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| <h1>SRC/zgsisx.c File Reference</h1>Computes an approximate solutions of linear equations A*X=B or A'*X=B. <a href="#_details">More...</a> |
| <p> |
| <code>#include "<a class="el" href="slu__zdefs_8h-source.html">slu_zdefs.h</a>"</code><br> |
| <table border="0" cellpadding="0" cellspacing="0"> |
| <tr><td></td></tr> |
| <tr><td colspan="2"><br><h2>Functions</h2></td></tr> |
| <tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="zgsisx_8c.html#2757feaa11de219577144d87b69e9ca9">zgsisx</a> (<a class="el" href="structsuperlu__options__t.html">superlu_options_t</a> *options, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="ilu__zdrop__row_8c.html#c900805a486cbb8489e3c176ed6e0d8e">A</a>, int *perm_c, int *perm_r, int *etree, char *equed, double *R, double *C, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *L, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *U, void *work, int lwork, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *B, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *X, double *recip_pivot_growth, double *rcond, <a class="el" href="structmem__usage__t.html">mem_usage_t</a> *mem_usage, <a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> *stat, int *info)</td></tr> |
| |
| </table> |
| <hr><a name="_details"></a><h2>Detailed Description</h2> |
| <pre> |
| -- SuperLU routine (version 4.1) -- |
| Lawrence Berkeley National Laboratory. |
| November, 2010 |
| </pre> <hr><h2>Function Documentation</h2> |
| <a class="anchor" name="2757feaa11de219577144d87b69e9ca9"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">void zgsisx </td> |
| <td>(</td> |
| <td class="paramtype"><a class="el" href="structsuperlu__options__t.html">superlu_options_t</a> * </td> |
| <td class="paramname"> <em>options</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td> |
| <td class="paramname"> <em>A</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>perm_c</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>perm_r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>etree</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">char * </td> |
| <td class="paramname"> <em>equed</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">double * </td> |
| <td class="paramname"> <em>R</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">double * </td> |
| <td class="paramname"> <em>C</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td> |
| <td class="paramname"> <em>L</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td> |
| <td class="paramname"> <em>U</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">void * </td> |
| <td class="paramname"> <em>work</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int </td> |
| <td class="paramname"> <em>lwork</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td> |
| <td class="paramname"> <em>B</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td> |
| <td class="paramname"> <em>X</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">double * </td> |
| <td class="paramname"> <em>recip_pivot_growth</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">double * </td> |
| <td class="paramname"> <em>rcond</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structmem__usage__t.html">mem_usage_t</a> * </td> |
| <td class="paramname"> <em>mem_usage</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype"><a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> * </td> |
| <td class="paramname"> <em>stat</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>info</em></td><td> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td><td width="100%"></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| |
| <p> |
| <pre> |
| Purpose |
| =======</pre><p> |
| <pre> ZGSISX computes an approximate solutions of linear equations |
| A*X=B or A'*X=B, using the ILU factorization from <a class="el" href="slu__zdefs_8h.html#2fee39459dfac17529487ea539648cfb">zgsitrf()</a>. |
| An estimation of the condition number is provided. |
| The routine performs the following steps:</pre><p> |
| <pre> 1. If A is stored column-wise (A->Stype = SLU_NC):</pre><p> |
| <pre> 1.1. If options->Equil = YES or options->RowPerm = LargeDiag, scaling |
| factors are computed to equilibrate the system: |
| options->Trans = NOTRANS: |
| diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B |
| options->Trans = TRANS: |
| (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B |
| options->Trans = CONJ: |
| (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B |
| Whether or not the system will be equilibrated depends on the |
| scaling of the matrix A, but if equilibration is used, A is |
| overwritten by diag(R)*A*diag(C) and B by diag(R)*B |
| (if options->Trans=NOTRANS) or diag(C)*B (if options->Trans |
| = TRANS or CONJ).</pre><p> |
| <pre> 1.2. Permute columns of A, forming A*Pc, where Pc is a permutation |
| matrix that usually preserves sparsity. |
| For more details of this step, see <a class="el" href="sp__preorder_8c.html" title="Permute and performs functions on columns of orginal matrix.">sp_preorder.c</a>.</pre><p> |
| <pre> 1.3. If options->Fact != FACTORED, the LU decomposition is used to |
| factor the matrix A (after equilibration if options->Equil = YES) |
| as Pr*A*Pc = L*U, with Pr determined by partial pivoting.</pre><p> |
| <pre> 1.4. Compute the reciprocal pivot growth factor.</pre><p> |
| <pre> 1.5. If some U(i,i) = 0, so that U is exactly singular, then the |
| routine fills a small number on the diagonal entry, that is |
| U(i,i) = ||A(:,i)||_oo * options->ILU_FillTol ** (1 - i / n), |
| and info will be increased by 1. The factored form of A is used |
| to estimate the condition number of the preconditioner. If the |
| reciprocal of the condition number is less than machine precision, |
| info = A->ncol+1 is returned as a warning, but the routine still |
| goes on to solve for X.</pre><p> |
| <pre> 1.6. The system of equations is solved for X using the factored form |
| of A.</pre><p> |
| <pre> 1.7. options->IterRefine is not used</pre><p> |
| <pre> 1.8. If equilibration was used, the matrix X is premultiplied by |
| diag(C) (if options->Trans = NOTRANS) or diag(R) |
| (if options->Trans = TRANS or CONJ) so that it solves the |
| original system before equilibration.</pre><p> |
| <pre> 1.9. options for ILU only |
| 1) If options->RowPerm = LargeDiag, MC64 is used to scale and |
| permute the matrix to an I-matrix, that is Pr*Dr*A*Dc has |
| entries of modulus 1 on the diagonal and off-diagonal entries |
| of modulus at most 1. If MC64 fails, <a class="el" href="dgsequ_8c.html#af22b247cc134fb0ba90285e84ccebb4" title="Driver related.">dgsequ()</a> is used to |
| equilibrate the system. |
| ( Default: LargeDiag ) |
| 2) options->ILU_DropTol = tau is the threshold for dropping. |
| For L, it is used directly (for the whole row in a supernode); |
| For U, ||A(:,i)||_oo * tau is used as the threshold |
| for the i-th column. |
| If a secondary dropping rule is required, tau will |
| also be used to compute the second threshold. |
| ( Default: 1e-4 ) |
| 3) options->ILU_FillFactor = gamma, used as the initial guess |
| of memory growth. |
| If a secondary dropping rule is required, it will also |
| be used as an upper bound of the memory. |
| ( Default: 10 ) |
| 4) options->ILU_DropRule specifies the dropping rule. |
| Option Meaning |
| ====== =========== |
| DROP_BASIC: Basic dropping rule, supernodal based ILUTP(tau). |
| DROP_PROWS: Supernodal based ILUTP(p,tau), p = gamma*nnz(A)/n. |
| DROP_COLUMN: Variant of ILUTP(p,tau), for j-th column, |
| p = gamma * nnz(A(:,j)). |
| DROP_AREA: Variation of ILUTP, for j-th column, use |
| nnz(F(:,1:j)) / nnz(A(:,1:j)) to control memory. |
| DROP_DYNAMIC: Modify the threshold tau during factorizaion: |
| If nnz(L(:,1:j)) / nnz(A(:,1:j)) > gamma |
| tau_L(j) := MIN(tau_0, tau_L(j-1) * 2); |
| Otherwise |
| tau_L(j) := MAX(tau_0, tau_L(j-1) / 2); |
| tau_U(j) uses the similar rule. |
| NOTE: the thresholds used by L and U are separate. |
| DROP_INTERP: Compute the second dropping threshold by |
| interpolation instead of sorting (default). |
| In this case, the actual fill ratio is not |
| guaranteed smaller than gamma. |
| DROP_PROWS, DROP_COLUMN and DROP_AREA are mutually exclusive. |
| ( Default: DROP_BASIC | DROP_AREA ) |
| 5) options->ILU_Norm is the criterion of measuring the magnitude |
| of a row in a supernode of L. ( Default is INF_NORM ) |
| options->ILU_Norm RowSize(x[1:n]) |
| ================= =============== |
| ONE_NORM ||x||_1 / n |
| TWO_NORM ||x||_2 / sqrt(n) |
| INF_NORM max{|x[i]|} |
| 6) options->ILU_MILU specifies the type of MILU's variation. |
