614 lines
25 KiB
C
614 lines
25 KiB
C
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/*! @file sgssvx.c
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* \brief Solves the system of linear equations A*X=B or A'*X=B
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*
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* <pre>
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* -- SuperLU routine (version 3.0) --
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* Univ. of California Berkeley, Xerox Palo Alto Research Center,
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* and Lawrence Berkeley National Lab.
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* October 15, 2003
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* </pre>
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*/
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#include "slu_sdefs.h"
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/*! \brief
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*
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* <pre>
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* Purpose
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* =======
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*
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* SGSSVX solves the system of linear equations A*X=B or A'*X=B, using
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* the LU factorization from sgstrf(). Error bounds on the solution and
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* a condition estimate are also provided. It performs the following steps:
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*
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* 1. If A is stored column-wise (A->Stype = SLU_NC):
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*
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* 1.1. If options->Equil = YES, scaling factors are computed to
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* equilibrate the system:
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* options->Trans = NOTRANS:
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* diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
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* options->Trans = TRANS:
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* (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
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* options->Trans = CONJ:
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* (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
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* Whether or not the system will be equilibrated depends on the
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* scaling of the matrix A, but if equilibration is used, A is
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* overwritten by diag(R)*A*diag(C) and B by diag(R)*B
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* (if options->Trans=NOTRANS) or diag(C)*B (if options->Trans
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* = TRANS or CONJ).
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*
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* 1.2. Permute columns of A, forming A*Pc, where Pc is a permutation
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* matrix that usually preserves sparsity.
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* For more details of this step, see sp_preorder.c.
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*
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* 1.3. If options->Fact != FACTORED, the LU decomposition is used to
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* factor the matrix A (after equilibration if options->Equil = YES)
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* as Pr*A*Pc = L*U, with Pr determined by partial pivoting.
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*
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* 1.4. Compute the reciprocal pivot growth factor.
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*
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* 1.5. If some U(i,i) = 0, so that U is exactly singular, then the
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* routine returns with info = i. Otherwise, the factored form of
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* A is used to estimate the condition number of the matrix A. If
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* the reciprocal of the condition number is less than machine
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* precision, info = A->ncol+1 is returned as a warning, but the
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* routine still goes on to solve for X and computes error bounds
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* as described below.
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*
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* 1.6. The system of equations is solved for X using the factored form
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* of A.
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*
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* 1.7. If options->IterRefine != NOREFINE, iterative refinement is
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* applied to improve the computed solution matrix and calculate
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* error bounds and backward error estimates for it.
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*
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* 1.8. If equilibration was used, the matrix X is premultiplied by
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* diag(C) (if options->Trans = NOTRANS) or diag(R)
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* (if options->Trans = TRANS or CONJ) so that it solves the
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* original system before equilibration.
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*
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* 2. If A is stored row-wise (A->Stype = SLU_NR), apply the above algorithm
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* to the transpose of A:
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*
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* 2.1. If options->Equil = YES, scaling factors are computed to
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* equilibrate the system:
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* options->Trans = NOTRANS:
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* diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
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* options->Trans = TRANS:
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* (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
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* options->Trans = CONJ:
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* (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
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* Whether or not the system will be equilibrated depends on the
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* scaling of the matrix A, but if equilibration is used, A' is
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* overwritten by diag(R)*A'*diag(C) and B by diag(R)*B
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* (if trans='N') or diag(C)*B (if trans = 'T' or 'C').
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*
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* 2.2. Permute columns of transpose(A) (rows of A),
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* forming transpose(A)*Pc, where Pc is a permutation matrix that
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* usually preserves sparsity.
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* For more details of this step, see sp_preorder.c.
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*
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* 2.3. If options->Fact != FACTORED, the LU decomposition is used to
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* factor the transpose(A) (after equilibration if
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* options->Fact = YES) as Pr*transpose(A)*Pc = L*U with the
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* permutation Pr determined by partial pivoting.
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*
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* 2.4. Compute the reciprocal pivot growth factor.
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*
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* 2.5. If some U(i,i) = 0, so that U is exactly singular, then the
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* routine returns with info = i. Otherwise, the factored form
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* of transpose(A) is used to estimate the condition number of the
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* matrix A. If the reciprocal of the condition number
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* is less than machine precision, info = A->nrow+1 is returned as
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* a warning, but the routine still goes on to solve for X and
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* computes error bounds as described below.
