upgtr(3)

NAME
upgtr - {up,op}gtr: generate Q from hetrd

SYNOPSIS

  Functions

subroutine cupgtr (uplo, n, ap, tau, q, ldq, work, info)
CUPGTR
subroutine dopgtr (uplo, n, ap, tau, q, ldq, work, info)
DOPGTR
subroutine sopgtr (uplo, n, ap, tau, q, ldq, work, info)
SOPGTR
subroutine zupgtr (uplo, n, ap, tau, q, ldq, work, info)
ZUPGTR

Detailed Description

Function Documentation

  subroutine cupgtr (character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldq, * ) q, integer ldq, complex, dimension( * ) work, integer info)

CUPGTR

Purpose:

    !>
    !> CUPGTR generates a complex unitary matrix Q which is defined as the
    !> product of n-1 elementary reflectors H(i) of order n, as returned by
    !> CHPTRD using packed storage:
    !>
    !> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
    !>
    !> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U': Upper triangular packed storage used in previous
    !>                 call to CHPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to CHPTRD.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix Q. N >= 0.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          The vectors which define the elementary reflectors, as
    !>          returned by CHPTRD.
    !>

    TAU

    !>          TAU is COMPLEX array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by CHPTRD.
    !>

    Q

    !>          Q is COMPLEX array, dimension (LDQ,N)
    !>          The N-by-N unitary matrix Q.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>          The leading dimension of the array Q. LDQ >= max(1,N).
    !>

    WORK

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

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dopgtr (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) tau, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) work, integer info)

DOPGTR

Purpose:

    !>
    !> DOPGTR generates a real orthogonal matrix Q which is defined as the
    !> product of n-1 elementary reflectors H(i) of order n, as returned by
    !> DSPTRD using packed storage:
    !>
    !> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
    !>
    !> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U': Upper triangular packed storage used in previous
    !>                 call to DSPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to DSPTRD.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix Q. N >= 0.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          The vectors which define the elementary reflectors, as
    !>          returned by DSPTRD.
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by DSPTRD.
    !>

    Q

    !>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
    !>          The N-by-N orthogonal matrix Q.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>          The leading dimension of the array Q. LDQ >= max(1,N).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (N-1)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sopgtr (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) work, integer info)

SOPGTR

Purpose:

    !>
    !> SOPGTR generates a real orthogonal matrix Q which is defined as the
    !> product of n-1 elementary reflectors H(i) of order n, as returned by
    !> SSPTRD using packed storage:
    !>
    !> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
    !>
    !> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U': Upper triangular packed storage used in previous
    !>                 call to SSPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to SSPTRD.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix Q. N >= 0.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          The vectors which define the elementary reflectors, as
    !>          returned by SSPTRD.
    !>

    TAU

    !>          TAU is REAL array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by SSPTRD.
    !>

    Q

    !>          Q is REAL array, dimension (LDQ,N)
    !>          The N-by-N orthogonal matrix Q.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>          The leading dimension of the array Q. LDQ >= max(1,N).
    !>

    WORK

    !>          WORK is REAL array, dimension (N-1)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zupgtr (character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) tau, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work, integer info)

ZUPGTR

Purpose:

    !>
    !> ZUPGTR generates a complex unitary matrix Q which is defined as the
    !> product of n-1 elementary reflectors H(i) of order n, as returned by
    !> ZHPTRD using packed storage:
    !>
    !> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
    !>
    !> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U': Upper triangular packed storage used in previous
    !>                 call to ZHPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to ZHPTRD.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix Q. N >= 0.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          The vectors which define the elementary reflectors, as
    !>          returned by ZHPTRD.
    !>

    TAU

    !>          TAU is COMPLEX*16 array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by ZHPTRD.
    !>

    Q

    !>          Q is COMPLEX*16 array, dimension (LDQ,N)
    !>          The N-by-N unitary matrix Q.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>          The leading dimension of the array Q. LDQ >= max(1,N).
    !>

    WORK

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

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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