# ctplqt2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **ctplqt2** (M, **N**, L, A, **LDA**, B, **LDB**, T, LDT, INFO)

## Function/Subroutine Documentation

### subroutine ctplqt2 (integer M, integer N, integer L, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldt, * ) T, integer LDT, integer INFO)

**Purpose:**

CTPLQT2 computes a LQ a factorization of a complex 'triangular-pentagonal' matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

**Parameters:***M*M is INTEGER The total number of rows of the matrix B. M >= 0.

*N*N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.

*L*L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.

*A*A is COMPLEX array, dimension (LDA,M) On entry, the lower triangular M-by-M matrix A. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

*B*B is COMPLEX array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B. The first N-L columns are rectangular, and the last L columns are lower trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).

*T*T is COMPLEX array, dimension (LDT,M) The N-by-N upper triangular factor T of the block reflector. See Further Details.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= max(1,M)

*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.

**Date:**June 2017

**Further Details:**

The input matrix C is a M-by-(M+N) matrix

C = [ A ][ B ]

where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 left of a M-by-L upper trapezoidal matrix B2:

B = [ B1 ][ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L lower trapezoidal.

The lower trapezoidal matrix B2 consists of the first L columns of a N-by-N lower triangular matrix, where 0 <= L <= **MIN(M,N)**. If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular.

The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C

C = [ A ][ B ] [ A ] <- lower triangular M-by-M [ B ] <- M-by-N pentagonal

so that W can be represented as

W = [ I ][ V ] [ I ] <- identity, M-by-M [ V ] <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which we call V above. Note that V has the same form as B; that is,

W = [ V1 ][ V2 ] [ V1 ] <- M-by-(N-L) rectangular [ V2 ] <- M-by-L lower trapezoidal.

The rows of V represent the vectors which define the H(i)'s. The (M+N)-by-(M+N) block reflector H is then given by

H = I - W**T * T * W

where W^H is the conjugate transpose of W and T is the upper triangular factor of the block reflector.

Definition at line 162 of file ctplqt2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ctplqt2(3) is an alias of ctplqt2.f(3).