Zgssv Zgssvx

Zgssv() Sub Zgssv ( N As  Long, Val() As  Complex, Ptr() As  Long, Ind() As  Long, B() As  Complex, RCond As  Double, Optional Info As  Long, Optional Format As  Long = 0, Optional Base As  Long = -1, Optional Nrhs As  Long = 1, Optional ColPerm As  String = "A", Optional Thresh As  Double = 1, Optional SymMode As  String = "N"  ) Solves the system of linear equations A*X = B (direct method) (complex sparse matrix) (SuperLU) (simple driver) Purpose This routine solves the system of linear equations A*X = B, using the LU factorization, where A is a general N x N complex sparse matrix. A condition estimate is also computed. It performs the following steps: If A is stored column-wise (CSC): 1.1. Permute the columns of A, forming A*Pc, where Pc is a permutation matrix. 1.2. Factor A as Pr*A*Pc = L*U with the permutation Pr determined by Gaussian elimination with partial pivoting. L is unit lower triangular with offdiagonal entries bounded by 1 in magnitude, and U is upper triangular. 1.3. Solve the system of equations A*X = B using the factored form of A. If A is stored row-wise (CSR), apply the above algorithm to the transpose of A: 2.1. Permute columns of transpose(A) (rows of A), forming transpose(A)*Pc, where Pc is a permutation matrix. 2.2. Factor A as Pr*transpose(A)*Pc = L*U with the permutation Pr determined by Gaussian elimination with partial pivoting. L is unit lower triangular with offdiagonal entries bounded by 1 in magnitude, and U is upper triangular. 2.3. Solve the system of equations A*X = B using the factored form of A. Parameters [in] N Number of rows and columns of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] Val() Array Val(LVal - 1) (LVal >= Nnz) (Nnz is the number of nonzero elements of the matrix) Values of nonzero elements of the matrix A. [in] Ptr() Array Ptr(LPtr - 1) (LPtr >= N + 1) Column pointers (if CSC) or row pointers (if CSR) of the matrix A. [in] Ind() Array Ind(LInd - 1) (LInd >= Nnz) Row indices (if CSC) or column indices (if CSR) of the matrix A. [in,out] B() Array B(LB1 - 1, LB2 - 1) (LB1 >= N, LB2 >= Nrhs) (2D array) or B(LB - 1) (LB >= N, Nrhs = 1) (1D array) [in] N x Nrhs right hand side matrix B. [out] The solution matrix X. [out] Rcond Estimated reciprocal of the condition number of the matrix A. [out] Info (Optional) = 0: Successful exit. < 0: The (-Info)-th argument is invalid. = -10000: Unrecoverble error occured in SuperLU routine. = i > 0 and <= N: U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. = i > N: Memory allocation failure occurred. i - N is the number of bytes allocated. [in] Format (Optional) Sparse matrix format. (default = 0) = 0: CSR format. = 1: CSC format. [in] Base (Optional) Indexing of Rowptr() and Colind(). = 0: Zero-based (C style) indexing: Starting index is 0. = 1: One-based (Fortran style) indexing: Starting index is 1. (default: Assumes 1 if Ptr(0) = 1, otherwise 0) [in] Nrhs (Optional) Number of right hand sides, i.e., number of columns of the matrix B. (Nrhs >= 0) (If Nrhs = 0, returns without computation) (default = 1) [in] ColPerm (Optional) Specifies the type of column ordering to reduce fill-in. = "A": Approximate minimum degree (AMD) ordering. = "N": Natural ordering (No ordering) (Pc = I). = "M": Multiple minimum degree (MMD) ordering on A^T*A. = "P": Multiple minimum degree (MMD) ordering on A^T + A. (default = "A") [in] Thresh (Optional) Specifies the threshold used for a diagonal entry to be an acceptable pivot (0 <= Thresh <= 1). (default = 1) [in] SymMode (Optional) Specifies whether to use symmetric mode. Symmetric mode gives preference to diagonal pivots, and uses an (A^T + A)-based column permutation algorithm. = "N": Do not use symmetric mode. = "S": Use symmetric mode. (default = "N") Reference SuperLU Example Program Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( 0.78+0.16i -0.9-1.46i 0.48-1.08i ) A = ( 0.73+0.63i 1.58-1.24 -0.41-0.91i ) ( 0.23-1.37i 0.79+0.64i -0.73-1.5i ) ( 0.2126-0.2904i ) B = ( -0.3028+0.3346i ) ( -1.2905-1.0346i ) Sub Ex_Zgssv() Const N = 3, Nnz = N * N Dim A(Nnz - 1) As Complex, Ia(N) As Long, Ja(Nnz - 1) As Long Dim B(N - 1) As Complex Dim RCond As Double, Info As Long A(0) = Cmplx(0.78, 0.16): A(1) = Cmplx(-0.9, -1.46): A(2) = Cmplx(0.48, -1.08): A(3) = Cmplx(0.73, 0.63): A(4) = Cmplx(1.58, -1.24): A(5) = Cmplx(-0.41, -0.91): A(6) = Cmplx(0.23, -1.37): A(7) = Cmplx(0.79, 0.64): A(8) = Cmplx(-0.73, -1.5) Ia(0) = 0: Ia(1) = 3: Ia(2) = 6: Ia(3) = 9 Ja(0) = 0: Ja(1) = 1: Ja(2) = 2: Ja(3) = 0: Ja(4) = 1: Ja(5) = 2: Ja(6) = 0: Ja(7) = 1: Ja(8) = 2 B(0) = Cmplx(0.2126, -0.2904): B(1) = Cmplx(-0.3028, 0.3346): B(2) = Cmplx(-1.2905, -1.0346) Call Zgssv(N, A(), Ia(), Ja(), B(), RCond, Info) Debug.Print "X =" Debug.Print "(" + CStr(Creal(B(0))) + ", " + CStr(Cimag(B(0))) + ")" Debug.Print "(" + CStr(Creal(B(1))) + ", " + CStr(Cimag(B(1))) + ")" Debug.Print "(" + CStr(Creal(B(2))) + ", " + CStr(Cimag(B(2))) + ")" Debug.Print "RCond = " + CStr(RCond) + ", Info = " + CStr(Info) End Sub Example Results X = (0.59, -0.28) (-0.2, -3.99999999999999E-02) (0.24, -0.49) RCond = 0.194425064735609, Info = 0