# zgemqrt.f - Man Page

SRC/zgemqrt.f

## Synopsis

### Functions/Subroutines

subroutine **zgemqrt** (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)**ZGEMQRT**

## Function/Subroutine Documentation

### subroutine zgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, 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)

**ZGEMQRT**

**Purpose:**

ZGEMQRT 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 orthogonal 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 ZGEQRT. 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.

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

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

*LDV*LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).

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

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= NB.

*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*NB if SIDE = 'L', or M*NB 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 **zgemqrt.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK