ROOT 6.13/01 Reference Guide |
Sparse Symmetric Decomposition class.
Solve a sparse symmetric system of linear equations using a method based on Gaussian elimination as discussed in Duff and Reid, ACM Trans. Math. Software 9 (1983), 302-325.
Definition at line 43 of file TDecompSparse.h.
Public Member Functions | |
TDecompSparse () | |
Default constructor. More... | |
TDecompSparse (Int_t nRows, Int_t nr_nonZeros, Int_t verbose) | |
Constructor for a matrix with nrows and unspecified number of columns . More... | |
TDecompSparse (Int_t row_lwb, Int_t row_upb, Int_t nr_nonZeros, Int_t verbose) | |
Constructor for a matrix with row range, [row_lwb..row_upb] and unspecified column range . More... | |
TDecompSparse (const TMatrixDSparse &a, Int_t verbose) | |
Constructor for matrix A . More... | |
TDecompSparse (const TDecompSparse &another) | |
Copy constructor. More... | |
virtual | ~TDecompSparse () |
virtual Bool_t | Decompose () |
Decomposition engine . More... | |
virtual void | Det (Double_t &, Double_t &) |
Matrix determinant det = d1*TMath::Power(2.,d2) More... | |
virtual Int_t | GetNcols () const |
virtual Int_t | GetNrows () const |
TDecompSparse & | operator= (const TDecompSparse &source) |
Assignment operator. More... | |
void | Print (Option_t *opt="") const |
Print class members. More... | |
virtual void | SetMatrix (const TMatrixDSparse &a) |
Set matrix to be decomposed . More... | |
void | SetVerbose (Int_t v) |
virtual Bool_t | Solve (TVectorD &b) |
Solve Ax=b . Solution returned in b. More... | |
virtual TVectorD | Solve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | Solve (TMatrixDColumn &) |
virtual Bool_t | TransSolve (TVectorD &b) |
virtual TVectorD | TransSolve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | TransSolve (TMatrixDColumn &) |
Public Member Functions inherited from TDecompBase | |
TDecompBase () | |
Default constructor. More... | |
TDecompBase (const TDecompBase &another) | |
Copy constructor. More... | |
virtual | ~TDecompBase () |
virtual Double_t | Condition () |
Matrix condition number. More... | |
Int_t | GetColLwb () const |
Double_t | GetCondition () const |
Double_t | GetDet1 () const |
Double_t | GetDet2 () const |
Int_t | GetRowLwb () const |
Double_t | GetTol () const |
virtual Bool_t | MultiSolve (TMatrixD &B) |
Solve set of equations with RHS in columns of B. More... | |
TDecompBase & | operator= (const TDecompBase &source) |
Assignment operator. More... | |
void | Print (Option_t *opt="") const |
Print class members. More... | |
Double_t | SetTol (Double_t tol) |
Protected Member Functions | |
Int_t | ErrorFlag () |
virtual const TMatrixDBase & | GetDecompMatrix () const |
Double_t | GetThresholdPivoting () |
Double_t | GetTreatAsZero () |
Int_t | IError () |
void | InitParam () |
initializing control parameters More... | |
Int_t | MinIntWorkspace () |
Int_t | MinRealWorkspace () |
void | SetThresholdPivoting (Double_t piv) |
void | SetTreatAsZero (Double_t tol) |
Protected Member Functions inherited from TDecompBase | |
Int_t | Hager (Double_t &est, Int_t iter=5) |
void | ResetStatus () |
Static Protected Member Functions | |
static void | CopyUpperTriang (const TMatrixDSparse &a, Double_t *b) |
Static function, copying the non-zero entries in the upper triangle to array b . More... | |
