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- SSPGV - compute all the eigenvalues and, optionally, the eigenvectors of
- a real generalized symmetric-definite eigenproblem, of the form
- A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
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- SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
- SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )
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- CHARACTER JOBZ, UPLO
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- INTEGER INFO, ITYPE, LDZ, N
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- REAL AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )
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- PPPPUUUURRRRPPPPOOOOSSSSEEEE
- SSPGV computes all the eigenvalues and, optionally, the eigenvectors of a
- real generalized symmetric-definite eigenproblem, of the form
- A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B
- are assumed to be symmetric, stored in packed format, and B is also
- positive definite.
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- ITYPE (input) INTEGER
- Specifies the problem type to be solved:
- = 1: A*x = (lambda)*B*x
- = 2: A*B*x = (lambda)*x
- = 3: B*A*x = (lambda)*x
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- JOBZ (input) CHARACTER*1
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors.
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- UPLO (input) CHARACTER*1
- = 'U': Upper triangles of A and B are stored;
- = 'L': Lower triangles of A and B are stored.
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- N (input) INTEGER
- The order of the matrices A and B. N >= 0.
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- AP (input/output) REAL array, dimension
- (N*(N+1)/2) On entry, the upper or lower triangle of the
- symmetric matrix A, packed columnwise in a linear array. The j-
- th column of A is stored in the array AP as follows: if UPLO =
- 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i
- + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
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- On exit, the contents of AP are destroyed.
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- BP (input/output) REAL array, dimension (N*(N+1)/2)
- On entry, the upper or lower triangle of the symmetric matrix B,
- packed columnwise in a linear array. The j-th column of B is
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- stored in the array BP as follows: if UPLO = 'U', BP(i + (j-
- 1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-
- j)/2) = B(i,j) for j<=i<=n.
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- On exit, the triangular factor U or L from the Cholesky
- factorization B = U**T*U or B = L*L**T, in the same storage
- format as B.
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- W (output) REAL array, dimension (N)
- If INFO = 0, the eigenvalues in ascending order.
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- Z (output) REAL array, dimension (LDZ, N)
- If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
- eigenvectors. The eigenvectors are normalized as follows: if
- ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I.
- If JOBZ = 'N', then Z is not referenced.
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- LDZ (input) INTEGER
- The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
- 'V', LDZ >= max(1,N).
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- WORK (workspace) REAL array, dimension (3*N)
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- INFO (output) INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: SPPTRF or SSPEV returned an error code:
- <= N: if INFO = i, SSPEV failed to converge; i off-diagonal
- elements of an intermediate tridiagonal form did not converge to
- zero. > N: if INFO = n + i, for 1 <= i <= n, then the leading
- minor of order i of B is not positive definite. The
- factorization of B could not be completed and no eigenvalues or
- eigenvectors were computed.
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