hpgv(3)

NAME
hpgv - {hp,sp}gv: eig, QR iteration

SYNOPSIS

  Functions

subroutine chpgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork, info)
CHPGV
subroutine dspgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)
DSPGV
subroutine sspgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)
SSPGV
subroutine zhpgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork, info)
ZHPGV

Detailed Description

Function Documentation

  subroutine chpgv (integer itype, character jobz, character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) bp, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CHPGV

Purpose:

    !>
    !> CHPGV computes all the eigenvalues and, optionally, the eigenvectors
    !> of a complex generalized Hermitian-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 Hermitian, stored in packed format,
    !> and B is also positive definite.
    !>

Parameters
    ITYPE

    !>          ITYPE is 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

    !>          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.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian 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

    !>          BP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, in the same storage
    !>          format as B.
    !>

    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.  The eigenvectors are normalized as follows:
    !>          if ITYPE = 1 or 2, Z**H*B*Z = I;
    !>          if ITYPE = 3, Z**H*inv(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 >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (max(1, 2*N-1))
    !>

    RWORK

    !>          RWORK is REAL array, dimension (max(1, 3*N-2))
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  CPPTRF or CHPEV returned an error code:
    !>             <= N:  if INFO = i, CHPEV failed to converge;
    !>                    i off-diagonal elements of an intermediate
    !>                    tridiagonal form did not convergeto zero;
    !>             > N:   if INFO = N + i, for 1 <= i <= n, then the leading
    !>                    principal minor of order i of B is not positive.
    !>                    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.

  subroutine dspgv (integer itype, character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) bp, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)

DSPGV

Purpose:

    !>
    !> DSPGV 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.
    !>

Parameters
    ITYPE

    !>          ITYPE is 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

    !>          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.
    !>

    AP

    !>          AP is 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

    !>          BP is 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

    !>          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.  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

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,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:  DPPTRF or DSPEV returned an error code:
    !>             <= N:  if INFO = i, DSPEV 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
    !>                    principal minor of order i of B is not positive.
    !>                    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.

  subroutine sspgv (integer itype, character jobz, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)

SSPGV

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.
    !>

Parameters
    ITYPE

    !>          ITYPE is 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

    !>          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.
    !>

    AP

    !>          AP is 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

    !>          BP is 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

    !>          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.  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

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,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:  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
    !>                    principal minor of order i of B is not positive.
    !>                    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.

  subroutine zhpgv (integer itype, character jobz, character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZHPGV

Purpose:

    !>
    !> ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
    !> of a complex generalized Hermitian-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 Hermitian, stored in packed format,
    !> and B is also positive definite.
    !>

Parameters
    ITYPE

    !>          ITYPE is 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

    !>          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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian 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

    !>          BP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, in the same storage
    !>          format as B.
    !>

    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.  The eigenvectors are normalized as follows:
    !>          if ITYPE = 1 or 2, Z**H*B*Z = I;
    !>          if ITYPE = 3, Z**H*inv(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 >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (max(1, 2*N-1))
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  ZPPTRF or ZHPEV returned an error code:
    !>             <= N:  if INFO = i, ZHPEV failed to converge;
    !>                    i off-diagonal elements of an intermediate
    !>                    tridiagonal form did not convergeto zero;
    !>             > N:   if INFO = N + i, for 1 <= i <= n, then the leading
    !>                    principal minor of order i of B is not positive.
    !>                    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.

Author

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