#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zhpgvx_(integer *itype, char *jobz, char *range, char * uplo, integer *n, doublecomplex *ap, doublecomplex *bp, doublereal * vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex *work, doublereal *rwork, integer *iwork, integer * ifail, integer *info ) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZHPGVX computes selected eigenvalues and, optionally, 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. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. 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. RANGE (input) CHARACTER*1 = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found. 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. VL (input) DOUBLE PRECISION VU (input) DOUBLE PRECISION If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. IL (input) INTEGER IU (input) INTEGER If RANGE='I', the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. ABSTOL (input) DOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing AP to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S'). M (output) INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. W (output) DOUBLE PRECISION array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. Z (output) COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'N', then Z is not referenced. If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). 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 an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. 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 (2*N) RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) IWORK (workspace) INTEGER array, dimension (5*N) IFAIL (output) INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: ZPPTRF or ZHPEVX returned an error code: <= N: if INFO = i, ZHPEVX failed to converge; i eigenvectors failed to converge. Their indices are stored in array IFAIL. > 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. Further Details =============== Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA ===================================================================== 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 j; extern logical lsame_(char *, char *); static char trans[1]; static logical upper, wantz; extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex * , doublecomplex *, integer *); static logical alleig, indeig, valeig; extern /* Subroutine */ int xerbla_(char *, integer *), zhpgst_( integer *, char *, integer *, doublecomplex *, doublecomplex *, integer *), zhpevx_(char *, char *, char *, integer *, doublecomplex *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, doublecomplex *, integer * , doublecomplex *, doublereal *, integer *, integer *, integer *), zpptrf_(char *, integer *, doublecomplex *, integer *); --ap; --bp; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --rwork; --iwork; --ifail; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); *info = 0; if (*itype < 1 || *itype > 3) { *info = -1; } else if (! (wantz || lsame_(jobz, "N"))) { *info = -2; } else if (! (alleig || valeig || indeig)) { *info = -3; } else if (! (upper || lsame_(uplo, "L"))) { *info = -4; } else if (*n < 0) { *info = -5; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -9; } } else if (indeig) { if (*il < 1) { *info = -10; } else if (*iu < min(*n,*il) || *iu > *n) { *info = -11; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZHPGVX", &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); zhpevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], & z__[z_offset], ldz, &work[1], &rwork[1], &iwork[1], &ifail[1], info); if (wantz) { /* Backtransform eigenvectors to the original problem. */ if (*info > 0) { *m = *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 = *m; for (j = 1; j <= i__1; ++j) { ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 1], &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 = *m; for (j = 1; j <= i__1; ++j) { ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 1], &c__1); /* L20: */ } } } return 0; /* End of ZHPGVX */ } /* zhpgvx_ */