SSPGV(3F) SSPGV(3F)
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
SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, ITYPE, LDZ, N
REAL AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )
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.
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) 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 jth
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) 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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SSPGV(3F) SSPGV(3F)
stored in the array BP as follows: if UPLO = 'U', BP(i + (j1)*j/2)
= B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*nj)/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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace) REAL array, dimension (3*N)
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.
SSPGV(3F) SSPGV(3F)
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
SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, ITYPE, LDZ, N
REAL AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )
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.
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) 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 jth
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) 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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SSPGV(3F) SSPGV(3F)
stored in the array BP as follows: if UPLO = 'U', BP(i + (j1)*j/2)
= B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*nj)/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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace) REAL array, dimension (3*N)
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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