# geqrt2 - Man Page

geqrt2: QR factor, with T, level 2

## Synopsis

### Functions

subroutine **cgeqrt2** (m, n, a, lda, t, ldt, info)**CGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

subroutine **dgeqrt2** (m, n, a, lda, t, ldt, info)**DGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

subroutine **sgeqrt2** (m, n, a, lda, t, ldt, info)**SGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

subroutine **zgeqrt2** (m, n, a, lda, t, ldt, info)**ZGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Detailed Description

## Function Documentation

### subroutine cgeqrt2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

**CGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

CGEQRT2 computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q.

**Parameters***M*M is INTEGER The number of rows of the matrix A. M >= N.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is COMPLEX array, dimension (LDA,N) On entry, the complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details.

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

*T*T is COMPLEX array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.

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

*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**H where V**H is the conjugate transpose of V.

Definition at line **126** of file **cgeqrt2.f**.

### subroutine dgeqrt2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

**DGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

DGEQRT2 computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q.

**Parameters***M*M is INTEGER The number of rows of the matrix A. M >= N.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details.

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

*T*T is DOUBLE PRECISION array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.

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

*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V.

Definition at line **126** of file **dgeqrt2.f**.

### subroutine sgeqrt2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

**SGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

SGEQRT2 computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q.

**Parameters***M*M is INTEGER The number of rows of the matrix A. M >= N.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is REAL array, dimension (LDA,N) On entry, the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details.

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

*T*T is REAL array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.

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

*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V.

Definition at line **126** of file **sgeqrt2.f**.

### subroutine zgeqrt2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

**ZGEQRT2** computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q.

**Parameters***M*M is INTEGER The number of rows of the matrix A. M >= N.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details.

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

*T*T is COMPLEX*16 array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.

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

*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**H where V**H is the conjugate transpose of V.

Definition at line **126** of file **zgeqrt2.f**.

## Author

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