static void | Factor (const Int_t n, const Int_t nz, TArrayI &Airn, TArrayI &Aicn, TArrayD &Aa, TArrayI &Aiw, TArrayI &Aikeep, const Int_t nsteps, Int_t &maxfrt, TArrayI &Aiw1, Int_t *icntl, Double_t *cntl, Int_t *info) |
Factorization routine, the workhorse for the decomposition step. More... | |
static void | Factor_sub1 (const Int_t n, const Int_t nz, Int_t &nz1, Double_t *a, const Int_t la, Int_t *irn, Int_t *icn, Int_t *iw, const Int_t liw, Int_t *perm, Int_t *iw2, Int_t *icntl, Int_t *info) |
Help routine for factorization. More... | |
static void | Factor_sub2 (const Int_t n, const Int_t nz, Double_t *a, const Int_t la, Int_t *iw, const Int_t liw, Int_t *perm, Int_t *nstk, const Int_t nsteps, Int_t &maxfrt, Int_t *nelim, Int_t *iw2, Int_t *icntl, Double_t *cntl, Int_t *info) |
Help routine for factorization. More... | |
static void | Factor_sub3 (Double_t *a, Int_t *iw, Int_t &j1, Int_t &j2, const Int_t itop, const Int_t ireal, Int_t &ncmpbr, Int_t &ncmpbi) |
Help routine for factorization. More... | |
static Int_t | IDiag (Int_t ix, Int_t iy) |
static void | InitPivot (const Int_t n, const Int_t nz, TArrayI &Airn, TArrayI &Aicn, TArrayI &Aiw, TArrayI &Aikeep, TArrayI &Aiw1, Int_t &nsteps, const Int_t iflag, Int_t *icntl, Double_t *cntl, Int_t *info, Double_t &ops) |
Setup Pivoting variables. More... | |
static void | InitPivot_sub1 (const Int_t n, const Int_t nz, Int_t *irn, Int_t *icn, Int_t *iw, Int_t *ipe, Int_t *iq, Int_t *flag, Int_t &iwfr, Int_t *icntl, Int_t *info) |
Help routine for pivoting setup. More... | |
static void | InitPivot_sub2 (const Int_t n, Int_t *ipe, Int_t *iw, const Int_t lw, Int_t &iwfr, Int_t *nv, Int_t *nxt, Int_t *lst, Int_t *ipd, Int_t *flag, const Int_t iovflo, Int_t &ncmpa, const Double_t fratio) |
Help routine for pivoting setup. More... | |
static void | InitPivot_sub2a (const Int_t n, Int_t *ipe, Int_t *iw, const Int_t lw, Int_t &iwfr, Int_t &ncmpa) |
Help routine for pivoting setup. More... | |
static void | InitPivot_sub3 (const Int_t n, const Int_t nz, Int_t *irn, Int_t *icn, Int_t *perm, Int_t *iw, Int_t *ipe, Int_t *iq, Int_t *flag, Int_t &iwfr, Int_t *icntl, Int_t *info) |
Help routine for pivoting setup. More... | |
static void | InitPivot_sub4 (const Int_t n, Int_t *ipe, Int_t *iw, const Int_t lw, Int_t &iwfr, Int_t *ips, Int_t *ipv, Int_t *nv, Int_t *flag, Int_t &ncmpa) |
Help routine for pivoting setup. More... | |
static void | InitPivot_sub5 (const Int_t n, Int_t *ipe, Int_t *nv, Int_t *ips, Int_t *ne, Int_t *na, Int_t *nd, Int_t &nsteps, const Int_t nemin) |
Help routine for pivoting setup. More... | |
static void | InitPivot_sub6 (const Int_t n, const Int_t nz, Int_t *irn, Int_t *icn, Int_t *perm, Int_t *na, Int_t *ne, Int_t *nd, const Int_t nsteps, Int_t *lstki, Int_t *lstkr, Int_t *iw, Int_t *info, Double_t &ops) |
Help routine for pivoting setup. More... | |
static Int_t | NonZerosUpperTriang (const TMatrixDSparse &a) |
Static function, returning the number of non-zero entries in the upper triangular matrix . More... | |
static void | Solve (const Int_t n, TArrayD &Aa, TArrayI &Aiw, TArrayD &Aw, const Int_t maxfrt, TVectorD &b, TArrayI &Aiw1, const Int_t nsteps, Int_t *icntl, Int_t *info) |
Main routine for solving Ax=b. More... | |
