array of matrix values iwork  workspace array used by itpack

int sbini_ (  integer *  nn, integer *  nz, integer *  ia, integer *  ja, doublereal *  a, integer *  iwork )

Initialize sparse matrix storage Parameters: nn  order of matrix nz  maximum number of non-zero values ia  array of row offsets ja  array of column indices a  array of matrix values iwork  workspace array used by itpack

int sbsij_ (  integer *  nn, integer *  nz, integer *  ia, integer *  ja, doublereal *  a, integer *  iwork, integer *  ii, integer *  jj, doublereal *  vall, integer *  mode, integer *  levell, integer *  noutt, integer *  ierr )

Insert entry into sparse matrix Parameters: nn  order of matrix nz  maximum number of non-zero values ia  array of row offsets ja  array of column indices a  array of matrix values iwork  workspace array used by itpack ii  row index of value to add jj  column index of value to add vall  value to add mode  flag for type of adding to be done levell  specifier for level of output noutt  specifier for output ierr  holds error flag on return

int scal_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  d__, integer *  level, integer *  nout, integer *  ier )

int sor_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Successive overrelaxation Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int ssorcg_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Symmetric successive overrelaxation conjugate gradient Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int ssorsi_ (  integer *  nn, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, integer *  iwksp, integer *  nw, doublereal *  wksp, integer *  iparm, doublereal *  rparm, integer *  ierr )

Symmetric successive overrelaxation semi-iteration Parameters: nn  Order of linear system ia  array of row offsets ja  array of column indices a  array of matrix values rhs  array of right hand side of system u  solution array iwksp  int array used by itpack for calculations nw  size of iwskp and wksp wksp  double array used by itpack for calculations iparm  array of 12 integer parameters rparm  array of 12 double parameters ierr  holds error flag on return

int sum3_ (  integer *  n, doublereal *  c1, doublereal *  x1, doublereal *  c2, doublereal *  x2, doublereal *  c3, doublereal *  x3 )

doublereal tau_ (  integer *  ii  )

E_f timer_ (  real *  timdmy  )

logical tstchg_ (  integer *  ibmth  )

int unscal_ (  integer *  n, integer *  ia, integer *  ja, doublereal *  a, doublereal *  rhs, doublereal *  u, doublereal *  d__ )

int vevmw_ (  integer *  n, doublereal *  v, doublereal *  w )

int vevpw_ (  integer *  n, doublereal *  v, doublereal *  w )

int vfill_ (  integer *  n, doublereal *  v, doublereal *  val )

Fill all entires of nn-sized array u with value Parameters: n  size of array v  array val  value to fill array with

int vout_ (  integer *  n, doublereal *  v, integer *  iswt, integer *  noutt )

int wevmw_ (  integer *  n, doublereal *  v, doublereal *  w )

int zbrent_ (  integer *  n, doublereal *  tri, doublereal *  eps, integer *  nsig, doublereal *  aa, doublereal *  bb, integer *  maxfnn, integer *  ier )

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