kusano 7d535a
kusano 7d535a
<meta content="text/html;charset=UTF-8" http-equiv="Content-Type">
kusano 7d535a
<title>SuperLU: SRC/dgsisx.c File Reference</title>
kusano 7d535a
<link href="doxygen.css" rel="stylesheet" type="text/css">
kusano 7d535a
<link href="tabs.css" rel="stylesheet" type="text/css">
kusano 7d535a
kusano 7d535a
kusano 7d535a
kusano 7d535a
  
kusano 7d535a
    
    kusano 7d535a
          
  • Main Page
  • kusano 7d535a
          
  • Data Structures
  • kusano 7d535a
          
  • Files
  • kusano 7d535a
        
    kusano 7d535a
      
    kusano 7d535a
    kusano 7d535a
    kusano 7d535a

    SRC/dgsisx.c File Reference

    Computes an approximate solutions of linear equations A*X=B or A'*X=B. More...
    kusano 7d535a

    kusano 7d535a
    #include "slu_ddefs.h"
    kusano 7d535a
    kusano 7d535a
    kusano 7d535a

    Functions

    kusano 7d535a
    void dgsisx (superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r, int *etree, char *equed, double *R, double *C, SuperMatrix *L, SuperMatrix *U, void *work, int lwork, SuperMatrix *B, SuperMatrix *X, double *recip_pivot_growth, double *rcond, mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info)
    kusano 7d535a
    kusano 7d535a
    kusano 7d535a

    Detailed Description

    kusano 7d535a
    kusano 7d535a
     -- SuperLU routine (version 4.1) --
    kusano 7d535a
     Lawrence Berkeley National Laboratory.
    kusano 7d535a
     November, 2010
    kusano 7d535a
      

    Function Documentation

    kusano 7d535a
    kusano 7d535a
    kusano 7d535a
    kusano 7d535a
          
    kusano 7d535a
            
    kusano 7d535a
              void dgsisx           
    kusano 7d535a
              (
    kusano 7d535a
              superlu_options_t
    kusano 7d535a
               options, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              SuperMatrix
    kusano 7d535a
               A, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              int * 
    kusano 7d535a
               perm_c, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              int * 
    kusano 7d535a
               perm_r, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              int * 
    kusano 7d535a
               etree, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              char * 
    kusano 7d535a
               equed, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              double * 
    kusano 7d535a
               R, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              double * 
    kusano 7d535a
               C, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              SuperMatrix
    kusano 7d535a
               L, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              SuperMatrix
    kusano 7d535a
               U, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              void * 
    kusano 7d535a
               work, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              int 
    kusano 7d535a
               lwork, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              SuperMatrix
    kusano 7d535a
               B, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              SuperMatrix
    kusano 7d535a
               X, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              double * 
    kusano 7d535a
               recip_pivot_growth, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              double * 
    kusano 7d535a
               rcond, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              mem_usage_t
    kusano 7d535a
               mem_usage, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              SuperLUStat_t
    kusano 7d535a
               stat, 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              
    kusano 7d535a
              int * 
    kusano 7d535a
               info 
    kusano 7d535a
            
    kusano 7d535a
            
    kusano 7d535a
              
    kusano 7d535a
              )
    kusano 7d535a
              
    kusano 7d535a
            
    kusano 7d535a
          
    kusano 7d535a
    kusano 7d535a
    kusano 7d535a
    kusano 7d535a

    kusano 7d535a
    kusano 7d535a
     Purpose
    kusano 7d535a
     =======

    kusano 7d535a
     DGSISX computes an approximate solutions of linear equations
    kusano 7d535a
     A*X=B or A'*X=B, using the ILU factorization from dgsitrf().
    kusano 7d535a
     An estimation of the condition number is provided. 
    kusano 7d535a
     The routine performs the following steps:

    kusano 7d535a
       1. If A is stored column-wise (A->Stype = SLU_NC):

    kusano 7d535a
    	1.1. If options->Equil = YES or options->RowPerm = LargeDiag, scaling
    kusano 7d535a
    	     factors are computed to equilibrate the system:
    kusano 7d535a
    	     options->Trans = NOTRANS:
    kusano 7d535a
    		 diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
    kusano 7d535a
    	     options->Trans = TRANS:
    kusano 7d535a
    		 (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
    kusano 7d535a
    	     options->Trans = CONJ:
    kusano 7d535a
    		 (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
    kusano 7d535a
    	     Whether or not the system will be equilibrated depends on the
    kusano 7d535a
    	     scaling of the matrix A, but if equilibration is used, A is
    kusano 7d535a
    	     overwritten by diag(R)*A*diag(C) and B by diag(R)*B
    kusano 7d535a
    	     (if options->Trans=NOTRANS) or diag(C)*B (if options->Trans
    kusano 7d535a
    	     = TRANS or CONJ).

