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larz(3) Library Functions Manual 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:

!>

Definition at line 146 of file clarz.f.

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:

!>

Definition at line 144 of file dlarz.f.

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:

!>

Definition at line 144 of file slarz.f.

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:

!>

Definition at line 146 of file zlarz.f.

Author

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