Man page - gemqrt(3)

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Manual

gemqrt

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, complex, dimension( ldv, * ) v, integer ldv,complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, *) c, integer ldc, complex, dimension( * ) work, integer info)
subroutine dgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, double precision, dimension( ldv, * ) v, integerldv, double precision, dimension( ldt, * ) t, integer ldt, doubleprecision, dimension( ldc, * ) c, integer ldc, double precision,dimension( * ) work, integer info)
subroutine sgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, real, dimension( ldv, * ) v, integer ldv, real,dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c,integer ldc, real, dimension( * ) work, integer info)
subroutine zgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, 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)
Author

NAME

gemqrt - gemqrt: multiply by Q from geqrt

SYNOPSIS

Functions

subroutine cgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
CGEMQRT
subroutine dgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
DGEMQRT
subroutine sgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
SGEMQRT
subroutine zgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
ZGEMQRT

Detailed Description

Function Documentation

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

CGEMQRT

Purpose:

CGEMQRT 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 orthogonal 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 CGEQRT.

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.

NB

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

V

V is COMPLEX array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGEQRT in the first K columns of its array argument A.

LDV

LDV is INTEGER
The leading dimension of the array V.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

T

T is COMPLEX array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CGEQRT, stored as a NB-by-N matrix.

LDT

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

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*NB if SIDE = ’L’, or M*NB 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 dgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, double precision, dimension( ldv, * ) v, integerldv, double precision, dimension( ldt, * ) t, integer ldt, doubleprecision, dimension( ldc, * ) c, integer ldc, double precision,dimension( * ) work, integer info)

DGEMQRT

Purpose:

DGEMQRT 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 DGEQRT.

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.

NB

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

V

V is DOUBLE PRECISION array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRT in the first K columns of its array argument A.

LDV

LDV is INTEGER
The leading dimension of the array V.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

T

T is DOUBLE PRECISION array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by DGEQRT, stored as a NB-by-N matrix.

LDT

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

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*NB if SIDE = ’L’, or M*NB 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 sgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, real, dimension( ldv, * ) v, integer ldv, real,dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c,integer ldc, real, dimension( * ) work, integer info)

SGEMQRT

Purpose:

SGEMQRT 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 SGEQRT.

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;
= ’T’: 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.

NB

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

V

V is REAL array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGEQRT in the first K columns of its array argument A.

LDV

LDV is INTEGER
The leading dimension of the array V.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

T

T is REAL array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by SGEQRT, stored as a NB-by-N matrix.

LDT

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

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*NB if SIDE = ’L’, or M*NB 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 zgemqrt (character side, character trans, integer m, integer n,integer k, integer nb, 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)

ZGEMQRT

Purpose:

ZGEMQRT 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 orthogonal 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 ZGEQRT.

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.

NB

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

V

V is COMPLEX*16 array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQRT in the first K columns of its array argument A.

LDV

LDV is INTEGER
The leading dimension of the array V.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

T

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

LDT

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

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*NB if SIDE = ’L’, or M*NB 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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