    kusano 7d535a
    	1.2. Permute columns of A, forming A*Pc, where Pc is a permutation
    kusano 7d535a
    	     matrix that usually preserves sparsity.
    kusano 7d535a
    	     For more details of this step, see sp_preorder.c.

    kusano 7d535a
    	1.3. If options->Fact != FACTORED, the LU decomposition is used to
    kusano 7d535a
    	     factor the matrix A (after equilibration if options->Equil = YES)
    kusano 7d535a
    	     as Pr*A*Pc = L*U, with Pr determined by partial pivoting.

    kusano 7d535a
    	1.4. Compute the reciprocal pivot growth factor.

    kusano 7d535a
    	1.5. If some U(i,i) = 0, so that U is exactly singular, then the
    kusano 7d535a
    	     routine fills a small number on the diagonal entry, that is
    kusano 7d535a
    		U(i,i) = ||A(:,i)||_oo * options->ILU_FillTol ** (1 - i / n),
    kusano 7d535a
    	     and info will be increased by 1. The factored form of A is used
    kusano 7d535a
    	     to estimate the condition number of the preconditioner. If the
    kusano 7d535a
    	     reciprocal of the condition number is less than machine precision,
    kusano 7d535a
    	     info = A->ncol+1 is returned as a warning, but the routine still
    kusano 7d535a
    	     goes on to solve for X.

    kusano 7d535a
    	1.6. The system of equations is solved for X using the factored form
    kusano 7d535a
    	     of A.

    kusano 7d535a
    	1.7. options->IterRefine is not used

    kusano 7d535a
    	1.8. If equilibration was used, the matrix X is premultiplied by
    kusano 7d535a
    	     diag(C) (if options->Trans = NOTRANS) or diag(R)
    kusano 7d535a
    	     (if options->Trans = TRANS or CONJ) so that it solves the
    kusano 7d535a
    	     original system before equilibration.

