---
name: "gemlqt"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/gemlqt"
---

# gemlqt(3)

gemlqt: multiply by Q from gelqt

## NAME

gemlqt - 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**

## Detailed Description

## 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:**

```
!>
!> SGEMLQT 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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