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SUBROUTINE <a name="CHPEVD.1"></a><a href="chpevd.f.html#CHPEVD.1">CHPEVD</a>( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
$ RWORK, LRWORK, IWORK, LIWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CHPEVD.21"></a><a href="chpevd.f.html#CHPEVD.1">CHPEVD</a> computes all the eigenvalues and, optionally, eigenvectors of
</span><span class="comment">*</span><span class="comment"> a complex Hermitian matrix A in packed storage. If eigenvectors are
</span><span class="comment">*</span><span class="comment"> desired, it uses a divide and conquer algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The divide and conquer algorithm makes very mild assumptions about
</span><span class="comment">*</span><span class="comment"> floating point arithmetic. It will work on machines with a guard
</span><span class="comment">*</span><span class="comment"> digit in add/subtract, or on those binary machines without guard
</span><span class="comment">*</span><span class="comment"> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
</span><span class="comment">*</span><span class="comment"> Cray-2. It could conceivably fail on hexadecimal or decimal machines
</span><span class="comment">*</span><span class="comment"> without guard digits, but we know of none.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> JOBZ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment"> = 'V': Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the Hermitian matrix
</span><span class="comment">*</span><span class="comment"> A, packed columnwise in a linear array. The j-th column of A
</span><span class="comment">*</span><span class="comment"> is stored in the array AP as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, AP is overwritten by values generated during the
</span><span class="comment">*</span><span class="comment"> reduction to tridiagonal form. If UPLO = 'U', the diagonal
</span><span class="comment">*</span><span class="comment"> and first superdiagonal of the tridiagonal matrix T overwrite
</span><span class="comment">*</span><span class="comment"> the corresponding elements of A, and if UPLO = 'L', the
</span><span class="comment">*</span><span class="comment"> diagonal and first subdiagonal of T overwrite the
</span><span class="comment">*</span><span class="comment"> corresponding elements of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (output) COMPLEX array, dimension (LDZ, N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
</span><span class="comment">*</span><span class="comment"> eigenvectors of the matrix A, with the i-th column of Z
</span><span class="comment">*</span><span class="comment"> holding the eigenvector associated with W(i).
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Z. LDZ >= 1, and if
</span><span class="comment">*</span><span class="comment"> JOBZ = 'V', LDZ >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the required LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of array WORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LWORK must be at least N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the required sizes of the WORK, RWORK and
</span><span class="comment">*</span><span class="comment"> IWORK arrays, returns these values as the first entries of
</span><span class="comment">*</span><span class="comment"> the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.86"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LRWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of array RWORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LRWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LRWORK must be at least
</span><span class="comment">*</span><span class="comment"> 1 + 5*N + 2*N**2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LRWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment"> routine only calculates the required sizes of the WORK, RWORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment"> of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.102"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LIWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of array IWORK.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment"> routine only calculates the required sizes of the WORK, RWORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment"> of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.116"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i, the algorithm failed to converge; i
</span><span class="comment">*</span><span class="comment"> off-diagonal elements of an intermediate tridiagonal
</span><span class="comment">*</span><span class="comment"> form did not converge to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL LQUERY, WANTZ
INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
$ ISCALE, LIWMIN, LLRWK, LLWRK, LRWMIN, LWMIN
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