    kusano 7d535a
    	1.9. options for ILU only
    kusano 7d535a
    	     1) If options->RowPerm = LargeDiag, MC64 is used to scale and
    kusano 7d535a
    		permute the matrix to an I-matrix, that is Pr*Dr*A*Dc has
    kusano 7d535a
    		entries of modulus 1 on the diagonal and off-diagonal entries
    kusano 7d535a
    		of modulus at most 1. If MC64 fails, dgsequ() is used to
    kusano 7d535a
    		equilibrate the system.
    kusano 7d535a
                  ( Default: LargeDiag )
    kusano 7d535a
    	     2) options->ILU_DropTol = tau is the threshold for dropping.
    kusano 7d535a
    		For L, it is used directly (for the whole row in a supernode);
    kusano 7d535a
    		For U, ||A(:,i)||_oo * tau is used as the threshold
    kusano 7d535a
    	        for the	i-th column.
    kusano 7d535a
    		If a secondary dropping rule is required, tau will
    kusano 7d535a
    	        also be used to compute the second threshold.
    kusano 7d535a
                  ( Default: 1e-4 )
    kusano 7d535a
    	     3) options->ILU_FillFactor = gamma, used as the initial guess
    kusano 7d535a
    		of memory growth.
    kusano 7d535a
    		If a secondary dropping rule is required, it will also
    kusano 7d535a
                  be used as an upper bound of the memory.
    kusano 7d535a
                  ( Default: 10 )
    kusano 7d535a
    	     4) options->ILU_DropRule specifies the dropping rule.
    kusano 7d535a
    		Option	      Meaning
    kusano 7d535a
    		======	      ===========
    kusano 7d535a
    		DROP_BASIC:   Basic dropping rule, supernodal based ILUTP(tau).
    kusano 7d535a
    		DROP_PROWS:   Supernodal based ILUTP(p,tau), p = gamma*nnz(A)/n.
    kusano 7d535a
    		DROP_COLUMN:  Variant of ILUTP(p,tau), for j-th column,
    kusano 7d535a
    			      p = gamma * nnz(A(:,j)).
    kusano 7d535a
    		DROP_AREA:    Variation of ILUTP, for j-th column, use
    kusano 7d535a
    			      nnz(F(:,1:j)) / nnz(A(:,1:j)) to control memory.
    kusano 7d535a
    		DROP_DYNAMIC: Modify the threshold tau during factorizaion:
    kusano 7d535a
    			      If nnz(L(:,1:j)) / nnz(A(:,1:j)) > gamma
    kusano 7d535a
    				  tau_L(j) := MIN(tau_0, tau_L(j-1) * 2);
    kusano 7d535a
    			      Otherwise
    kusano 7d535a
    				  tau_L(j) := MAX(tau_0, tau_L(j-1) / 2);
    kusano 7d535a
    			      tau_U(j) uses the similar rule.
    kusano 7d535a
    			      NOTE: the thresholds used by L and U are separate.
    kusano 7d535a
    		DROP_INTERP:  Compute the second dropping threshold by
    kusano 7d535a
    			      interpolation instead of sorting (default).
    kusano 7d535a
    			      In this case, the actual fill ratio is not
    kusano 7d535a
    			      guaranteed smaller than gamma.
    kusano 7d535a
    		DROP_PROWS, DROP_COLUMN and DROP_AREA are mutually exclusive.
    kusano 7d535a
    		( Default: DROP_BASIC | DROP_AREA )
    kusano 7d535a
    	     5) options->ILU_Norm is the criterion of measuring the magnitude
    kusano 7d535a
    		of a row in a supernode of L. ( Default is INF_NORM )
    kusano 7d535a
    		options->ILU_Norm	RowSize(x[1:n])
    kusano 7d535a
    		=================	===============
    kusano 7d535a
    		ONE_NORM		||x||_1 / n
    kusano 7d535a
    		TWO_NORM		||x||_2 / sqrt(n)
    kusano 7d535a
    		INF_NORM		max{|x[i]|}
    kusano 7d535a
    	     6) options->ILU_MILU specifies the type of MILU's variation.
    kusano 7d535a
    		= SILU: do not perform Modified ILU;
    kusano 7d535a
    		= SMILU_1 (not recommended):
    kusano 7d535a
    		    U(i,i) := U(i,i) + sum(dropped entries);
    kusano 7d535a
    		= SMILU_2:
    kusano 7d535a
    		    U(i,i) := U(i,i) + SGN(U(i,i)) * sum(dropped entries);
    kusano 7d535a
    		= SMILU_3:
    kusano 7d535a
    		    U(i,i) := U(i,i) + SGN(U(i,i)) * sum(|dropped entries|);
    kusano 7d535a
    		NOTE: Even SMILU_1 does not preserve the column sum because of
    kusano 7d535a
    		late dropping.
    kusano 7d535a
                  ( Default: SILU )
    kusano 7d535a
    	     7) options->ILU_FillTol is used as the perturbation when
    kusano 7d535a
    		encountering zero pivots. If some U(i,i) = 0, so that U is
    kusano 7d535a
    		exactly singular, then
    kusano 7d535a
    		   U(i,i) := ||A(:,i)|| * options->ILU_FillTol ** (1 - i / n).
    kusano 7d535a
                  ( Default: 1e-2 )

    kusano 7d535a
       2. If A is stored row-wise (A->Stype = SLU_NR), apply the above algorithm
    kusano 7d535a
    	to the transpose of A:

    kusano 7d535a
    	2.1. If options->Equil = YES or options->RowPerm = LargeDiag, scaling
    kusano 7d535a
    	     factors are computed to equilibrate the system:
    kusano 7d535a
    	     options->Trans = NOTRANS:
    kusano 7d535a
    		 diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
    kusano 7d535a
    	     options->Trans = TRANS:
    kusano 7d535a
    		 (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
    kusano 7d535a
    	     options->Trans = CONJ:
    kusano 7d535a
    		 (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
    kusano 7d535a
    	     Whether or not the system will be equilibrated depends on the
    kusano 7d535a
    	     scaling of the matrix A, but if equilibration is used, A' is
    kusano 7d535a
    	     overwritten by diag(R)*A'*diag(C) and B by diag(R)*B
    kusano 7d535a
    	     (if trans='N') or diag(C)*B (if trans = 'T' or 'C').

    kusano 7d535a
    	2.2. Permute columns of transpose(A) (rows of A),
    kusano 7d535a
    	     forming transpose(A)*Pc, where Pc is a permutation matrix that
    kusano 7d535a
    	     usually preserves sparsity.
    kusano 7d535a
    	     For more details of this step, see sp_preorder.c.

    kusano 7d535a
    	2.3. If options->Fact != FACTORED, the LU decomposition is used to
    kusano 7d535a
    	     factor the transpose(A) (after equilibration if
    kusano 7d535a
    	     options->Fact = YES) as Pr*transpose(A)*Pc = L*U with the
    kusano 7d535a
    	     permutation Pr determined by partial pivoting.

    kusano 7d535a
    	2.4. Compute the reciprocal pivot growth factor.

    kusano 7d535a
    	2.5. If some U(i,i) = 0, so that U is exactly singular, then the
    kusano 7d535a
    	     routine fills a small number on the diagonal entry, that is
    kusano 7d535a
    		 U(i,i) = ||A(:,i)||_oo * options->ILU_FillTol ** (1 - i / n).
    kusano 7d535a
    	     And info will be increased by 1. The factored form of A is used
    kusano 7d535a
    	     to estimate the condition number of the preconditioner. If the
    kusano 7d535a
    	     reciprocal of the condition number is less than machine precision,
    kusano 7d535a
    	     info = A->ncol+1 is returned as a warning, but the routine still
    kusano 7d535a
    	     goes on to solve for X.

    kusano 7d535a
    	2.6. The system of equations is solved for X using the factored form
    kusano 7d535a
    	     of transpose(A).

    kusano 7d535a
    	2.7. If options->IterRefine is not used.

    kusano 7d535a
    	2.8. If equilibration was used, the matrix X is premultiplied by
    kusano 7d535a
    	     diag(C) (if options->Trans = NOTRANS) or diag(R)
    kusano 7d535a
    	     (if options->Trans = TRANS or CONJ) so that it solves the
    kusano 7d535a
    	     original system before equilibration.

    kusano 7d535a
       See supermatrix.h for the definition of 'SuperMatrix' structure.

    kusano 7d535a
     Arguments
    kusano 7d535a
     =========

    kusano 7d535a
     options (input) superlu_options_t*
    kusano 7d535a
    	   The structure defines the input parameters to control
    kusano 7d535a
    	   how the LU decomposition will be performed and how the
    kusano 7d535a
    	   system will be solved.

    kusano 7d535a
     A	   (input/output) SuperMatrix*
    kusano 7d535a
    	   Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
    kusano 7d535a
    	   of the linear equations is A->nrow. Currently, the type of A can be:
    kusano 7d535a
    	   Stype = SLU_NC or SLU_NR, Dtype = SLU_D, Mtype = SLU_GE.
    kusano 7d535a
    	   In the future, more general A may be handled.

    kusano 7d535a
    	   On entry, If options->Fact = FACTORED and equed is not 'N',
    kusano 7d535a
    	   then A must have been equilibrated by the scaling factors in
    kusano 7d535a
    	   R and/or C.
    kusano 7d535a
    	   On exit, A is not modified
    kusano 7d535a
             if options->Equil = NO, or
    kusano 7d535a
             if options->Equil = YES but equed = 'N' on exit, or
    kusano 7d535a
             if options->RowPerm = NO.

    kusano 7d535a
    	   Otherwise, if options->Equil = YES and equed is not 'N',
    kusano 7d535a
    	   A is scaled as follows:
    kusano 7d535a
    	   If A->Stype = SLU_NC:
    kusano 7d535a
    	     equed = 'R':  A := diag(R) * A
    kusano 7d535a
    	     equed = 'C':  A := A * diag(C)
    kusano 7d535a
    	     equed = 'B':  A := diag(R) * A * diag(C).
    kusano 7d535a
    	   If A->Stype = SLU_NR:
    kusano 7d535a
    	     equed = 'R':  transpose(A) := diag(R) * transpose(A)
    kusano 7d535a
    	     equed = 'C':  transpose(A) := transpose(A) * diag(C)
    kusano 7d535a
    	     equed = 'B':  transpose(A) := diag(R) * transpose(A) * diag(C).

