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Expressions régulières,
Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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dspgvd(l) |
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DSPGVD - 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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SUBROUTINE DSPGVD( |
ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO ) | ||
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CHARACTER |
JOBZ, UPLO | ||
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INTEGER |
INFO, ITYPE, LDZ, LIWORK, LWORK, N | ||
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INTEGER |
IWORK( * ) | ||
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DOUBLE |
PRECISION AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * ) |
DSPGVD 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.
If eigenvectors are desired, it uses a divide and conquer
algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. 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.
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
JOBZ (input) CHARACTER*1
= ’N’: Compute
eigenvalues only;
= ’V’: Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= ’U’: Upper
triangles of A and B are stored;
= ’L’: Lower triangles of A and B are
stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
AP (input/output) DOUBLE PRECISION 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.
On exit, the contents of AP are destroyed.
BP (input/output) DOUBLE PRECISION 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 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.
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.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) DOUBLE PRECISION 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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = ’V’, LDZ >= max(1,N).
WORK (workspace/output) DOUBLE PRECISION 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 >= 1. If JOBZ = ’N’ and N > 1, LWORK >= 2*N. If JOBZ = ’V’ and N > 1, LWORK >= 1 + 6*N + 2*N**2.
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.
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 JOBZ = ’N’ or N <= 1, LIWORK >= 1. If JOBZ = ’V’ and N > 1, LIWORK >= 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 = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEVD returned an error code:
<= N: if INFO = i, DSPEVD 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.
Based on
contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA
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dspgvd(l) | |