sspgv(l) [redhat man page]

SSPGV(l)								 )								  SSPGV(l)

NAME

       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

SYNOPSIS

       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, * )

PURPOSE

       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.

ARGUMENTS

       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 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) 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
	       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) 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.

LAPACK version 3.0						   15 June 2000 							  SSPGV(l)

SSBGV(l)								 )								  SSBGV(l)

NAME

       SSBGV  - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the
       form A*x=(lambda)*B*x

SYNOPSIS

       SUBROUTINE SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO )

	   CHARACTER	 JOBZ, UPLO

	   INTEGER	 INFO, KA, KB, LDAB, LDBB, LDZ, N

	   REAL 	 AB( LDAB, * ), BB( LDBB, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE

       SSBGV computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem,  of  the
       form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite.

ARGUMENTS

       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.

       KA      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.

       KB      (input) INTEGER
	       The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0.

       AB      (input/output) REAL array, dimension (LDAB, N)
	       On  entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array.  The j-th column
	       of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO
	       = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

	       On exit, the contents of AB are destroyed.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KA+1.

       BB      (input/output) REAL array, dimension (LDBB, N)
	       On  entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array.  The j-th column
	       of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO
	       = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).

	       On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by SPBSTF.

       LDBB    (input) INTEGER
	       The leading dimension of the array BB.  LDBB >= KB+1.

       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, with the i-th column of Z holding the eigenvector associ-
	       ated with W(i). The eigenvectors are normalized so that Z**T*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 >= 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:  if INFO = i, and i is:
	       <= N:  the algorithm 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 SPBSTF
	       returned  INFO  =  i: B is not positive definite.  The factorization of B could not be completed and no eigenvalues or eigenvectors
	       were computed.

LAPACK version 3.0						   15 June 2000 							  SSBGV(l)