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*
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* 2.6. The system of equations is solved for X using the factored form
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* of transpose(A).
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*
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* 2.7. If options->IterRefine != NOREFINE, iterative refinement is
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* applied to improve the computed solution matrix and calculate
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* error bounds and backward error estimates for it.
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*
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* 2.8. If equilibration was used, the matrix X is premultiplied by
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* diag(C) (if options->Trans = NOTRANS) or diag(R)
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* (if options->Trans = TRANS or CONJ) so that it solves the
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* original system before equilibration.
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*
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* See supermatrix.h for the definition of 'SuperMatrix' structure.
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*
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* Arguments
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* =========
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*
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* options (input) superlu_options_t*
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* The structure defines the input parameters to control
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* how the LU decomposition will be performed and how the
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* system will be solved.
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*
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* A (input/output) SuperMatrix*
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* Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
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* of the linear equations is A->nrow. Currently, the type of A can be:
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* Stype = SLU_NC or SLU_NR, Dtype = SLU_D, Mtype = SLU_GE.
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* In the future, more general A may be handled.
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*
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* On entry, If options->Fact = FACTORED and equed is not 'N',
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* then A must have been equilibrated by the scaling factors in
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* R and/or C.
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* On exit, A is not modified if options->Equil = NO, or if
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* options->Equil = YES but equed = 'N' on exit.
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* Otherwise, if options->Equil = YES and equed is not 'N',
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* A is scaled as follows:
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* If A->Stype = SLU_NC:
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* equed = 'R': A := diag(R) * A
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* equed = 'C': A := A * diag(C)
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* equed = 'B': A := diag(R) * A * diag(C).
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* If A->Stype = SLU_NR:
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* equed = 'R': transpose(A) := diag(R) * transpose(A)
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* equed = 'C': transpose(A) := transpose(A) * diag(C)
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* equed = 'B': transpose(A) := diag(R) * transpose(A) * diag(C).
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*
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* perm_c (input/output) int*
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* If A->Stype = SLU_NC, Column permutation vector of size A->ncol,
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* which defines the permutation matrix Pc; perm_c[i] = j means
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* column i of A is in position j in A*Pc.
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* On exit, perm_c may be overwritten by the product of the input
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* perm_c and a permutation that postorders the elimination tree
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* of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
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* is already in postorder.
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*
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* If A->Stype = SLU_NR, column permutation vector of size A->nrow,
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* which describes permutation of columns of transpose(A)
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* (rows of A) as described above.
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*
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* perm_r (input/output) int*
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* If A->Stype = SLU_NC, row permutation vector of size A->nrow,
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* which defines the permutation matrix Pr, and is determined
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* by partial pivoting. perm_r[i] = j means row i of A is in
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* position j in Pr*A.
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*
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* If A->Stype = SLU_NR, permutation vector of size A->ncol, which
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* determines permutation of rows of transpose(A)
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* (columns of A) as described above.
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*
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* If options->Fact = SamePattern_SameRowPerm, the pivoting routine
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* will try to use the input perm_r, unless a certain threshold
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* criterion is violated. In that case, perm_r is overwritten by a
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* new permutation determined by partial pivoting or diagonal
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* threshold pivoting.
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* Otherwise, perm_r is output argument.
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*
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* etree (input/output) int*, dimension (A->ncol)
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* Elimination tree of Pc'*A'*A*Pc.
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* If options->Fact != FACTORED and options->Fact != DOFACT,
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* etree is an input argument, otherwise it is an output argument.
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* Note: etree is a vector of parent pointers for a forest whose
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* vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.
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*
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* equed (input/output) char*
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* Specifies the form of equilibration that was done.
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* = 'N': No equilibration.
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* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
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* = 'C': Column equilibration, i.e., A was postmultiplied by diag(C).
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* = 'B': Both row and column equilibration, i.e., A was replaced
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* by diag(R)*A*diag(C).
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* If options->Fact = FACTORED, equed is an input argument,
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* otherwise it is an output argument.
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*
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* R (input/output) float*, dimension (A->nrow)
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* The row scale factors for A or transpose(A).
