zhesv zhesvx zhpsv zhpsvx

zhesv() void zhesv ( char  uplo, int  n, int  nrhs, int  lda, doublecomplex  a[], int  ipiv[], int  ldb, doublecomplex  b[], doublecomplex  work[], int  lwork, int *  info  ) (Simple driver) Solution to system of linear equations AX = B for a Hermitian matrix 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 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] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, n)) [in,out] a[][] Array a[la][lda] (la >= n) [in] n x n Hermitian matrix A. The upper or lower triangular part is to be referenced in accordance with uplo. [out] If info = 0, 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 zhetrf. [out] ipiv[] Array ipiv[lipiv] (lipiv >= n) Details of the interchanges and the block structure of D, as determined by zhetrf. 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] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The length of work[] (lwork >= 1) For best performance, lwork >= max(1, n*nb), where nb is the optimal blocksize for zhetrf. For lwork < n, the factorization will be done with Level 2 BLAS. For lwork >= n, the factorization will be done with Level 3 BLAS. If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work array and returns the value in work[0]. [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) = -4: The argument lda had an illegal value (lda < max(1, n)) = -7: The argument ldb had an illegal value (ldb < max(1, n)) = -10: The argument lwork had an illegal value (lwork too small) = i > 0: The i-th element of 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