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SSYEVD(l)) SSYEVD(l)NAMESSYEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix ASYNOPSISSUBROUTINE SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, INFO ) CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LIWORK, LWORK, N INTEGER IWORK( * ) REAL A( LDA, * ), W( * ), WORK( * )PURPOSESSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric 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. Because of large use of BLAS of level 3, SSYEVD needs N**2 more workspace than SSYEVX.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. A (input/output) REAL array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper trian- gular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 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 > 1, LWORK must be at least 2*N+1. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*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 IWORK. If N <= 1, LIWORK must be at least 1. If JOBZ = 'N' and N > 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, 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.-iFURTHER DETAILSBased on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee.LAPACK version 3.015 June 2000 SSYEVD(l)

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