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* If equed = 'R' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
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* (if A->Stype = SLU_NR) is multiplied on the left by diag(R).
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* If equed = 'N' or 'C', R is not accessed.
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* If options->Fact = FACTORED, R is an input argument,
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* otherwise, R is output.
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* If options->zFact = FACTORED and equed = 'R' or 'B', each element
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* of R must be positive.
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*
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* C (input/output) float*, dimension (A->ncol)
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* The column scale factors for A or transpose(A).
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* If equed = 'C' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
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* (if A->Stype = SLU_NR) is multiplied on the right by diag(C).
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* If equed = 'N' or 'R', C is not accessed.
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* If options->Fact = FACTORED, C is an input argument,
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* otherwise, C is output.
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* If options->Fact = FACTORED and equed = 'C' or 'B', each element
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* of C must be positive.
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*
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* L (output) SuperMatrix*
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* The factor L from the factorization
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* Pr*A*Pc=L*U (if A->Stype SLU_= NC) or
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* Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
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* Uses compressed row subscripts storage for supernodes, i.e.,
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* L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
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*
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* U (output) SuperMatrix*
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* The factor U from the factorization
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* Pr*A*Pc=L*U (if A->Stype = SLU_NC) or
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* Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
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* Uses column-wise storage scheme, i.e., U has types:
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* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
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*
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* work (workspace/output) void*, size (lwork) (in bytes)
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* User supplied workspace, should be large enough
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* to hold data structures for factors L and U.
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* On exit, if fact is not 'F', L and U point to this array.
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*
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* lwork (input) int
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* Specifies the size of work array in bytes.
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* = 0: allocate space internally by system malloc;
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* > 0: use user-supplied work array of length lwork in bytes,
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* returns error if space runs out.
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* = -1: the routine guesses the amount of space needed without
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* performing the factorization, and returns it in
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* mem_usage->total_needed; no other side effects.
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*
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* See argument 'mem_usage' for memory usage statistics.
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*
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* B (input/output) SuperMatrix*
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* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
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* On entry, the right hand side matrix.
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* If B->ncol = 0, only LU decomposition is performed, the triangular
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* solve is skipped.
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* On exit,
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* if equed = 'N', B is not modified; otherwise
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* if A->Stype = SLU_NC:
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* if options->Trans = NOTRANS and equed = 'R' or 'B',
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* B is overwritten by diag(R)*B;
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* if options->Trans = TRANS or CONJ and equed = 'C' of 'B',
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* B is overwritten by diag(C)*B;
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* if A->Stype = SLU_NR:
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* if options->Trans = NOTRANS and equed = 'C' or 'B',
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* B is overwritten by diag(C)*B;
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* if options->Trans = TRANS or CONJ and equed = 'R' of 'B',
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* B is overwritten by diag(R)*B.
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*
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* X (output) SuperMatrix*
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* X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
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* If info = 0 or info = A->ncol+1, X contains the solution matrix
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* to the original system of equations. Note that A and B are modified
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* on exit if equed is not 'N', and the solution to the equilibrated
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* system is inv(diag(C))*X if options->Trans = NOTRANS and
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* equed = 'C' or 'B', or inv(diag(R))*X if options->Trans = 'T' or 'C'
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* and equed = 'R' or 'B'.
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*
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* recip_pivot_growth (output) float*
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* The reciprocal pivot growth factor max_j( norm(A_j)/norm(U_j) ).
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* The infinity norm is used. If recip_pivot_growth is much less
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* than 1, the stability of the LU factorization could be poor.
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*
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* rcond (output) float*
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* The estimate of the reciprocal condition number of the matrix A
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* after equilibration (if done). If rcond is less than the machine
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* precision (in particular, if rcond = 0), the matrix is singular
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* to working precision. This condition is indicated by a return
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* code of info > 0.
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*
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* FERR (output) float*, dimension (B->ncol)
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* The estimated forward error bound for each solution vector
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* X(j) (the j-th column of the solution matrix X).
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* If XTRUE is the true solution corresponding to X(j), FERR(j)
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* is an estimated upper bound for the magnitude of the largest
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* element in (X(j) - XTRUE) divided by the magnitude of the
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* largest element in X(j). The estimate is as reliable as
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* the estimate for RCOND, and is almost always a slight
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* overestimate of the true error.