static void | Solve_sub1 (const Int_t n, Double_t *a, Int_t *iw, Double_t *w, Double_t *rhs, Int_t *iw2, const Int_t nblk, Int_t &latop, Int_t *icntl) |
Help routine for solving. More... | |
static void | Solve_sub2 (const Int_t n, Double_t *a, Int_t *iw, Double_t *w, Double_t *rhs, Int_t *iw2, const Int_t nblk, const Int_t latop, Int_t *icntl) |
Help routine for solving. More... | |
Static Protected Member Functions inherited from TDecompBase | |
static void | DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2) |
Protected Attributes | |
TMatrixDSparse | fA |
Double_t | fCntl [6] |
TArrayI | fColFact |
TArrayD | fFact |
Int_t | fIcntl [31] |
TArrayI | fIkeep |
Int_t | fInfo [21] |
Double_t | fIPessimism |
TArrayI | fIw |
TArrayI | fIw1 |
TArrayI | fIw2 |
Int_t | fMaxfrt |
Int_t | fNnonZeros |
Int_t | fNrows |
Int_t | fNsteps |
Double_t | fPrecision |
TArrayI | fRowFact |
Double_t | fRPessimism |
Int_t | fVerbose |
TArrayD | fW |
Protected Attributes inherited from TDecompBase | |
Int_t | fColLwb |
Double_t | fCondition |
Double_t | fDet1 |
Double_t | fDet2 |
Int_t | fRowLwb |
Double_t | fTol |
Additional Inherited Members | |
Protected Types inherited from TDecompBase | |
enum | { kWorkMax = 100 } |
enum | EMatrixDecompStat { kInit = BIT(14), kPatternSet = BIT(15), kValuesSet = BIT(16), kMatrixSet = BIT(17), kDecomposed = BIT(18), kDetermined = BIT(19), kCondition = BIT(20), kSingular = BIT(21) } |
#include <TDecompSparse.h>
TDecompSparse::TDecompSparse | ( | ) |
Default constructor.
Definition at line 30 of file TDecompSparse.cxx.
TDecompSparse::TDecompSparse | ( | Int_t | nRows, |
Int_t | nr_nonZeros, | ||
Int_t | verbose | ||
) |
Constructor for a matrix with nrows and unspecified number of columns .
nr_nonZeros is the total number of non-zero entries in the matrix .
Definition at line 41 of file TDecompSparse.cxx.
TDecompSparse::TDecompSparse | ( | Int_t | row_lwb, |
Int_t | row_upb, | ||
Int_t | nr_nonZeros, | ||
Int_t | verbose | ||
) |
Constructor for a matrix with row range, [row_lwb..row_upb] and unspecified column range .
nr_nonZeros is the total number of non-zero entries in the matrix .
Definition at line 67 of file TDecompSparse.cxx.
TDecompSparse::TDecompSparse | ( | const TMatrixDSparse & | a, |
Int_t | verbose | ||
) |
Constructor for matrix A .
Definition at line 94 of file TDecompSparse.cxx.
TDecompSparse::TDecompSparse | ( | const TDecompSparse & | another | ) |
Copy constructor.
Definition at line 107 of file TDecompSparse.cxx.
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Definition at line 148 of file TDecompSparse.h.
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Static function, copying the non-zero entries in the upper triangle to array b .
User should allocate enough memory for array b .
Definition at line 139 of file TDecompSparse.cxx.
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Decomposition engine .
If the decomposition succeeds, bit kDecomposed is set .
Implements TDecompBase.
Definition at line 234 of file TDecompSparse.cxx.
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Matrix determinant det = d1*TMath::Power(2.,d2)
Reimplemented from TDecompBase.
Definition at line 169 of file TDecompSparse.h.
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Definition at line 124 of file TDecompSparse.h.
