Man page - unmql(3)

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Manual

unmql

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cunmql (character side, character trans, integer m, integer n,integer k, complex, dimension( lda, * ) a, integer lda, complex,dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc,complex, dimension( * ) work, integer lwork, integer info)
subroutine dormql (character side, character trans, integer m, integer n,integer k, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( * ) tau, double precision, dimension( ldc, * ) c,integer ldc, double precision, dimension( * ) work, integer lwork,integer info)
subroutine sormql (character side, character trans, integer m, integer n,integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )work, integer lwork, integer info)
subroutine zunmql (character side, character trans, integer m, integer n,integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,complex*16, dimension( * ) work, integer lwork, integer info)
Author

NAME

unmql - {un,or}mql: multiply by Q from geqlf

SYNOPSIS

Functions

subroutine cunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMQL
subroutine dormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQL
subroutine sormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMQL
subroutine zunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
ZUNMQL

Detailed Description

Function Documentation

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

CUNMQL

Purpose:

CUNMQL 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 unitary matrix defined as the product of k
elementary reflectors

Q = H(k) . . . H(2) H(1)

as returned by CGEQLF. 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.

A

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

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).

TAU

TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQLF.

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

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

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For good performance, LWORK should generally be larger.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK 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.

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

DORMQL

Purpose:

DORMQL 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(k) . . . H(2) H(1)

as returned by DGEQLF. 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.

A

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

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).

TAU

TAU is DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQLF.

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

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

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For good performance, LWORK should generally be larger.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK 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.

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

SORMQL

Purpose:

SORMQL 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(k) . . . H(2) H(1)

as returned by SGEQLF. 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.

A

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

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).

TAU

TAU is REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQLF.

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

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For good performance, LWORK should generally be larger.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK 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.

subroutine zunmql (character side, character trans, integer m, integer n,integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,complex*16, dimension( * ) work, integer lwork, integer info)

ZUNMQL

Purpose:

ZUNMQL 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 unitary matrix defined as the product of k
elementary reflectors

Q = H(k) . . . H(2) H(1)

as returned by ZGEQLF. 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.

A

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

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).

TAU

TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQLF.

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

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

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For good performance, LWORK should generally be larger.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK 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.

Author

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