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* If options->IterRefine = NOREFINE, ferr = 1.0.
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*
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* BERR (output) float*, dimension (B->ncol)
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* The componentwise relative backward error of each solution
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* vector X(j) (i.e., the smallest relative change in
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* any element of A or B that makes X(j) an exact solution).
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* If options->IterRefine = NOREFINE, berr = 1.0.
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*
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* mem_usage (output) mem_usage_t*
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* Record the memory usage statistics, consisting of following fields:
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* - for_lu (float)
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* The amount of space used in bytes for L\U data structures.
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* - total_needed (float)
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* The amount of space needed in bytes to perform factorization.
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* - expansions (int)
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* The number of memory expansions during the LU factorization.
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*
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* stat (output) SuperLUStat_t*
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* Record the statistics on runtime and floating-point operation count.
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* See slu_util.h for the definition of 'SuperLUStat_t'.
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*
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* info (output) int*
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* = 0: successful exit
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* < 0: if info = -i, the i-th argument had an illegal value
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* > 0: if info = i, and i is
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* <= A->ncol: U(i,i) is exactly zero. The factorization has
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* been completed, but the factor U is exactly
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* singular, so the solution and error bounds
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* could not be computed.
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* = A->ncol+1: U is nonsingular, but RCOND is less than machine
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* precision, meaning that the matrix is singular to
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* working precision. Nevertheless, the solution and
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* error bounds are computed because there are a number
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* of situations where the computed solution can be more
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* accurate than the value of RCOND would suggest.
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* > A->ncol+1: number of bytes allocated when memory allocation
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* failure occurred, plus A->ncol.
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* </pre>
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*/
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void
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sgssvx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
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int *etree, char *equed, float *R, float *C,
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SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
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SuperMatrix *B, SuperMatrix *X, float *recip_pivot_growth,
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float *rcond, float *ferr, float *berr,
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mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info )
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{
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DNformat *Bstore, *Xstore;
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float *Bmat, *Xmat;
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int ldb, ldx, nrhs;
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SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
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SuperMatrix AC; /* Matrix postmultiplied by Pc */
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int colequ, equil, nofact, notran, rowequ, permc_spec;
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trans_t trant;
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char norm[1];
