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SUBROUTINE <a name="DSPGVD.1"></a><a href="dspgvd.f.html#DSPGVD.1">DSPGVD</a>( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ LWORK, 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, ITYPE, LDZ, LIWORK, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
DOUBLE PRECISION AP( * ), BP( * ), W( * ), 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="DSPGVD.21"></a><a href="dspgvd.f.html#DSPGVD.1">DSPGVD</a> computes all the eigenvalues, and optionally, the eigenvectors
</span><span class="comment">*</span><span class="comment"> of a real generalized symmetric-definite eigenproblem, of the form
</span><span class="comment">*</span><span class="comment"> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
</span><span class="comment">*</span><span class="comment"> B are assumed to be symmetric, stored in packed format, and B is also
</span><span class="comment">*</span><span class="comment"> positive definite.
</span><span class="comment">*</span><span class="comment"> If eigenvectors are 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"> ITYPE (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specifies the problem type to be solved:
</span><span class="comment">*</span><span class="comment"> = 1: A*x = (lambda)*B*x
</span><span class="comment">*</span><span class="comment"> = 2: A*B*x = (lambda)*x
</span><span class="comment">*</span><span class="comment"> = 3: B*A*x = (lambda)*x
</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 triangles of A and B are stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangles of A and B are 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 matrices A and B. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric 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, the contents of AP are destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric matrix
</span><span class="comment">*</span><span class="comment"> B, packed columnwise in a linear array. The j-th column of B
</span><span class="comment">*</span><span class="comment"> is stored in the array BP as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, the triangular factor U or L from the Cholesky
</span><span class="comment">*</span><span class="comment"> factorization B = U**T*U or B = L*L**T, in the same storage
</span><span class="comment">*</span><span class="comment"> format as B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDZ, N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
</span><span class="comment">*</span><span class="comment"> eigenvectors. The eigenvectors are normalized as follows:
</span><span class="comment">*</span><span class="comment"> if ITYPE = 1 or 2, Z**T*B*Z = I;
</span><span class="comment">*</span><span class="comment"> if ITYPE = 3, Z**T*inv(B)*Z = 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) DOUBLE PRECISION 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 the array WORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LWORK >= 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
</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 and IWORK
</span><span class="comment">*</span><span class="comment"> arrays, returns these values as the first entries of the WORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, and no error message related to LWORK or
</span><span class="comment">*</span><span class="comment"> 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 the array IWORK.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LIWORK >= 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 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 and IWORK arrays, and no error message related to
</span><span class="comment">*</span><span class="comment"> LWORK 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: <a name="DPPTRF.121"></a><a href="dpptrf.f.html#DPPTRF.1">DPPTRF</a> or <a name="DSPEVD.121"></a><a href="dspevd.f.html#DSPEVD.1">DSPEVD</a> returned an error code:
</span><span class="comment">*</span><span class="comment"> <= N: if INFO = i, <a name="DSPEVD.122"></a><a href="dspevd.f.html#DSPEVD.1">DSPEVD</a> failed to converge;
</span><span class="comment">*</span><span class="comment"> i off-diagonal elements of an intermediate
</span><span class="comment">*</span><span class="comment"> tridiagonal form did not converge to zero;
</span><span class="comment">*</span><span class="comment"> > N: if INFO = N + i, for 1 <= i <= N, then the leading
</span><span class="comment">*</span><span class="comment"> minor of order i of B is not positive definite.
</span><span class="comment">*</span><span class="comment"> The factorization of B could not be completed and
</span><span class="comment">*</span><span class="comment"> no eigenvalues or eigenvectors were computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
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