hpevd(3)

NAME
hpevd - {hp,sp}evd: eig, divide and conquer

SYNOPSIS

  Functions

subroutine chpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dspevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info)
DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine sspevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info)
SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

  subroutine chpevd (character jobz, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
    !> a complex Hermitian matrix A in packed storage.  If eigenvectors are
    !> desired, it uses a divide and conquer algorithm.
    !>
    !>

Parameters
    JOBZ

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

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  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, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    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 orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(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,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of array WORK.
    !>          If N <= 1,               LWORK must be at least 1.
    !>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
    !>          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the required sizes of the WORK, RWORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is REAL array, dimension (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of array RWORK.
    !>          If N <= 1,               LRWORK must be at least 1.
    !>          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
    !>          If JOBZ = 'V' and N > 1, LRWORK must be at least
    !>                    1 + 5*N + 2*N**2.
    !>
    !>          If LRWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the required sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of array IWORK.
    !>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the required sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dspevd (character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> DSPEVD computes all the eigenvalues and, optionally, eigenvectors
    !> of a real symmetric matrix A in packed storage. If eigenvectors are
    !> desired, it uses a divide and conquer algorithm.
    !>
    !>

Parameters
    JOBZ

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

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  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, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    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 orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If N <= 1,               LWORK must be at least 1.
    !>          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
    !>          If JOBZ = 'V' and N > 1, LWORK must be at least
    !>                                                 1 + 6*N + N**2.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the required sizes of the WORK and IWORK
    !>          arrays, returns these values as the first entries of the WORK
    !>          and IWORK arrays, and no error message related to LWORK or
    !>          LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of the array IWORK.
    !>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the required sizes of the WORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK and IWORK arrays, and no error message related to
    !>          LWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sspevd (character jobz, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> SSPEVD computes all the eigenvalues and, optionally, eigenvectors
    !> of a real symmetric matrix A in packed storage. If eigenvectors are
    !> desired, it uses a divide and conquer algorithm.
    !>
    !>

Parameters
    JOBZ

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

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  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, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    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 orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If N <= 1,               LWORK must be at least 1.
    !>          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
    !>          If JOBZ = 'V' and N > 1, LWORK must be at least
    !>                                                 1 + 6*N + N**2.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the required sizes of the WORK and IWORK
    !>          arrays, returns these values as the first entries of the WORK
    !>          and IWORK arrays, and no error message related to LWORK or
    !>          LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of the array IWORK.
    !>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the required sizes of the WORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK and IWORK arrays, and no error message related to
    !>          LWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zhpevd (character jobz, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
    !> a complex Hermitian matrix A in packed storage.  If eigenvectors are
    !> desired, it uses a divide and conquer algorithm.
    !>
    !>

Parameters
    JOBZ

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

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  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, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    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 orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(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,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of array WORK.
    !>          If N <= 1,               LWORK must be at least 1.
    !>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
    !>          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the required sizes of the WORK, RWORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of array RWORK.
    !>          If N <= 1,               LRWORK must be at least 1.
    !>          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
    !>          If JOBZ = 'V' and N > 1, LRWORK must be at least
    !>                    1 + 5*N + 2*N**2.
    !>
    !>          If LRWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the required sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of array IWORK.
    !>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the required sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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