larz(3)

NAME
larz - larz: apply reflector

SYNOPSIS

  Functions

subroutine clarz (side, m, n, l, v, incv, tau, c, ldc, work)
CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
subroutine dlarz (side, m, n, l, v, incv, tau, c, ldc, work)
DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
subroutine slarz (side, m, n, l, v, incv, tau, c, ldc, work)
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
subroutine zlarz (side, m, n, l, v, incv, tau, c, ldc, work)
ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Detailed Description

Function Documentation

  subroutine clarz (character side, integer m, integer n, integer l, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)

CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:

    !>
    !> CLARZ applies a complex elementary reflector H to a complex
    !> M-by-N matrix C, from either the left or the right. H is represented
    !> in the form
    !>
    !>       H = I - tau * v * v**H
    !>
    !> where tau is a complex scalar and v is a complex vector.
    !>
    !> If tau = 0, then H is taken to be the unit matrix.
    !>
    !> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
    !> tau.
    !>
    !> H is a product of k elementary reflectors as returned by CTZRZF.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': form  H * C
    !>          = 'R': form  C * H
    !>

    M

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

    N

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

    L

    !>          L is INTEGER
    !>          The number of entries of the vector V containing
    !>          the meaningful part of the Householder vectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is COMPLEX array, dimension (1+(L-1)*abs(INCV))
    !>          The vector v in the representation of H as returned by
    !>          CTZRZF. V is not used if TAU = 0.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between elements of v. INCV <> 0.
    !>

    TAU

    !>          TAU is COMPLEX
    !>          The value tau in the representation of H.
    !>

    C

    !>          C is COMPLEX array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
    !>          or C * H if SIDE = 'R'.
    !>

    LDC

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

    WORK

    !>          WORK is COMPLEX array, dimension
    !>                         (N) if SIDE = 'L'
    !>                      or (M) if SIDE = 'R'
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

  subroutine dlarz (character side, integer m, integer n, integer l, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:

    !>
    !> DLARZ applies a real elementary reflector H to a real M-by-N
    !> matrix C, from either the left or the right. H is represented in the
    !> form
    !>
    !>       H = I - tau * v * v**T
    !>
    !> where tau is a real scalar and v is a real vector.
    !>
    !> If tau = 0, then H is taken to be the unit matrix.
    !>
    !>
    !> H is a product of k elementary reflectors as returned by DTZRZF.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': form  H * C
    !>          = 'R': form  C * H
    !>

    M

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

    N

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

    L

    !>          L is INTEGER
    !>          The number of entries of the vector V containing
    !>          the meaningful part of the Householder vectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
    !>          The vector v in the representation of H as returned by
    !>          DTZRZF. V is not used if TAU = 0.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between elements of v. INCV <> 0.
    !>

    TAU

    !>          TAU is DOUBLE PRECISION
    !>          The value tau in the representation of H.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
    !>          or C * H if SIDE = 'R'.
    !>

    LDC

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

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension
    !>                         (N) if SIDE = 'L'
    !>                      or (M) if SIDE = 'R'
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

  subroutine slarz (character side, integer m, integer n, integer l, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)

SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:

    !>
    !> SLARZ applies a real elementary reflector H to a real M-by-N
    !> matrix C, from either the left or the right. H is represented in the
    !> form
    !>
    !>       H = I - tau * v * v**T
    !>
    !> where tau is a real scalar and v is a real vector.
    !>
    !> If tau = 0, then H is taken to be the unit matrix.
    !>
    !>
    !> H is a product of k elementary reflectors as returned by STZRZF.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': form  H * C
    !>          = 'R': form  C * H
    !>

    M

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

    N

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

    L

    !>          L is INTEGER
    !>          The number of entries of the vector V containing
    !>          the meaningful part of the Householder vectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is REAL array, dimension (1+(L-1)*abs(INCV))
    !>          The vector v in the representation of H as returned by
    !>          STZRZF. V is not used if TAU = 0.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between elements of v. INCV <> 0.
    !>

    TAU

    !>          TAU is REAL
    !>          The value tau in the representation of H.
    !>

    C

    !>          C is REAL array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
    !>          or C * H if SIDE = 'R'.
    !>

    LDC

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

    WORK

    !>          WORK is REAL array, dimension
    !>                         (N) if SIDE = 'L'
    !>                      or (M) if SIDE = 'R'
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

  subroutine zlarz (character side, integer m, integer n, integer l, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)

ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:

    !>
    !> ZLARZ applies a complex elementary reflector H to a complex
    !> M-by-N matrix C, from either the left or the right. H is represented
    !> in the form
    !>
    !>       H = I - tau * v * v**H
    !>
    !> where tau is a complex scalar and v is a complex vector.
    !>
    !> If tau = 0, then H is taken to be the unit matrix.
    !>
    !> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
    !> tau.
    !>
    !> H is a product of k elementary reflectors as returned by ZTZRZF.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': form  H * C
    !>          = 'R': form  C * H
    !>

    M

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

    N

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

    L

    !>          L is INTEGER
    !>          The number of entries of the vector V containing
    !>          the meaningful part of the Householder vectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
    !>          The vector v in the representation of H as returned by
    !>          ZTZRZF. V is not used if TAU = 0.
    !>

    INCV

    !>          INCV is INTEGER
    !>          The increment between elements of v. INCV <> 0.
    !>

    TAU

    !>          TAU is COMPLEX*16
    !>          The value tau in the representation of H.
    !>

    C

    !>          C is COMPLEX*16 array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
    !>          or C * H if SIDE = 'R'.
    !>

    LDC

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

    WORK

    !>          WORK is COMPLEX*16 array, dimension
    !>                         (N) if SIDE = 'L'
    !>                      or (M) if SIDE = 'R'
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

Author

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