Man page - larz(3)

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Manual

larz

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

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, doubleprecision, dimension( * ) v, integer incv, double precision tau, doubleprecision, 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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