    kusano 7d535a
             If options->RowPerm = LargeDiag, MC64 is used to scale and permute
    kusano 7d535a
                the matrix to an I-matrix, that is A is modified as follows:
    kusano 7d535a
                P*Dr*A*Dc has entries of modulus 1 on the diagonal and 
    kusano 7d535a
                off-diagonal entries of modulus at most 1. P is a permutation
    kusano 7d535a
                obtained from MC64.
    kusano 7d535a
                If MC64 fails, dgsequ() is used to equilibrate the system,
    kusano 7d535a
                and A is scaled as above, there is no permutation involved.

    kusano 7d535a
     perm_c  (input/output) int*
    kusano 7d535a
    	   If A->Stype = SLU_NC, Column permutation vector of size A->ncol,
    kusano 7d535a
    	   which defines the permutation matrix Pc; perm_c[i] = j means
    kusano 7d535a
    	   column i of A is in position j in A*Pc.
    kusano 7d535a
    	   On exit, perm_c may be overwritten by the product of the input
    kusano 7d535a
    	   perm_c and a permutation that postorders the elimination tree
    kusano 7d535a
    	   of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
    kusano 7d535a
    	   is already in postorder.

    kusano 7d535a
    	   If A->Stype = SLU_NR, column permutation vector of size A->nrow,
    kusano 7d535a
    	   which describes permutation of columns of transpose(A) 
    kusano 7d535a
    	   (rows of A) as described above.

    kusano 7d535a
     perm_r  (input/output) int*
    kusano 7d535a
    	   If A->Stype = SLU_NC, row permutation vector of size A->nrow, 
    kusano 7d535a
    	   which defines the permutation matrix Pr, and is determined
    kusano 7d535a
    	   by partial pivoting.  perm_r[i] = j means row i of A is in 
    kusano 7d535a
    	   position j in Pr*A.

    kusano 7d535a
    	   If A->Stype = SLU_NR, permutation vector of size A->ncol, which
    kusano 7d535a
    	   determines permutation of rows of transpose(A)
    kusano 7d535a
    	   (columns of A) as described above.

    kusano 7d535a
    	   If options->Fact = SamePattern_SameRowPerm, the pivoting routine
    kusano 7d535a
    	   will try to use the input perm_r, unless a certain threshold
    kusano 7d535a
    	   criterion is violated. In that case, perm_r is overwritten by a
    kusano 7d535a
    	   new permutation determined by partial pivoting or diagonal
    kusano 7d535a
    	   threshold pivoting.
    kusano 7d535a
    	   Otherwise, perm_r is output argument.

    kusano 7d535a
     etree   (input/output) int*,  dimension (A->ncol)
    kusano 7d535a
    	   Elimination tree of Pc'*A'*A*Pc.
    kusano 7d535a
    	   If options->Fact != FACTORED and options->Fact != DOFACT,
    kusano 7d535a
    	   etree is an input argument, otherwise it is an output argument.
    kusano 7d535a
    	   Note: etree is a vector of parent pointers for a forest whose
    kusano 7d535a
    	   vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.

    kusano 7d535a
     equed   (input/output) char*
    kusano 7d535a
    	   Specifies the form of equilibration that was done.
    kusano 7d535a
    	   = 'N': No equilibration.
    kusano 7d535a
    	   = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
    kusano 7d535a
    	   = 'C': Column equilibration, i.e., A was postmultiplied by diag(C).
    kusano 7d535a
    	   = 'B': Both row and column equilibration, i.e., A was replaced 
    kusano 7d535a
    		  by diag(R)*A*diag(C).
    kusano 7d535a
    	   If options->Fact = FACTORED, equed is an input argument,
    kusano 7d535a
    	   otherwise it is an output argument.

    kusano 7d535a
     R	   (input/output) double*, dimension (A->nrow)
    kusano 7d535a
    	   The row scale factors for A or transpose(A).
    kusano 7d535a
    	   If equed = 'R' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
    kusano 7d535a
    	       (if A->Stype = SLU_NR) is multiplied on the left by diag(R).
    kusano 7d535a
    	   If equed = 'N' or 'C', R is not accessed.
    kusano 7d535a
    	   If options->Fact = FACTORED, R is an input argument,
    kusano 7d535a
    	       otherwise, R is output.
    kusano 7d535a
    	   If options->zFact = FACTORED and equed = 'R' or 'B', each element
    kusano 7d535a
    	       of R must be positive.

