---
name: "ctpmlqt.f"
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/ctpmlqt.f"
---

# ctpmlqt.f(3)

## NAME

SRC/ctpmlqt.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ctpmlqt** (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)\
 **CTPMLQT**

## Function/Subroutine Documentation

### subroutine ctpmlqt (character side, character trans, integer m, integer n, integer k, integer l, integer mb, complex, dimension( ldv, \* ) v, integer ldv, complex, dimension( ldt, \* ) t, integer ldt, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldb, \* ) b, integer ldb, complex, dimension( \* ) work, integer info)

**CTPMLQT**

**Purpose:**

```
!>
!> CTPMLQT applies a complex unitary matrix Q obtained from a
!>  complex block reflector H to a general
!> complex matrix C, which consists of two blocks A and B.
!>
```

**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 B. M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix B. N >= 0.
!>
```

*K*

```
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>
```

*L*

```
!>          L is INTEGER
!>          The order of the trapezoidal part of V.
!>          K >= L >= 0.  See Further Details.
!>
```

*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 CTPLQT.
!>
```

*V*

```
!>          V is COMPLEX array, dimension (LDV,K)
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          CTPLQT in B.  See Further Details.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= K.
!>
```

*T*

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

*LDT*

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

*A*

```
!>          A is COMPLEX array, dimension
!>          (LDA,N) if SIDE = 'L' or
!>          (LDA,K) if SIDE = 'R'
!>          On entry, the K-by-N or M-by-K matrix A.
!>          On exit, A is overwritten by the corresponding block of
!>          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,K);
!>          If SIDE = 'R', LDA >= max(1,M).
!>
```

*B*

```
!>          B is COMPLEX array, dimension (LDB,N)
!>          On entry, the M-by-N matrix B.
!>          On exit, B is overwritten by the corresponding block of
!>          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.
!>          LDB >= 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.

**Further Details:**

```
!>
!>  The columns of the pentagonal matrix V contain the elementary reflectors
!>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
!>  trapezoidal block V2:
!>
!>        V = [V1] [V2].
!>
!>
!>  The size of the trapezoidal block V2 is determined by the parameter L,
!>  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
!>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
!>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
!>
!>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
!>                      [B]
!>
!>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
!>
!>  The complex unitary matrix Q is formed from V and T.
!>
!>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
!>
!>  If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
!>
!>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
!>
!>  If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
!>
```

Definition at line **197** of file **ctpmlqt.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.