#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zhpgv_(integer *itype, char *jobz, char *uplo, integer * n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex *work, doublereal *rwork, integer * info) { /* -- LAPACK driver routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= ZHPGV computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian, stored in packed format, and B is also positive definite. Arguments ========= ITYPE (input) INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) INTEGER The order of the matrices A and B. N >= 0. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed. BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H, in the same storage format as B. W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = 'N', then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1)) RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: ZPPTRF or ZHPEV returned an error code: <= N: if INFO = i, ZHPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not convergeto zero; > N: if INFO = N + i, for 1 <= i <= n, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer z_dim1, z_offset, i__1; /* Local variables */ static integer neig, j; extern logical lsame_(char *, char *); static char trans[1]; static logical upper; extern /* Subroutine */ int zhpev_(char *, char *, integer *, doublecomplex *, doublereal *, doublecomplex *, integer *, doublecomplex *, doublereal *, integer *); static logical wantz; extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex * , doublecomplex *, integer *), xerbla_( char *, integer *), zhpgst_(integer *, char *, integer *, doublecomplex *, doublecomplex *, integer *), zpptrf_( char *, integer *, doublecomplex *, integer *); #define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1 #define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)] --ap; --bp; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; --rwork; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); *info = 0; if (*itype < 0 || *itype > 3) { *info = -1; } else if (! (wantz || lsame_(jobz, "N"))) { *info = -2; } else if (! (upper || lsame_(uplo, "L"))) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHPGV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Form a Cholesky factorization of B. */ zpptrf_(uplo, n, &bp[1], info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem and solve. */ zhpgst_(itype, uplo, n, &ap[1], &bp[1], info); zhpev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], & rwork[1], info); if (wantz) { /* Backtransform eigenvectors to the original problem. */ neig = *n; if (*info > 0) { neig = *info - 1; } if (*itype == 1 || *itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ if (upper) { *(unsigned char *)trans = 'N'; } else { *(unsigned char *)trans = 'C'; } i__1 = neig; for (j = 1; j <= i__1; ++j) { ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z___ref(1, j), & c__1); /* L10: */ } } else if (*itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (upper) { *(unsigned char *)trans = 'C'; } else { *(unsigned char *)trans = 'N'; } i__1 = neig; for (j = 1; j <= i__1; ++j) { ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z___ref(1, j), & c__1); /* L20: */ } } } return 0; /* End of ZHPGV */ } /* zhpgv_ */ #undef z___ref #undef z___subscr