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int i, j, info1;
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float amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
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int relax, panel_size;
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float diag_pivot_thresh;
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double t0; /* temporary time */
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double *utime;
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/* External functions */
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extern float slangs(char *, SuperMatrix *);
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Bstore = B->Store;
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Xstore = X->Store;
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Bmat = Bstore->nzval;
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Xmat = Xstore->nzval;
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ldb = Bstore->lda;
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ldx = Xstore->lda;
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nrhs = B->ncol;
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*info = 0;
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nofact = (options->Fact != FACTORED);
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equil = (options->Equil == YES);
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notran = (options->Trans == NOTRANS);
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if ( nofact ) {
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*(unsigned char *)equed = 'N';
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rowequ = FALSE;
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colequ = FALSE;
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} else {
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rowequ = lsame_(equed, "R") || lsame_(equed, "B");
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colequ = lsame_(equed, "C") || lsame_(equed, "B");
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smlnum = slamch_("Safe minimum");
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bignum = 1. / smlnum;
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}
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#if 0
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printf("dgssvx: Fact=%4d, Trans=%4d, equed=%c\n",
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options->Fact, options->Trans, *equed);
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#endif
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/* Test the input parameters */
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if (!nofact && options->Fact != DOFACT && options->Fact != SamePattern &&
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options->Fact != SamePattern_SameRowPerm &&
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!notran && options->Trans != TRANS && options->Trans != CONJ &&
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!equil && options->Equil != NO)
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*info = -1;
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else if ( A->nrow != A->ncol || A->nrow < 0 ||
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(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
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A->Dtype != SLU_S || A->Mtype != SLU_GE )
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*info = -2;
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else if (options->Fact == FACTORED &&
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!(rowequ || colequ || lsame_(equed, "N")))
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*info = -6;
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else {
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if (rowequ) {
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rcmin = bignum;
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rcmax = 0.;
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for (j = 0; j < A->nrow; ++j) {
|
|
rcmin = SUPERLU_MIN(rcmin, R[j]);
|
|
rcmax = SUPERLU_MAX(rcmax, R[j]);
|
|
}
|
|
if (rcmin <= 0.) *info = -7;
|
|
else if ( A->nrow > 0)
|
|
rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
|
|
else rowcnd = 1.;
|
|
}
|
|
if (colequ && *info == 0) {
|
|
rcmin = bignum;
|
|
rcmax = 0.;
|
|
for (j = 0; j < A->nrow; ++j) {
|
|
rcmin = SUPERLU_MIN(rcmin, C[j]);
|
|
rcmax = SUPERLU_MAX(rcmax, C[j]);
|
|
}
|
|
if (rcmin <= 0.) *info = -8;
|
|
else if (A->nrow > 0)
|
|
colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
|
|
else colcnd = 1.;
|
|
}
|
|
if (*info == 0) {
|
|
if ( lwork < -1 ) *info = -12;
|
|
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
|
|
B->Stype != SLU_DN || B->Dtype != SLU_S ||
|
|
B->Mtype != SLU_GE )
|
|
*info = -13;
|
|
else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
|
|
(B->ncol != 0 && B->ncol != X->ncol) ||
|
|
X->Stype != SLU_DN ||
|
|
X->Dtype != SLU_S || X->Mtype != SLU_GE )
|
|
*info = -14;
|
|
}
|
|
}
|
|
