gemlqt(3)

NAME
gemlqt - gemlqt: multiply by Q from gelqt

SYNOPSIS

  Functions

subroutine cgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
CGEMLQT
subroutine dgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
DGEMLQT
subroutine sgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
SGEMLQT
subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
ZGEMLQT

Detailed Description

Function Documentation

  subroutine cgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CGEMLQT

Purpose:

    !>
    !> CGEMLQT overwrites the general complex M-by-N matrix C with
    !>
    !>                 SIDE = 'L'     SIDE = 'R'
    !> TRANS = 'N':      Q C            C Q
    !> TRANS = 'C':   Q**H C            C Q**H
    !>
    !> where Q is a complex unitary matrix defined as the product of K
    !> elementary reflectors:
    !>
    !>       Q = H(1) H(2) . . . H(K) = I - V T V**H
    !>
    !> generated using the compact WY representation as returned by CGELQT.
    !>
    !> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**H from the Left;
    !>          = 'R': apply Q or Q**H from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'C':  Conjugate transpose, apply Q**H.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    MB

    !>          MB is INTEGER
    !>          The block size used for the storage of T.  K >= MB >= 1.
    !>          This must be the same value of MB used to generate T
    !>          in CGELQT.
    !>

    V

    !>          V is COMPLEX array, dimension
    !>                               (LDV,M) if SIDE = 'L',
    !>                               (LDV,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          CGELQT in the first K rows of its array argument A.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V. LDV >= max(1,K).
    !>

    T

    !>          T is COMPLEX array, dimension (LDT,K)
    !>          The upper triangular factors of the block reflectors
    !>          as returned by CGELQT, stored as a MB-by-K matrix.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= MB.
    !>

    C

    !>          C is COMPLEX array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX array. The dimension of
    !>          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
    !>

    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 dgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DGEMLQT

Purpose:

    !>
    !> DGEMLQT overwrites the general real M-by-N matrix C with
    !>
    !>                 SIDE = 'L'     SIDE = 'R'
    !> TRANS = 'N':      Q C            C Q
    !> TRANS = 'T':   Q**T C            C Q**T
    !>
    !> where Q is a real orthogonal matrix defined as the product of K
    !> elementary reflectors:
    !>
    !>       Q = H(1) H(2) . . . H(K) = I - V T V**T
    !>
    !> generated using the compact WY representation as returned by DGELQT.
    !>
    !> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left;
    !>          = 'R': apply Q or Q**T from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'C':  Transpose, apply Q**T.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    MB

    !>          MB is INTEGER
    !>          The block size used for the storage of T.  K >= MB >= 1.
    !>          This must be the same value of MB used to generate T
    !>          in DGELQT.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension
    !>                               (LDV,M) if SIDE = 'L',
    !>                               (LDV,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          DGELQT in the first K rows of its array argument A.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.  LDV >= max(1,K).
    !>

    T

    !>          T is DOUBLE PRECISION array, dimension (LDT,K)
    !>          The upper triangular factors of the block reflectors
    !>          as returned by DGELQT, stored as a MB-by-K matrix.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= MB.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array. The dimension of
    !>          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
    !>

    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 sgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SGEMLQT

Purpose:

    !>
    !> SGEMLQT overwrites the general real M-by-N matrix C with
    !>
    !>                 SIDE = 'L'     SIDE = 'R'
    !> TRANS = 'N':      Q C            C Q
    !> TRANS = 'T':   Q**T C            C Q**T
    !>
    !> where Q is a real orthogonal matrix defined as the product of K
    !> elementary reflectors:
    !>
    !>       Q = H(1) H(2) . . . H(K) = I - V T V**T
    !>
    !> generated using the compact WY representation as returned by SGELQT.
    !>
    !> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left;
    !>          = 'R': apply Q or Q**T from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'C':  Transpose, apply Q**T.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    MB

    !>          MB is INTEGER
    !>          The block size used for the storage of T.  K >= MB >= 1.
    !>          This must be the same value of MB used to generate T
    !>          in SGELQT.
    !>

    V

    !>          V is REAL array, dimension
    !>                               (LDV,M) if SIDE = 'L',
    !>                               (LDV,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          SGELQT in the first K rows of its array argument A.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V. LDV >= max(1,K).
    !>

    T

    !>          T is REAL array, dimension (LDT,K)
    !>          The upper triangular factors of the block reflectors
    !>          as returned by SGELQT, stored as a MB-by-K matrix.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= MB.
    !>

    C

    !>          C is REAL array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is REAL array. The dimension of
    !>          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
    !>

    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 zgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZGEMLQT

Purpose:

    !>
    !> ZGEMLQT overwrites the general complex M-by-N matrix C with
    !>
    !>                 SIDE = 'L'     SIDE = 'R'
    !> TRANS = 'N':      Q C            C Q
    !> TRANS = 'C':   Q**H C            C Q**H
    !>
    !> where Q is a complex unitary matrix defined as the product of K
    !> elementary reflectors:
    !>
    !>       Q = H(1) H(2) . . . H(K) = I - V T V**H
    !>
    !> generated using the compact WY representation as returned by ZGELQT.
    !>
    !> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**H from the Left;
    !>          = 'R': apply Q or Q**H from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'C':  Conjugate transpose, apply Q**H.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    MB

    !>          MB is INTEGER
    !>          The block size used for the storage of T.  K >= MB >= 1.
    !>          This must be the same value of MB used to generate T
    !>          in ZGELQT.
    !>

    V

    !>          V is COMPLEX*16 array, dimension
    !>                               (LDV,M) if SIDE = 'L',
    !>                               (LDV,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          ZGELQT in the first K rows of its array argument A.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V. LDV >= max(1,K).
    !>

    T

    !>          T is COMPLEX*16 array, dimension (LDT,K)
    !>          The upper triangular factors of the block reflectors
    !>          as returned by ZGELQT, stored as a MB-by-K matrix.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= MB.
    !>

    C

    !>          C is COMPLEX*16 array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX*16 array. The dimension of
    !>          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
    !>

    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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