    kusano 7d535a
     C	   (input/output) double*, dimension (A->ncol)
    kusano 7d535a
    	   The column scale factors for A or transpose(A).
    kusano 7d535a
    	   If equed = 'C' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
    kusano 7d535a
    	       (if A->Stype = SLU_NR) is multiplied on the right by diag(C).
    kusano 7d535a
    	   If equed = 'N' or 'R', C is not accessed.
    kusano 7d535a
    	   If options->Fact = FACTORED, C is an input argument,
    kusano 7d535a
    	       otherwise, C is output.
    kusano 7d535a
    	   If options->Fact = FACTORED and equed = 'C' or 'B', each element
    kusano 7d535a
    	       of C must be positive.

    kusano 7d535a
     L	   (output) SuperMatrix*
    kusano 7d535a
    	   The factor L from the factorization
    kusano 7d535a
    	       Pr*A*Pc=L*U		(if A->Stype SLU_= NC) or
    kusano 7d535a
    	       Pr*transpose(A)*Pc=L*U	(if A->Stype = SLU_NR).
    kusano 7d535a
    	   Uses compressed row subscripts storage for supernodes, i.e.,
    kusano 7d535a
    	   L has types: Stype = SLU_SC, Dtype = SLU_D, Mtype = SLU_TRLU.

    kusano 7d535a
     U	   (output) SuperMatrix*
    kusano 7d535a
    	   The factor U from the factorization
    kusano 7d535a
    	       Pr*A*Pc=L*U		(if A->Stype = SLU_NC) or
    kusano 7d535a
    	       Pr*transpose(A)*Pc=L*U	(if A->Stype = SLU_NR).
    kusano 7d535a
    	   Uses column-wise storage scheme, i.e., U has types:
    kusano 7d535a
    	   Stype = SLU_NC, Dtype = SLU_D, Mtype = SLU_TRU.

    kusano 7d535a
     work    (workspace/output) void*, size (lwork) (in bytes)
    kusano 7d535a
    	   User supplied workspace, should be large enough
    kusano 7d535a
    	   to hold data structures for factors L and U.
    kusano 7d535a
    	   On exit, if fact is not 'F', L and U point to this array.

    kusano 7d535a
     lwork   (input) int
    kusano 7d535a
    	   Specifies the size of work array in bytes.
    kusano 7d535a
    	   = 0:  allocate space internally by system malloc;
    kusano 7d535a
    	   > 0:  use user-supplied work array of length lwork in bytes,
    kusano 7d535a
    		 returns error if space runs out.
    kusano 7d535a
    	   = -1: the routine guesses the amount of space needed without
    kusano 7d535a
    		 performing the factorization, and returns it in
    kusano 7d535a
    		 mem_usage->total_needed; no other side effects.

    kusano 7d535a
    	   See argument 'mem_usage' for memory usage statistics.

    kusano 7d535a
     B	   (input/output) SuperMatrix*
    kusano 7d535a
    	   B has types: Stype = SLU_DN, Dtype = SLU_D, Mtype = SLU_GE.
    kusano 7d535a
    	   On entry, the right hand side matrix.
    kusano 7d535a
    	   If B->ncol = 0, only LU decomposition is performed, the triangular
    kusano 7d535a
    			   solve is skipped.
    kusano 7d535a
    	   On exit,
    kusano 7d535a
    	      if equed = 'N', B is not modified; otherwise
    kusano 7d535a
    	      if A->Stype = SLU_NC:
    kusano 7d535a
    		 if options->Trans = NOTRANS and equed = 'R' or 'B',
    kusano 7d535a
    		    B is overwritten by diag(R)*B;
    kusano 7d535a
    		 if options->Trans = TRANS or CONJ and equed = 'C' of 'B',
    kusano 7d535a
    		    B is overwritten by diag(C)*B;
    kusano 7d535a
    	      if A->Stype = SLU_NR:
    kusano 7d535a
    		 if options->Trans = NOTRANS and equed = 'C' or 'B',
    kusano 7d535a
    		    B is overwritten by diag(C)*B;
    kusano 7d535a
    		 if options->Trans = TRANS or CONJ and equed = 'R' of 'B',
    kusano 7d535a
    		    B is overwritten by diag(R)*B.

