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SSBEVD(l)) SSBEVD(l)NAMESSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix ASYNOPSISSUBROUTINE SSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO ) CHARACTER JOBZ, UPLO INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N INTEGER IWORK( * ) REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )PURPOSESSBEVD computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arith- metic. 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.ARGUMENTSJOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub- diagonals if UPLO = 'L'. KD >= 0. AB (input/output) REAL array, dimension (LDAB, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th col- umn of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD + 1. W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) REAL array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(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/output) REAL array, dimension (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 must be at least 1. If JOBZ = 'N' and N > 2, LWORK must be at least 2*N. If JOBZ = 'V' and N > 2, LWORK must be at least ( 1 + 5*N + 2*N**2 ). If LWORK =, 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. IWORK (workspace/output) INTEGER array, dimension (LIWORK) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of the array LIWORK. If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N. If LIWORK =-1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO =-1, the i-th argument had an illegal value > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.-iLAPACK version 3.015 June 2000 SSBEVD(l)

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