#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zhesv_(char *uplo, integer *n, integer *nrhs, doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *work, integer *lwork, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZHESV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-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-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, 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. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (output) INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by ZHETRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; /* Local variables */ static integer nb; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int zhetrf_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zhetrs_(char *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *); static integer lwkopt; static logical lquery; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --work; /* Function Body */ *info = 0; lquery = *lwork == -1; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*lda < max(1,*n)) { *info = -5; } else if (*ldb < max(1,*n)) { *info = -8; } else if (*lwork < 1 && ! lquery) { *info = -10; } if (*info == 0) { if (*n == 0) { lwkopt = 1; } else { nb = ilaenv_(&c__1, "ZHETRF", uplo, n, &c_n1, &c_n1, &c_n1, ( ftnlen)6, (ftnlen)1); lwkopt = *n * nb; } work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHESV ", &i__1); return 0; } else if (lquery) { return 0; } /* Compute the factorization A = U*D*U' or A = L*D*L'. */ zhetrf_(uplo, n, &a[a_offset], lda, &ipiv[1], &work[1], lwork, info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ zhetrs_(uplo, n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb, info); } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; /* End of ZHESV */ } /* zhesv_ */