heev - {he,sy}ev: eig, QR iteration

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subroutinecheev(characterjobz,characteruplo,integern,complex,dimension(lda,*)a,integerlda,real,dimension(*)w,complex,dimension(*)work,integerlwork,real,dimension(*)rwork,integerinfo)CHEEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforHEmatricesPurpose: CHEEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). W W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for CHETRD returned by ILAENV. If LWORK = -1, 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. RWORK RWORK is REAL array, dimension (max(1, 3*N-2)) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedsyev(characterjobz,characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)w,doubleprecision,dimension(*)work,integerlwork,integerinfo)DSYEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforSYmatricesPurpose: DSYEV computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). W W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The length of the array WORK. LWORK >= max(1,3*N-1). For optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for DSYTRD returned by ILAENV. If LWORK = -1, 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. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinessyev(characterjobz,characteruplo,integern,real,dimension(lda,*)a,integerlda,real,dimension(*)w,real,dimension(*)work,integerlwork,integerinfo)SSYEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforSYmatricesPurpose: SSYEV computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is REAL array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). W W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The length of the array WORK. LWORK >= max(1,3*N-1). For optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for SSYTRD returned by ILAENV. If LWORK = -1, 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. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezheev(characterjobz,characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)w,complex*16,dimension(*)work,integerlwork,doubleprecision,dimension(*)rwork,integerinfo)ZHEEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforHEmatricesPurpose: ZHEEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX*16 array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). W W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK LWORK is INTEGER The length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD returned by ILAENV. If LWORK = -1, 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. RWORK RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

heev - {he,sy}ev: eig, QR iteration

Functions subroutine cheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info) CHEEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforHEmatrices subroutine dsyev (jobz, uplo, n, a, lda, w, work, lwork, info) DSYEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforSYmatrices subroutine ssyev (jobz, uplo, n, a, lda, w, work, lwork, info) SSYEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforSYmatrices subroutine zheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info) ZHEEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforHEmatrices