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.

Definition at line 113 of file cupgtr.f.

  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.

Definition at line 113 of file dopgtr.f.

  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.

Definition at line 113 of file sopgtr.f.

  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.

Definition at line 113 of file zupgtr.f.

Author

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