zhesv zhesvx zhpsv zhpsvx

zhpsv() void zhpsv ( char  uplo, int  n, int  nrhs, doublecomplex  ap[], int  ipiv[], int  ldb, doublecomplex  b[], int *  info  ) (Simple driver) Solution to system of linear equations AX = B for a Hermitian matrix in packed form Purpose This routine computes the solution to a complex system of linear equations A * X = B where A is an n x n Hermitian matrix stored in packed form, and X and B are n x nrhs matrices. The diagonal pivoting method is used to factor A as A = U * D * U^H, if uplo = 'U', or A = L * D * L^H, if uplo = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1 x 1 and 2 x 2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. Parameters [in] uplo = 'U': Upper triangle of A is stored. = 'L': Lower triangle of A is stored. [in] n Number of linear equations, i.e., order of the matrix A. (n >= 0) (If n = 0, returns without computation) [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,out] ap[] Array ap[lap] (lap >= n(n + 1)/2) [in] n x n Hermitian matrix A in packed form. The upper or lower part is to be stored in accordance with uplo. [out] The block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U^H or A = L*D*L^H as computed by zhptrf, stored as a packed triangular matrix in the same storage format as A. [out] ipiv[] Array ipiv[lipiv] (lipiv >= n) Details of the interchanges and the block structure of D, as determined by zhptrf. If ipiv[k-1] > 0, then rows and columns k and ipiv[k-1] were interchanged, and k-th diagonal of D is a 1 x 1 diagonal block. If uplo = 'U' and ipiv[k-1] = ipiv[k-2] < 0, then rows and columns k-1 and -ipiv[k-1] were interchanged and (k-1)-th diagonal of D is a 2 x 2 diagonal block. If uplo = 'L' and ipiv[k-1] = ipiv[k] < 0, then rows and columns k+1 and -ipiv[k-1] were interchanged and k-th diagonal of D is a 2 x 2 diagonal block. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in,out] b[][] Array b[lb][ldb] (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 uplo had an illegal value (uplo != 'U' nor 'L') = -2: The argument n had an illegal value (n < 0) = -3: The argument nrhs had an illegal value (nrhs < 0) = -6: The argument ldb had an illegal value (ldb < max(1, n)) = i > 0: The i-th element of the factor D is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. Reference LAPACK