ungql(3)

NAME
ungql - {un,or}gql: generate explicit Q from geqlf

SYNOPSIS

  Functions
subroutine cungql (m, n, k, a, lda, tau, work, lwork, info)
CUNGQL
subroutine dorgql (m, n, k, a, lda, tau, work, lwork, info)
DORGQL
subroutine sorgql (m, n, k, a, lda, tau, work, lwork, info)
SORGQL
subroutine zungql (m, n, k, a, lda, tau, work, lwork, info)
ZUNGQL

Detailed Description

Function Documentation

  subroutine cungql (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CUNGQL

Purpose:

     CUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
     which is defined as the last N columns of a product of K elementary
     reflectors of order M
           Q  =  H(k) . . . H(2) H(1)
     as returned by CGEQLF.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix Q. M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix Q. M >= N >= 0.

    K

              K is INTEGER
              The number of elementary reflectors whose product defines the
              matrix Q. N >= K >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the (n-k+i)-th column must contain the vector which
              defines the elementary reflector H(i), for i = 1,2,...,k, as
              returned by CGEQLF in the last k columns of its array
              argument A.
              On exit, the M-by-N matrix Q.

    LDA

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

    TAU

              TAU is COMPLEX array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by CGEQLF.

    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 >= max(1,N).
              For optimum performance LWORK >= N*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 has an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file cungql.f.

  subroutine dorgql (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGQL

Purpose:

     DORGQL generates an M-by-N real matrix Q with orthonormal columns,
     which is defined as the last N columns of a product of K elementary
     reflectors of order M
           Q  =  H(k) . . . H(2) H(1)
     as returned by DGEQLF.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix Q. M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix Q. M >= N >= 0.

    K

              K is INTEGER
              The number of elementary reflectors whose product defines the
              matrix Q. N >= K >= 0.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the (n-k+i)-th column must contain the vector which
              defines the elementary reflector H(i), for i = 1,2,...,k, as
              returned by DGEQLF in the last k columns of its array
              argument A.
              On exit, the M-by-N matrix Q.

    LDA

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

    TAU

              TAU is DOUBLE PRECISION array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by DGEQLF.

    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).
              For optimum performance LWORK >= N*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 has an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file dorgql.f.

  subroutine sorgql (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGQL

Purpose:

     SORGQL generates an M-by-N real matrix Q with orthonormal columns,
     which is defined as the last N columns of a product of K elementary
     reflectors of order M
           Q  =  H(k) . . . H(2) H(1)
     as returned by SGEQLF.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix Q. M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix Q. M >= N >= 0.

    K

              K is INTEGER
              The number of elementary reflectors whose product defines the
              matrix Q. N >= K >= 0.

    A

              A is REAL array, dimension (LDA,N)
              On entry, the (n-k+i)-th column must contain the vector which
              defines the elementary reflector H(i), for i = 1,2,...,k, as
              returned by SGEQLF in the last k columns of its array
              argument A.
              On exit, the M-by-N matrix Q.

    LDA

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

    TAU

              TAU is REAL array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by SGEQLF.

    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).
              For optimum performance LWORK >= N*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 has an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file sorgql.f.

  subroutine zungql (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGQL

Purpose:

     ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
     which is defined as the last N columns of a product of K elementary
     reflectors of order M
           Q  =  H(k) . . . H(2) H(1)
     as returned by ZGEQLF.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix Q. M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix Q. M >= N >= 0.

    K

              K is INTEGER
              The number of elementary reflectors whose product defines the
              matrix Q. N >= K >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the (n-k+i)-th column must contain the vector which
              defines the elementary reflector H(i), for i = 1,2,...,k, as
              returned by ZGEQLF in the last k columns of its array
              argument A.
              On exit, the M-by-N matrix Q.

    LDA

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

    TAU

              TAU is COMPLEX*16 array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by ZGEQLF.

    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 >= max(1,N).
              For optimum performance LWORK >= N*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 has an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file zungql.f.

Author

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