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Factorization routine, the workhorse for the decomposition step.
Definition at line 581 of file TDecompSparse.cxx.
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Help routine for factorization.
Definition at line 1741 of file TDecompSparse.cxx.
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Help routine for factorization.
Definition at line 1883 of file TDecompSparse.cxx.
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Help routine for factorization.
Definition at line 2389 of file TDecompSparse.cxx.
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Implements TDecompBase.
Definition at line 139 of file TDecompSparse.h.
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Implements TDecompBase.
Definition at line 155 of file TDecompSparse.h.
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Implements TDecompBase.
Definition at line 154 of file TDecompSparse.h.
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Definition at line 130 of file TDecompSparse.h.
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Definition at line 131 of file TDecompSparse.h.
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Definition at line 119 of file TDecompSparse.h.
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Definition at line 121 of file TDecompSparse.h.
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initializing control parameters
Definition at line 413 of file TDecompSparse.cxx.
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Setup Pivoting variables.
Definition at line 470 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 836 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 975 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 1305 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 1349 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 1471 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 1548 of file TDecompSparse.cxx.
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Help routine for pivoting setup.
Definition at line 1637 of file TDecompSparse.cxx.
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Definition at line 123 of file TDecompSparse.h.
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Definition at line 122 of file TDecompSparse.h.
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Static function, returning the number of non-zero entries in the upper triangular matrix .
Definition at line 115 of file TDecompSparse.cxx.
TDecompSparse & TDecompSparse::operator= | ( | const TDecompSparse & | source | ) |
Assignment operator.
Definition at line 2702 of file TDecompSparse.cxx.
void TDecompSparse::Print | ( | Option_t * | opt = "" | ) | const |
Print class members.
Definition at line 2686 of file TDecompSparse.cxx.
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Set matrix to be decomposed .
Definition at line 161 of file TDecompSparse.cxx.
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Definition at line 136 of file TDecompSparse.h.
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Definition at line 137 of file TDecompSparse.h.
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Definition at line 150 of file TDecompSparse.h.
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Main routine for solving Ax=b.
Definition at line 738 of file TDecompSparse.cxx.
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Solve Ax=b . Solution returned in b.
Implements TDecompBase.
Definition at line 341 of file TDecompSparse.cxx.
Implements TDecompBase.
Definition at line 161 of file TDecompSparse.h.
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Implements TDecompBase.
Definition at line 162 of file TDecompSparse.h.
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Help routine for solving.
Definition at line 2423 of file TDecompSparse.cxx.
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Help routine for solving.
Definition at line 2553 of file TDecompSparse.cxx.
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Implements TDecompBase.
Definition at line 164 of file TDecompSparse.h.
Implements TDecompBase.
Definition at line 165 of file TDecompSparse.h.
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Implements TDecompBase.
Definition at line 166 of file TDecompSparse.h.
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Definition at line 69 of file TDecompSparse.h.
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Definition at line 50 of file TDecompSparse.h.
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Definition at line 75 of file TDecompSparse.h.
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Definition at line 72 of file TDecompSparse.h.
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Definition at line 49 of file TDecompSparse.h.
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Definition at line 57 of file TDecompSparse.h.
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Definition at line 51 of file TDecompSparse.h.
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Definition at line 65 of file TDecompSparse.h.
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Definition at line 58 of file TDecompSparse.h.
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Definition at line 59 of file TDecompSparse.h.
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Definition at line 60 of file TDecompSparse.h.
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Definition at line 62 of file TDecompSparse.h.
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Definition at line 71 of file TDecompSparse.h.
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Definition at line 70 of file TDecompSparse.h.
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Definition at line 61 of file TDecompSparse.h.
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Definition at line 53 of file TDecompSparse.h.
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Definition at line 74 of file TDecompSparse.h.
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Definition at line 66 of file TDecompSparse.h.
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Definition at line 47 of file TDecompSparse.h.
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Definition at line 63 of file TDecompSparse.h.