Man page - gemqr(3)

Packages contains this manual

Manual

gemqr

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgemqr (character side, character trans, integer m, integer n,integer k, complex, dimension( lda, * ) a, integer lda, complex,dimension( * ) t, integer tsize, complex, dimension( ldc, * ) c,integer ldc, complex, dimension( * ) work, integer lwork, integer info)
subroutine dgemqr (character side, character trans, integer m, integer n,integer k, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( * ) t, integer tsize, double precision,dimension( ldc, * ) c, integer ldc, double precision, dimension( * )work, integer lwork, integer info)
subroutine sgemqr (character side, character trans, integer m, integer n,integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *) t, integer tsize, real, dimension( ldc, * ) c, integer ldc, real,dimension( * ) work, integer lwork, integer info)
subroutine zgemqr (character side, character trans, integer m, integer n,integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( * ) t, integer tsize, complex*16, dimension( ldc, * ) c,integer ldc, complex*16, dimension( * ) work, integer lwork, integerinfo)
Author

NAME

gemqr - gemqr: multiply by Q from geqr

SYNOPSIS

Functions

subroutine cgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
CGEMQR
subroutine dgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMQR
subroutine sgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
SGEMQR
subroutine zgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
ZGEMQR

Detailed Description

Function Documentation

subroutine cgemqr (character side, character trans, integer m, integer n,integer k, complex, dimension( lda, * ) a, integer lda, complex,dimension( * ) t, integer tsize, complex, dimension( ldc, * ) c,integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CGEMQR

Purpose:

CGEMQR overwrites the general real M-by-N matrix C with

SIDE = ’L’ SIDE = ’R’
TRANS = ’N’: Q * C C * Q
TRANS = ’T’: Q**H * C C * Q**H

where Q is a complex unitary matrix defined as the product
of blocked elementary reflectors computed by tall skinny
QR factorization (CGEQR)

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 A. 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.

A

A is COMPLEX array, dimension (LDA,K)
Part of the data structure to represent Q as returned by CGEQR.

LDA

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

T

T is COMPLEX array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by CGEQR.

TSIZE

TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.

C

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

LDC

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

WORK

(workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the minimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= 1.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
is issued by XERBLA.

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.

Further Details

These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
CLATSQR or CGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, CGEQR will use either
CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
the QR factorization.
This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
multiply matrix Q by another matrix.
Further Details in CLAMTSQR or CGEMQRT.

subroutine dgemqr (character side, character trans, integer m, integer n,integer k, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( * ) t, integer tsize, double precision,dimension( ldc, * ) c, integer ldc, double precision, dimension( * )work, integer lwork, integer info)

DGEMQR

Purpose:

DGEMQR 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 blocked elementary reflectors computed by tall skinny
QR factorization (DGEQR)

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 A. 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.

A

A is DOUBLE PRECISION array, dimension (LDA,K)
Part of the data structure to represent Q as returned by DGEQR.

LDA

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

T

T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by DGEQR.

TSIZE

TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.

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 or Q**T*C or C*Q**T or C*Q.

LDC

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

WORK

(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the minimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= 1.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
is issued by XERBLA.

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.

Further Details

These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
DLATSQR or DGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, DGEQR will use either
DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
the QR factorization.
This version of DGEMQR will use either DLAMTSQR or DGEMQRT to
multiply matrix Q by another matrix.
Further Details in DLATMSQR or DGEMQRT.

subroutine sgemqr (character side, character trans, integer m, integer n,integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *) t, integer tsize, real, dimension( ldc, * ) c, integer ldc, real,dimension( * ) work, integer lwork, integer info)

SGEMQR

Purpose:

SGEMQR 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 blocked elementary reflectors computed by tall skinny
QR factorization (SGEQR)

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 A. 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.

A

A is REAL array, dimension (LDA,K)
Part of the data structure to represent Q as returned by SGEQR.

LDA

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

T

T is REAL array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by SGEQR.

TSIZE

TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.

C

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

LDC

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

WORK

(workspace) REAL array, dimension (MAX(1,LWORK))

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
is issued by XERBLA.

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.

Further Details

These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
SLATSQR or SGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, SGEQR will use either
SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute
the QR factorization.
This version of SGEMQR will use either SLAMTSQR or SGEMQRT to
multiply matrix Q by another matrix.
Further Details in SLAMTSQR or SGEMQRT.

subroutine zgemqr (character side, character trans, integer m, integer n,integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( * ) t, integer tsize, complex*16, dimension( ldc, * ) c,integer ldc, complex*16, dimension( * ) work, integer lwork, integerinfo)

ZGEMQR

Purpose:

ZGEMQR overwrites the general real M-by-N matrix C with

SIDE = ’L’ SIDE = ’R’
TRANS = ’N’: Q * C C * Q
TRANS = ’T’: Q**H * C C * Q**H

where Q is a complex unitary matrix defined as the product
of blocked elementary reflectors computed by tall skinny
QR factorization (ZGEQR)

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 A. 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.

A

A is COMPLEX*16 array, dimension (LDA,K)
Part of the data structure to represent Q as returned by ZGEQR.

LDA

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

T

T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by ZGEQR.

TSIZE

TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.

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 or Q**H*C or C*Q**H or C*Q.

LDC

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

WORK

(workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the minimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= 1.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
is issued by XERBLA.

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.

Further Details

These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
ZLATSQR or ZGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, ZGEQR will use either
ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute
the QR factorization.
This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to
multiply matrix Q by another matrix.
Further Details in ZLAMTSQR or ZGEMQRT.

Author

Generated automatically by Doxygen for LAPACK from the source code.