    kusano 7d535a
             If options->RowPerm = LargeDiag, MC64 is used to scale and permute
    kusano 7d535a
                the matrix A to an I-matrix. Then, in addition to the scaling
    kusano 7d535a
                above, B is further permuted by P*B if options->Trans = NOTRANS,
    kusano 7d535a
                where P is obtained from MC64.

    kusano 7d535a
     X	   (output) SuperMatrix*
    kusano 7d535a
    	   X has types: Stype = SLU_DN, Dtype = SLU_D, Mtype = SLU_GE.
    kusano 7d535a
    	   If info = 0 or info = A->ncol+1, X contains the solution matrix
    kusano 7d535a
    	   to the original system of equations. Note that A and B are modified
    kusano 7d535a
    	   on exit if equed is not 'N', and the solution to the equilibrated
    kusano 7d535a
    	   system is inv(diag(C))*X if options->Trans = NOTRANS and
    kusano 7d535a
    	   equed = 'C' or 'B', or inv(diag(R))*X if options->Trans = 'T' or 'C'
    kusano 7d535a
    	   and equed = 'R' or 'B'.

    kusano 7d535a
     recip_pivot_growth (output) double*
    kusano 7d535a
    	   The reciprocal pivot growth factor max_j( norm(A_j)/norm(U_j) ).
    kusano 7d535a
    	   The infinity norm is used. If recip_pivot_growth is much less
    kusano 7d535a
    	   than 1, the stability of the LU factorization could be poor.

    kusano 7d535a
     rcond   (output) double*
    kusano 7d535a
    	   The estimate of the reciprocal condition number of the matrix A
    kusano 7d535a
    	   after equilibration (if done). If rcond is less than the machine
    kusano 7d535a
    	   precision (in particular, if rcond = 0), the matrix is singular
    kusano 7d535a
    	   to working precision. This condition is indicated by a return
    kusano 7d535a
    	   code of info > 0.

    kusano 7d535a
     mem_usage (output) mem_usage_t*
    kusano 7d535a
    	   Record the memory usage statistics, consisting of following fields:
      kusano 7d535a
    • for_lu (float)
    • kusano 7d535a
      	     The amount of space used in bytes for L data structures.
    • total_needed (float)
    • kusano 7d535a
      	     The amount of space needed in bytes to perform factorization.
    • expansions (int)
    • kusano 7d535a
      	     The number of memory expansions during the LU factorization.
      kusano 7d535a

      kusano 7d535a
       stat   (output) SuperLUStat_t*
      kusano 7d535a
      	  Record the statistics on runtime and floating-point operation count.
      kusano 7d535a
      	  See slu_util.h for the definition of 'SuperLUStat_t'.

      kusano 7d535a
       info    (output) int*
      kusano 7d535a
      	   = 0: successful exit
      kusano 7d535a
      	   < 0: if info = -i, the i-th argument had an illegal value
      kusano 7d535a
      	   > 0: if info = i, and i is
      kusano 7d535a
      		<= A->ncol: number of zero pivots. They are replaced by small
      kusano 7d535a
      		      entries due to options->ILU_FillTol.
      kusano 7d535a
      		= A->ncol+1: U is nonsingular, but RCOND is less than machine
      kusano 7d535a
      		      precision, meaning that the matrix is singular to
      kusano 7d535a
      		      working precision. Nevertheless, the solution and
      kusano 7d535a
      		      error bounds are computed because there are a number
      kusano 7d535a
      		      of situations where the computed solution can be more
      kusano 7d535a
      		      accurate than the value of RCOND would suggest.
      kusano 7d535a
      		> A->ncol+1: number of bytes allocated when memory allocation
      kusano 7d535a
      		      failure occurred, plus A->ncol.
      kusano 7d535a
        
      kusano 7d535a
      kusano 7d535a

      kusano 7d535a
      kusano 7d535a

      <address style="text-align: right;"><small>Generated on Mon Nov 22 10:23:47 2010 for SuperLU by </small></address>
      kusano 7d535a
      kusano 7d535a
      doxygen 1.5.5 
      kusano 7d535a
      kusano 7d535a