zcgesv zgbsv zgbsvx zgesv zgesvx zgtsv zgtsvx zspsv zspsvx zsysv zsysvx

zgbsv() void zgbsv ( int  n, int  kl, int  ku, int  nrhs, int  ldab, doublecomplex  ab[], int  ipiv[], int  ldb, doublecomplex  b[], int *  info  ) (Simple driver) Solution to system of linear equations AX = B for a complex band matrix Purpose This routine computes the solution to a complex system of linear equations A * X = B where A is a band matrix of order n with kl sub-diagonals and ku super-diagonals, and X and B are n x nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U where L is a product of permutation and unit lower triangular matrices with kl sub-diagonals, and U is upper triangular with kl+ku super-diagonals. The factored form of A is then used to solve the system of equations A * X = B. Parameters [in] n Number of linear equations, i.e., order of the matrix A. (n >= 0) (If n = 0, returns without computation) [in] kl The number of sub-diagonals within the band of A. (kl >= 0) [in] ku The number of super-diagonals within the band of A. (ku >= 0) [in] nrhs Number of right hand sides, i.e., number of columns of the matrix B. (nrhs >= 0) (If nrhs = 0, returns without computation) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= 2kl + ku + 1) [in,out] ab[][] Array ab[lab][ldab] (lab >= n) [in] The matrix A in band matrix form, in rows kl+1 to 2kl+ku+1; rows 1 to kl of the array need not be set. [out] Details of the factorization: U is stored as an upper triangular band matrix with kl+ku super-diagonals in rows 1 to kl+ku+1, and the multipliers used during the factorization are stored in rows kl+ku+2 to 2*kl+ku+1. See below for further details. [out] ipiv() Array ipiv[lipiv] (lipiv >= n) Pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i-1]. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in,out] b[][] Array b[lb][ldab] (lb >= nrhs) [in] n x nrhs right hand side matrix B. [out] If info = 0, n x nrhs solution matrix X. [out] info = 0: Successful exit = -1: The argument n had an illegal value (n < 0) = -2: The argument kl had an illegal value (kl < 0) = -3: The argument ku had an illegal value (ku < 0) = -4: The argument nrhs had an illegal value (nrhs < 0) = -5: The argument ldab had an illegal value (ldab < 2kl+ku+1) = -8: The argument ldb had an illegal value (ldb < max(1, n)) = i > 0: The i-th diagonal element of the factor U is exactly zero. The factorization has been completed, but the factor U is exactly singular, and the solution has not been computed. Further Details The band matrix form is illustrated by the following example, when n = 6, kl = 2, ku = 1: On entry: * * * + + + * * + + + + * a12 a23 a34 a45 a56 a11 a22 a33 a44 a55 a66 a21 a32 a43 a54 a65 * a31 a42 a53 a64 * * On exit: * * * u14 u25 u36 * * u13 u24 u35 u46 * u12 u23 u34 u45 u56 u11 u22 u33 u44 u55 u66 m21 m32 m43 m54 m65 * m31 m42 m53 m64 * * Array elements marked * are not used by the routine; elements marked + need not be set on entry, but are required by the routine to store elements of U because of fill-in resulting from the row interchanges. Reference LAPACK