if (*info != 0) {
|
|
i = -(*info);
|
|
xerbla_("sgssvx", &i);
|
|
return;
|
|
}
|
|
|
|
/* Initialization for factor parameters */
|
|
panel_size = sp_ienv(1);
|
|
relax = sp_ienv(2);
|
|
diag_pivot_thresh = options->DiagPivotThresh;
|
|
|
|
utime = stat->utime;
|
|
|
|
/* Convert A to SLU_NC format when necessary. */
|
|
if ( A->Stype == SLU_NR ) {
|
|
NRformat *Astore = A->Store;
|
|
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
|
|
sCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
|
|
Astore->nzval, Astore->colind, Astore->rowptr,
|
|
SLU_NC, A->Dtype, A->Mtype);
|
|
if ( notran ) { /* Reverse the transpose argument. */
|
|
trant = TRANS;
|
|
notran = 0;
|
|
} else {
|
|
trant = NOTRANS;
|
|
notran = 1;
|
|
}
|
|
} else { /* A->Stype == SLU_NC */
|
|
trant = options->Trans;
|
|
AA = A;
|
|
}
|
|
|
|
if ( nofact && equil ) {
|
|
t0 = SuperLU_timer_();
|
|
/* Compute row and column scalings to equilibrate the matrix A. */
|
|
sgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
|
|
|
|
if ( info1 == 0 ) {
|
|
/* Equilibrate matrix A. */
|
|
slaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
|
|
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
|
|
colequ = lsame_(equed, "C") || lsame_(equed, "B");
|
|
}
|
|
utime[EQUIL] = SuperLU_timer_() - t0;
|
|
}
|
|
|
|
|
|
if ( nofact ) {
|
|
|
|
t0 = SuperLU_timer_();
|
|
/*
|
|
* Gnet column permutation vector perm_c[], according to permc_spec:
|
|
* permc_spec = NATURAL: natural ordering
|
|
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
|
|
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
|
|
* permc_spec = COLAMD: approximate minimum degree column ordering
|
|
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
|
|
*/
|
|
permc_spec = options->ColPerm;
|
|
if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
|
|
get_perm_c(permc_spec, AA, perm_c);
|
|
utime[COLPERM] = SuperLU_timer_() - t0;
|
|
|
|
t0 = SuperLU_timer_();
|
|
sp_preorder(options, AA, perm_c, etree, &AC);
|
|
utime[ETREE] = SuperLU_timer_() - t0;
|
|
|
|
/* printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
|
|
relax, panel_size, sp_ienv(3), sp_ienv(4));
|
|
fflush(stdout); */
|
|
|
|
/* Compute the LU factorization of A*Pc. */
|
|
t0 = SuperLU_timer_();
|
|
sgstrf(options, &AC, relax, panel_size, etree,
|
|
work, lwork, perm_c, perm_r, L, U, stat, info);
|
|
utime[FACT] = SuperLU_timer_() - t0;
|
|
|
|
if ( lwork == -1 ) {
|
|
mem_usage->total_needed = *info - A->ncol;
|
|
return;
|
|
}
|
|
}
|
|
|
|
if ( options->PivotGrowth ) {
|
|
if ( *info > 0 ) {
|
|
if ( *info <= A->ncol ) {
|
|
/* Compute the reciprocal pivot growth factor of the leading
|
|
rank-deficient *info columns of A. */
|
|
*recip_pivot_growth = sPivotGrowth(*info, AA, perm_c, L, U);
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
|
|
*recip_pivot_growth = sPivotGrowth(A->ncol, AA, perm_c, L, U);
|
|
}
|
|
|
|
if ( options->ConditionNumber ) {
|
|
/* Estimate the reciprocal of the condition number of A. */
|
|
t0 = SuperLU_timer_();
|
|
if ( notran ) {
|
|
*(unsigned char *)norm = '1';
|
|
} else {
|
|
*(unsigned char *)norm = 'I';
|
|
}
|
|
anorm = slangs(norm, AA);
|
|
sgscon(norm, L, U, anorm, rcond, stat, info);
|
|
utime[RCOND] = SuperLU_timer_() - t0;
|
|
}
|
|
|
|
if ( nrhs > 0 ) {
|
|
/* Scale the right hand side if equilibration was performed. */
|
|
if ( notran ) {
|
|
if ( rowequ ) {
|
|
for (j = 0; j < nrhs; ++j)
|
|
for (i = 0; i < A->nrow; ++i)
|
|
Bmat[i + j*ldb] *= R[i];
|
|
}
|
|
} else if ( colequ ) {
|
|
for (j = 0; j < nrhs; ++j)
|
|
for (i = 0; i < A->nrow; ++i)
|
|
Bmat[i + j*ldb] *= C[i];
|
|
}
|
|
|
|
/* Compute the solution matrix X. */
|
|
for (j = 0; j < nrhs; j++) /* Save a copy of the right hand sides */
|
|
for (i = 0; i < B->nrow; i++)
|
|
Xmat[i + j*ldx] = Bmat[i + j*ldb];
|
|
|
|
t0 = SuperLU_timer_();
|
|
sgstrs (trant, L, U, perm_c, perm_r, X, stat, info);
|
|
utime[SOLVE] = SuperLU_timer_() - t0;
|
|
|
|
/* Use iterative refinement to improve the computed solution and compute
|
|
error bounds and backward error estimates for it. */
|
|
t0 = SuperLU_timer_();
|
|
if ( options->IterRefine != NOREFINE ) {
|
|
sgsrfs(trant, AA, L, U, perm_c, perm_r, equed, R, C, B,
|
|
X, ferr, berr, stat, info);
|
|
} else {
|
|
for (j = 0; j < nrhs; ++j) ferr[j] = berr[j] = 1.0;
|
|
}
|
|
utime[REFINE] = SuperLU_timer_() - t0;
|
|
|
|
/* Transform the solution matrix X to a solution of the original system. */
|
|
if ( notran ) {
|
|
if ( colequ ) {
|
|
for (j = 0; j < nrhs; ++j)
|
|
for (i = 0; i < A->nrow; ++i)
|
|
Xmat[i + j*ldx] *= C[i];
|
|
}
|
|
} else if ( rowequ ) {
|
|
for (j = 0; j < nrhs; ++j)
|
|
for (i = 0; i < A->nrow; ++i)
|
|
Xmat[i + j*ldx] *= R[i];
|
|
}
|
|
} /* end if nrhs > 0 */
|
|
|
|
if ( options->ConditionNumber ) {
|
|
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
|
|
if ( *rcond < slamch_("E") ) *info = A->ncol + 1;
|
|
}
|
|
|
|
if ( nofact ) {
|
|
sQuerySpace(L, U, mem_usage);
|
|
Destroy_CompCol_Permuted(&AC);
|
|
}
|
|
if ( A->Stype == SLU_NR ) {
|
|
Destroy_SuperMatrix_Store(AA);
|
|
SUPERLU_FREE(AA);
|
|
}
|
|
|
|
}
|