#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int chbgvd_(char *jobz, char *uplo, integer *n, integer *ka, integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, real *rwork, integer *lrwork, integer *iwork, integer *liwork, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CHBGVD computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments ========= 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. KA (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB (input) INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0. AB (input/output) COMPLEX array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB (input/output) COMPLEX array, dimension (LDBB, N) On entry, the upper or lower triangle of the Hermitian band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**H*S, as returned by CPBSTF. LDBB (input) INTEGER The leading dimension of the array BB. LDBB >= KB+1. W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) COMPLEX array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so that Z**H*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 >= N. WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO=0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= N. If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK)) On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. LRWORK (input) INTEGER The dimension of array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = 'N' and N > 1, LRWORK >= N. If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK 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, and i is: <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then CPBSTF returned INFO = i: 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 complex c_b1 = {1.f,0.f}; static complex c_b2 = {0.f,0.f}; /* System generated locals */ integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1; /* Local variables */ static integer inde; static char vect[1]; static integer llwk2; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); extern logical lsame_(char *, char *); static integer iinfo, lwmin; static logical upper; static integer llrwk; static logical wantz; static integer indwk2; extern /* Subroutine */ int cstedc_(char *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, integer *, integer *, integer *, integer *), chbtrd_(char *, char *, integer *, integer *, complex *, integer *, real *, real *, complex *, integer *, complex *, integer *), chbgst_(char *, char *, integer *, integer *, integer *, complex * , integer *, complex *, integer *, complex *, integer *, complex * , real *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *), cpbstf_(char *, integer *, integer *, complex *, integer *, integer *); static integer indwrk, liwmin; extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *); static integer lrwmin; static logical lquery; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; bb_dim1 = *ldbb; bb_offset = 1 + bb_dim1; bb -= bb_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --rwork; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; *info = 0; if (*n <= 1) { lwmin = 1; lrwmin = 1; liwmin = 1; } else if (wantz) { /* Computing 2nd power */ i__1 = *n; lwmin = i__1 * i__1 << 1; /* Computing 2nd power */ i__1 = *n; lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); liwmin = *n * 5 + 3; } else { lwmin = *n; lrwmin = *n; liwmin = 1; } if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (upper || lsame_(uplo, "L"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ka < 0) { *info = -4; } else if (*kb < 0 || *kb > *ka) { *info = -5; } else if (*ldab < *ka + 1) { *info = -7; } else if (*ldbb < *kb + 1) { *info = -9; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -12; } if (*info == 0) { work[1].r = (real) lwmin, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -14; } else if (*lrwork < lrwmin && ! lquery) { *info = -16; } else if (*liwork < liwmin && ! lquery) { *info = -18; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHBGVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Form a split Cholesky factorization of B. */ cpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem. */ inde = 1; indwrk = inde + *n; indwk2 = *n * *n + 1; llwk2 = *lwork - indwk2 + 2; llrwk = *lrwork - indwrk + 2; chbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, &z__[z_offset], ldz, &work[1], &rwork[indwrk], &iinfo); /* Reduce Hermitian band matrix to tridiagonal form. */ if (wantz) { *(unsigned char *)vect = 'U'; } else { *(unsigned char *)vect = 'N'; } chbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], & z__[z_offset], ldz, &work[1], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. */ if (! wantz) { ssterf_(n, &w[1], &rwork[inde], info); } else { cstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], & llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info); cgemm_("N", "N", n, n, n, &c_b1, &z__[z_offset], ldz, &work[1], n, & c_b2, &work[indwk2], n); clacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz); } work[1].r = (real) lwmin, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; return 0; /* End of CHBGVD */ } /* chbgvd_ */