| = SILU: do not perform Modified ILU; |
| = SMILU_1 (not recommended): |
| U(i,i) := U(i,i) + sum(dropped entries); |
| = SMILU_2: |
| U(i,i) := U(i,i) + SGN(U(i,i)) * sum(dropped entries); |
| = SMILU_3: |
| U(i,i) := U(i,i) + SGN(U(i,i)) * sum(|dropped entries|); |
| NOTE: Even SMILU_1 does not preserve the column sum because of |
| late dropping. |
| ( Default: SILU ) |
| 7) options->ILU_FillTol is used as the perturbation when |
| encountering zero pivots. If some U(i,i) = 0, so that U is |
| exactly singular, then |
| U(i,i) := ||A(:,i)|| * options->ILU_FillTol ** (1 - i / n). |
| ( Default: 1e-2 )</pre><p> |
| <pre> 2. If A is stored row-wise (A->Stype = SLU_NR), apply the above algorithm |
| to the transpose of A:</pre><p> |
| <pre> 2.1. If options->Equil = YES or options->RowPerm = LargeDiag, scaling |
| factors are computed to equilibrate the system: |
| options->Trans = NOTRANS: |
| diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B |
| options->Trans = TRANS: |
| (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B |
| options->Trans = CONJ: |
| (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B |
| Whether or not the system will be equilibrated depends on the |
| scaling of the matrix A, but if equilibration is used, A' is |
| overwritten by diag(R)*A'*diag(C) and B by diag(R)*B |
| (if trans='N') or diag(C)*B (if trans = 'T' or 'C').</pre><p> |
| <pre> 2.2. Permute columns of transpose(A) (rows of A), |
| forming transpose(A)*Pc, where Pc is a permutation matrix that |
| usually preserves sparsity. |
| For more details of this step, see <a class="el" href="sp__preorder_8c.html" title="Permute and performs functions on columns of orginal matrix.">sp_preorder.c</a>.</pre><p> |
| <pre> 2.3. If options->Fact != FACTORED, the LU decomposition is used to |
| factor the transpose(A) (after equilibration if |
| options->Fact = YES) as Pr*transpose(A)*Pc = L*U with the |
| permutation Pr determined by partial pivoting.</pre><p> |
| <pre> 2.4. Compute the reciprocal pivot growth factor.</pre><p> |
| <pre> 2.5. If some U(i,i) = 0, so that U is exactly singular, then the |
| routine fills a small number on the diagonal entry, that is |
| U(i,i) = ||A(:,i)||_oo * options->ILU_FillTol ** (1 - i / n). |
| And info will be increased by 1. The factored form of A is used |
| to estimate the condition number of the preconditioner. If the |
| reciprocal of the condition number is less than machine precision, |
| info = A->ncol+1 is returned as a warning, but the routine still |
| goes on to solve for X.</pre><p> |
| <pre> 2.6. The system of equations is solved for X using the factored form |
| of transpose(A).</pre><p> |
| <pre> 2.7. If options->IterRefine is not used.</pre><p> |
| <pre> 2.8. If equilibration was used, the matrix X is premultiplied by |
| diag(C) (if options->Trans = NOTRANS) or diag(R) |
| (if options->Trans = TRANS or CONJ) so that it solves the |
| original system before equilibration.</pre><p> |
| <pre> See <a class="el" href="supermatrix_8h.html" title="Defines matrix types.">supermatrix.h</a> for the definition of 'SuperMatrix' structure.</pre><p> |
| <pre> Arguments |
| =========</pre><p> |
| <pre> options (input) superlu_options_t* |
| The structure defines the input parameters to control |
| how the LU decomposition will be performed and how the |
| system will be solved.</pre><p> |
| <pre> A (input/output) SuperMatrix* |
| Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number |
| of the linear equations is A->nrow. Currently, the type of A can be: |
| Stype = SLU_NC or SLU_NR, Dtype = SLU_Z, Mtype = SLU_GE. |
| In the future, more general A may be handled.</pre><p> |
| <pre> On entry, If options->Fact = FACTORED and equed is not 'N', |
| then A must have been equilibrated by the scaling factors in |
| R and/or C. |
| On exit, A is not modified |
| if options->Equil = NO, or |
| if options->Equil = YES but equed = 'N' on exit, or |
| if options->RowPerm = NO.</pre><p> |
| <pre> Otherwise, if options->Equil = YES and equed is not 'N', |
| A is scaled as follows: |
| If A->Stype = SLU_NC: |
| equed = 'R': A := diag(R) * A |
| equed = 'C': A := A * diag(C) |
| equed = 'B': A := diag(R) * A * diag(C). |
| If A->Stype = SLU_NR: |
| equed = 'R': transpose(A) := diag(R) * transpose(A) |
| equed = 'C': transpose(A) := transpose(A) * diag(C) |
| equed = 'B': transpose(A) := diag(R) * transpose(A) * diag(C).</pre><p> |
| <pre> If options->RowPerm = LargeDiag, MC64 is used to scale and permute |
| the matrix to an I-matrix, that is A is modified as follows: |
| P*Dr*A*Dc has entries of modulus 1 on the diagonal and |
| off-diagonal entries of modulus at most 1. P is a permutation |
| obtained from MC64. |
| If MC64 fails, <a class="el" href="slu__zdefs_8h.html#e112ddfff2798b7e4c090d96d2a8d80a" title="Driver related.">zgsequ()</a> is used to equilibrate the system, |
| and A is scaled as above, there is no permutation involved.</pre><p> |
| <pre> perm_c (input/output) int* |
| If A->Stype = SLU_NC, Column permutation vector of size A->ncol, |
| which defines the permutation matrix Pc; perm_c[i] = j means |
| column i of A is in position j in A*Pc. |
| On exit, perm_c may be overwritten by the product of the input |
| perm_c and a permutation that postorders the elimination tree |
| of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree |
| is already in postorder.</pre><p> |
| <pre> If A->Stype = SLU_NR, column permutation vector of size A->nrow, |
| which describes permutation of columns of transpose(A) |
| (rows of A) as described above.</pre><p> |
| <pre> perm_r (input/output) int* |
| If A->Stype = SLU_NC, row permutation vector of size A->nrow, |
| which defines the permutation matrix Pr, and is determined |
| by partial pivoting. perm_r[i] = j means row i of A is in |
| position j in Pr*A.</pre><p> |
| <pre> If A->Stype = SLU_NR, permutation vector of size A->ncol, which |
| determines permutation of rows of transpose(A) |
| (columns of A) as described above.</pre><p> |
| <pre> If options->Fact = SamePattern_SameRowPerm, the pivoting routine |
| will try to use the input perm_r, unless a certain threshold |
| criterion is violated. In that case, perm_r is overwritten by a |
| new permutation determined by partial pivoting or diagonal |
| threshold pivoting. |
| Otherwise, perm_r is output argument.</pre><p> |
| <pre> etree (input/output) int*, dimension (A->ncol) |
| Elimination tree of Pc'*A'*A*Pc. |
| If options->Fact != FACTORED and options->Fact != DOFACT, |
| etree is an input argument, otherwise it is an output argument. |
| Note: etree is a vector of parent pointers for a forest whose |
| vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.</pre><p> |
| <pre> equed (input/output) char* |
| Specifies the form of equilibration that was done. |
| = 'N': No equilibration. |
| = 'R': Row equilibration, i.e., A was premultiplied by diag(R). |
| = 'C': Column equilibration, i.e., A was postmultiplied by diag(C). |
| = 'B': Both row and column equilibration, i.e., A was replaced |
| by diag(R)*A*diag(C). |
| If options->Fact = FACTORED, equed is an input argument, |
| otherwise it is an output argument.</pre><p> |
| <pre> R (input/output) double*, dimension (A->nrow) |
| The row scale factors for A or transpose(A). |
| If equed = 'R' or 'B', A (if A->Stype = SLU_NC) or transpose(A) |
| (if A->Stype = SLU_NR) is multiplied on the left by diag(R). |
| If equed = 'N' or 'C', R is not accessed. |
| If options->Fact = FACTORED, R is an input argument, |
| otherwise, R is output. |
| If options->zFact = FACTORED and equed = 'R' or 'B', each element |
| of R must be positive.</pre><p> |
| <pre> C (input/output) double*, dimension (A->ncol) |
| The column scale factors for A or transpose(A). |
| If equed = 'C' or 'B', A (if A->Stype = SLU_NC) or transpose(A) |
| (if A->Stype = SLU_NR) is multiplied on the right by diag(C). |
| If equed = 'N' or 'R', C is not accessed. |
| If options->Fact = FACTORED, C is an input argument, |
| otherwise, C is output. |
| If options->Fact = FACTORED and equed = 'C' or 'B', each element |
| of C must be positive.</pre><p> |
| <pre> L (output) SuperMatrix* |
| The factor L from the factorization |
| Pr*A*Pc=L*U (if A->Stype SLU_= NC) or |
| Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR). |
| Uses compressed row subscripts storage for supernodes, i.e., |
| L has types: Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.</pre><p> |
| <pre> U (output) SuperMatrix* |
| The factor U from the factorization |
| Pr*A*Pc=L*U (if A->Stype = SLU_NC) or |
| Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR). |
