hbgv(3)

NAME
hbgv - {hb,sb}gv: eig, QR iteration

SYNOPSIS

  Functions
subroutine chbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
CHBGV
subroutine dsbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info)
DSBGV
subroutine ssbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info)
SSBGV
subroutine zhbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
ZHBGV

Detailed Description

Function Documentation

  subroutine chbgv (character jobz, character uplo, integer n, integer ka, integer kb, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CHBGV

Purpose:

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

Parameters
    JOBZ

              JOBZ is CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  N >= 0.

    KA

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

    KB

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

    AB

              AB is COMPLEX array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the Hermitian 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

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KA+1.

    BB

              BB is COMPLEX array, dimension (LDBB, N)
              On entry, the upper or lower triangle of the Hermitian 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**H*S, as returned by CPBSTF.

    LDBB

              LDBB is INTEGER
              The leading dimension of the array BB.  LDBB >= KB+1.

    W

              W is REAL array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

    Z

              Z is COMPLEX 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 associated with W(i). The eigenvectors are
              normalized so that Z**H*B*Z = I.
              If JOBZ = 'N', then Z is not referenced.

    LDZ

              LDZ is INTEGER
              The leading dimension of the array Z.  LDZ >= 1, and if
              JOBZ = 'V', LDZ >= N.

    WORK

              WORK is COMPLEX array, dimension (N)

    RWORK

              RWORK is REAL array, dimension (3*N)

    INFO

              INFO is 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 CPBSTF
                        returned INFO = i: B is not positive definite.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 181 of file chbgv.f.

  subroutine dsbgv (character jobz, character uplo, integer n, integer ka, integer kb, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)

DSBGV

Purpose:

     DSBGV 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.

Parameters
    JOBZ

              JOBZ is CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  N >= 0.

    KA

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

    KB

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

    AB

              AB is DOUBLE PRECISION 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

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KA+1.

    BB

              BB is DOUBLE PRECISION 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 DPBSTF.

    LDBB

              LDBB is INTEGER
              The leading dimension of the array BB.  LDBB >= KB+1.

    W

              W is DOUBLE PRECISION array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

    Z

              Z is DOUBLE PRECISION 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 associated with W(i). The eigenvectors are
              normalized so that Z**T*B*Z = I.
              If JOBZ = 'N', then Z is not referenced.

    LDZ

              LDZ is INTEGER
              The leading dimension of the array Z.  LDZ >= 1, and if
              JOBZ = 'V', LDZ >= N.

    WORK

              WORK is DOUBLE PRECISION array, dimension (3*N)

    INFO

              INFO is 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 DPBSTF
                        returned INFO = i: B is not positive definite.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 175 of file dsbgv.f.

  subroutine ssbgv (character jobz, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)

SSBGV

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.

Parameters
    JOBZ

              JOBZ is CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  N >= 0.

    KA

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

    KB

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

    AB

              AB is 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

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KA+1.

    BB

              BB is 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

              LDBB is INTEGER
              The leading dimension of the array BB.  LDBB >= KB+1.

    W

              W is REAL array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

    Z

              Z is 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 associated with W(i). The eigenvectors are
              normalized so that Z**T*B*Z = I.
              If JOBZ = 'N', then Z is not referenced.

    LDZ

              LDZ is INTEGER
              The leading dimension of the array Z.  LDZ >= 1, and if
              JOBZ = 'V', LDZ >= N.

    WORK

              WORK is REAL array, dimension (3*N)

    INFO

              INFO is 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.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 175 of file ssbgv.f.

  subroutine zhbgv (character jobz, character uplo, integer n, integer ka, integer kb, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZHBGV

Purpose:

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

Parameters
    JOBZ

              JOBZ is CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  N >= 0.

    KA

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

    KB

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

    AB

              AB is COMPLEX*16 array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the Hermitian 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

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KA+1.

    BB

              BB is COMPLEX*16 array, dimension (LDBB, N)
              On entry, the upper or lower triangle of the Hermitian 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**H*S, as returned by ZPBSTF.

    LDBB

              LDBB is INTEGER
              The leading dimension of the array BB.  LDBB >= KB+1.

    W

              W is DOUBLE PRECISION array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

    Z

              Z is COMPLEX*16 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 associated with W(i). The eigenvectors are
              normalized so that Z**H*B*Z = I.
              If JOBZ = 'N', then Z is not referenced.

    LDZ

              LDZ is INTEGER
              The leading dimension of the array Z.  LDZ >= 1, and if
              JOBZ = 'V', LDZ >= N.

    WORK

              WORK is COMPLEX*16 array, dimension (N)

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (3*N)

    INFO

              INFO is 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 ZPBSTF
                        returned INFO = i: B is not positive definite.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 181 of file zhbgv.f.

Author

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