ungtr(3)

NAME
ungtr - {un,or}gtr: generate Q from hetrd

SYNOPSIS

  Functions
subroutine cungtr (uplo, n, a, lda, tau, work, lwork, info)
CUNGTR
subroutine dorgtr (uplo, n, a, lda, tau, work, lwork, info)
DORGTR
subroutine sorgtr (uplo, n, a, lda, tau, work, lwork, info)
SORGTR
subroutine zungtr (uplo, n, a, lda, tau, work, lwork, info)
ZUNGTR

Detailed Description

Function Documentation

  subroutine cungtr (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CUNGTR

Purpose:

     CUNGTR generates a complex unitary matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by
     CHETRD:
     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 triangle of A contains elementary reflectors
                     from CHETRD;
              = 'L': Lower triangle of A contains elementary reflectors
                     from CHETRD.

    N

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

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the vectors which define the elementary reflectors,
              as returned by CHETRD.
              On exit, the N-by-N unitary matrix Q.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= N.

    TAU

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

    WORK

              WORK is COMPLEX array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= N-1.
              For optimum performance LWORK >= (N-1)*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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.

Definition at line 122 of file cungtr.f.

  subroutine dorgtr (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGTR

Purpose:

     DORGTR generates a real orthogonal matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by
     DSYTRD:
     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 triangle of A contains elementary reflectors
                     from DSYTRD;
              = 'L': Lower triangle of A contains elementary reflectors
                     from DSYTRD.

    N

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

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the vectors which define the elementary reflectors,
              as returned by DSYTRD.
              On exit, the N-by-N orthogonal matrix Q.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= max(1,N).

    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 DSYTRD.

    WORK

              WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,N-1).
              For optimum performance LWORK >= (N-1)*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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.

Definition at line 122 of file dorgtr.f.

  subroutine sorgtr (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGTR

Purpose:

     SORGTR generates a real orthogonal matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by
     SSYTRD:
     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 triangle of A contains elementary reflectors
                     from SSYTRD;
              = 'L': Lower triangle of A contains elementary reflectors
                     from SSYTRD.

    N

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

    A

              A is REAL array, dimension (LDA,N)
              On entry, the vectors which define the elementary reflectors,
              as returned by SSYTRD.
              On exit, the N-by-N orthogonal matrix Q.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= max(1,N).

    TAU

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

    WORK

              WORK is REAL array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= max(1,N-1).
              For optimum performance LWORK >= (N-1)*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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.

Definition at line 122 of file sorgtr.f.

  subroutine zungtr (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGTR

Purpose:

     ZUNGTR generates a complex unitary matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by
     ZHETRD:
     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 triangle of A contains elementary reflectors
                     from ZHETRD;
              = 'L': Lower triangle of A contains elementary reflectors
                     from ZHETRD.

    N

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

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the vectors which define the elementary reflectors,
              as returned by ZHETRD.
              On exit, the N-by-N unitary matrix Q.

    LDA

              LDA is INTEGER
              The leading dimension of the array A. LDA >= N.

    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 ZHETRD.

    WORK

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK >= N-1.
              For optimum performance LWORK >= (N-1)*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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.

Definition at line 122 of file zungtr.f.

Author

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