| Uses column-wise storage scheme, i.e., U has types: |
| Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.</pre><p> |
| <pre> work (workspace/output) void*, size (lwork) (in bytes) |
| User supplied workspace, should be large enough |
| to hold data structures for factors L and U. |
| On exit, if fact is not 'F', L and U point to this array.</pre><p> |
| <pre> lwork (input) int |
| Specifies the size of work array in bytes. |
| = 0: allocate space internally by system malloc; |
| > 0: use user-supplied work array of length lwork in bytes, |
| returns error if space runs out. |
| = -1: the routine guesses the amount of space needed without |
| performing the factorization, and returns it in |
| mem_usage->total_needed; no other side effects.</pre><p> |
| <pre> See argument 'mem_usage' for memory usage statistics.</pre><p> |
| <pre> B (input/output) SuperMatrix* |
| B has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE. |
| On entry, the right hand side matrix. |
| If B->ncol = 0, only LU decomposition is performed, the triangular |
| solve is skipped. |
| On exit, |
| if equed = 'N', B is not modified; otherwise |
| if A->Stype = SLU_NC: |
| if options->Trans = NOTRANS and equed = 'R' or 'B', |
| B is overwritten by diag(R)*B; |
| if options->Trans = TRANS or CONJ and equed = 'C' of 'B', |
| B is overwritten by diag(C)*B; |
| if A->Stype = SLU_NR: |
| if options->Trans = NOTRANS and equed = 'C' or 'B', |
| B is overwritten by diag(C)*B; |
| if options->Trans = TRANS or CONJ and equed = 'R' of 'B', |
| B is overwritten by diag(R)*B.</pre><p> |
| <pre> If options->RowPerm = LargeDiag, MC64 is used to scale and permute |
| the matrix A to an I-matrix. Then, in addition to the scaling |
| above, B is further permuted by P*B if options->Trans = NOTRANS, |
| where P is obtained from MC64.</pre><p> |
| <pre> X (output) SuperMatrix* |
| X has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE. |
| If info = 0 or info = A->ncol+1, X contains the solution matrix |
| to the original system of equations. Note that A and B are modified |
| on exit if equed is not 'N', and the solution to the equilibrated |
| system is inv(diag(C))*X if options->Trans = NOTRANS and |
| equed = 'C' or 'B', or inv(diag(R))*X if options->Trans = 'T' or 'C' |
| and equed = 'R' or 'B'.</pre><p> |
| <pre> recip_pivot_growth (output) double* |
| The reciprocal pivot growth factor max_j( norm(A_j)/norm(U_j) ). |
| The infinity norm is used. If recip_pivot_growth is much less |
| than 1, the stability of the LU factorization could be poor.</pre><p> |
| <pre> rcond (output) double* |
| The estimate of the reciprocal condition number of the matrix A |
| after equilibration (if done). If rcond is less than the machine |
| precision (in particular, if rcond = 0), the matrix is singular |
| to working precision. This condition is indicated by a return |
| code of info > 0.</pre><p> |
| <pre> mem_usage (output) mem_usage_t* |
| Record the memory usage statistics, consisting of following fields:<ul> |
| <li>for_lu (float) |
| The amount of space used in bytes for L data structures.</li><li>total_needed (float) |
| The amount of space needed in bytes to perform factorization.</li><li>expansions (int) |
| The number of memory expansions during the LU factorization.</li></ul> |
| </pre><p> |
| <pre> stat (output) SuperLUStat_t* |
| Record the statistics on runtime and floating-point operation count. |
| See <a class="el" href="slu__util_8h.html" title="Utility header file.">slu_util.h</a> for the definition of 'SuperLUStat_t'.</pre><p> |
| <pre> info (output) int* |
| = 0: successful exit |
| < 0: if info = -i, the i-th argument had an illegal value |
| > 0: if info = i, and i is |
| <= A->ncol: number of zero pivots. They are replaced by small |
| entries due to options->ILU_FillTol. |
| = A->ncol+1: U is nonsingular, but RCOND is less than machine |
| precision, meaning that the matrix is singular to |
| working precision. Nevertheless, the solution and |
| error bounds are computed because there are a number |
| of situations where the computed solution can be more |
| accurate than the value of RCOND would suggest. |
| > A->ncol+1: number of bytes allocated when memory allocation |
| failure occurred, plus A->ncol. |
| </pre> |
| </div> |
| </div><p> |
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