# geqrt3 - Man Page

geqrt3: QR factor, with T, recursive panel

## Synopsis

### Functions

recursive subroutine **cgeqrt3** (m, n, a, lda, t, ldt, info)

**CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.**

recursive subroutine **dgeqrt3** (m, n, a, lda, t, ldt, info)**DGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

recursive subroutine **sgeqrt3** (m, n, a, lda, t, ldt, info)**SGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

recursive subroutine **zgeqrt3** (m, n, a, lda, t, ldt, info)**ZGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Detailed Description

## Function Documentation

### recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

**CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.**

**Purpose:**

CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

**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. For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line **131** of file **cgeqrt3.f**.

### recursive subroutine dgeqrt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

**DGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

DGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

**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. For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line **131** of file **dgeqrt3.f**.

### recursive subroutine sgeqrt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

**SGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

SGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

**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. For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line **131** of file **sgeqrt3.f**.

### recursive subroutine zgeqrt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

**ZGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

ZGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

**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. For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line **131** of file **zgeqrt3.f**.

## Author

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