# gemlqt - Man Page

gemlqt: multiply by Q from gelqt

## Synopsis

### Functions

subroutine cgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
CGEMLQT
subroutine dgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
DGEMLQT
subroutine sgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
SGEMLQT
subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
ZGEMLQT

## Function Documentation

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

CGEMLQT

Purpose:

``` CGEMLQT 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(1) H(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by CGELQT.

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.```

MB

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

V

```          V is COMPLEX array, dimension
(LDV,M) if SIDE = 'L',
(LDV,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGELQT in the first K rows of its array argument A.```

LDV

```          LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).```

T

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

LDT

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

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*MB if SIDE = 'L', or  M*MB 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.

Definition at line 151 of file cgemlqt.f.

### subroutine dgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DGEMLQT

Purpose:

``` DGEMLQT 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 DGELQT.

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.```

MB

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

V

```          V is DOUBLE PRECISION array, dimension
(LDV,M) if SIDE = 'L',
(LDV,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGELQT in the first K rows of its array argument A.```

LDV

```          LDV is INTEGER
The leading dimension of the array V.  LDV >= max(1,K).```

T

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

LDT

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

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*MB if SIDE = 'L', or  M*MB 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.

Definition at line 166 of file dgemlqt.f.

### subroutine sgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SGEMLQT

Purpose:

``` DGEMLQT 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 SGELQT.

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.```

MB

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

V

```          V is REAL array, dimension
(LDV,M) if SIDE = 'L',
(LDV,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGELQT in the first K rows of its array argument A.```

LDV

```          LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).```

T

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

LDT

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

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*MB if SIDE = 'L', or  M*MB 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.

Definition at line 151 of file sgemlqt.f.

### subroutine zgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, 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)

ZGEMLQT

Purpose:

``` ZGEMLQT 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(1) H(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by ZGELQT.

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.```

MB

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

V

```          V is COMPLEX*16 array, dimension
(LDV,M) if SIDE = 'L',
(LDV,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGELQT in the first K rows of its array argument A.```

LDV

```          LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).```

T

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

LDT

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

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*MB if SIDE = 'L', or  M*MB 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.

Definition at line 166 of file zgemlqt.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK