# unglq - Man Page

{un,or}glq: generate explicit Q from gelqf

## Synopsis

### Functions

subroutine **cunglq** (m, n, k, a, lda, tau, work, lwork, info)**CUNGLQ**

subroutine **dorglq** (m, n, k, a, lda, tau, work, lwork, info)**DORGLQ**

subroutine **sorglq** (m, n, k, a, lda, tau, work, lwork, info)**SORGLQ**

subroutine **zunglq** (m, n, k, a, lda, tau, work, lwork, info)**ZUNGLQ**

## Detailed Description

## Function Documentation

### subroutine cunglq (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

**CUNGLQ**

**Purpose:**

CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k)**H . . . H(2)**H H(1)**H as returned by CGELQF.

**Parameters***M*M is INTEGER The number of rows of the matrix Q. M >= 0.

*N*N is INTEGER The number of columns of the matrix Q. N >= M.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.

*A*A is COMPLEX array, dimension (LDA,N) On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGELQF in the first k rows of its array argument A. On exit, the M-by-N matrix Q.

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

*TAU*TAU is COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGELQF.

*WORK*WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*INFO*INFO is INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument has an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **126** of file **cunglq.f**.

### subroutine dorglq (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

**DORGLQ**

**Purpose:**

DORGLQ generates an M-by-N real matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by DGELQF.

**Parameters***M*M is INTEGER The number of rows of the matrix Q. M >= 0.

*N*N is INTEGER The number of columns of the matrix Q. N >= M.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQF in the first k rows of its array argument A. On exit, the M-by-N matrix Q.

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

*TAU*TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF.

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument has an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **126** of file **dorglq.f**.

### subroutine sorglq (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

**SORGLQ**

**Purpose:**

SORGLQ generates an M-by-N real matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by SGELQF.

**Parameters***M*M is INTEGER The number of rows of the matrix Q. M >= 0.

*N*N is INTEGER The number of columns of the matrix Q. N >= M.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.

*A*A is REAL array, dimension (LDA,N) On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQF in the first k rows of its array argument A. On exit, the M-by-N matrix Q.

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

*TAU*TAU is REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGELQF.

*WORK*WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument has an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **126** of file **sorglq.f**.

### subroutine zunglq (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

**ZUNGLQ**

**Purpose:**

ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k)**H . . . H(2)**H H(1)**H as returned by ZGELQF.

**Parameters***M*M is INTEGER The number of rows of the matrix Q. M >= 0.

*N*N is INTEGER The number of columns of the matrix Q. N >= M.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQF in the first k rows of its array argument A. On exit, the M-by-N matrix Q.

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

*TAU*TAU is COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGELQF.

*WORK*WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK**INFO*INFO is INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument has an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **126** of file **zunglq.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.