# geqrt - Man Page

geqrt: QR factor, with T

## Synopsis

### Functions

subroutine **cgeqrt** (m, n, nb, a, lda, t, ldt, work, info)**CGEQRT**

subroutine **dgeqrt** (m, n, nb, a, lda, t, ldt, work, info)**DGEQRT**

subroutine **sgeqrt** (m, n, nb, a, lda, t, ldt, work, info)**SGEQRT**

subroutine **zgeqrt** (m, n, nb, a, lda, t, ldt, work, info)**ZGEQRT**

## Detailed Description

## Function Documentation

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

**CGEQRT**

**Purpose:**

CGEQRT computes a blocked 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 >= 0.

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

*NB*NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.

*A*A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

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

*T*T is COMPLEX array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.

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

*WORK*WORK is COMPLEX array, dimension (NB*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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 ... TB).

Definition at line **140** of file **cgeqrt.f**.

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

**DGEQRT**

**Purpose:**

DGEQRT computes a blocked 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 >= 0.

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

*NB*NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

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

*T*T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.

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

*WORK*WORK is DOUBLE PRECISION array, dimension (NB*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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 ... TB).

Definition at line **140** of file **dgeqrt.f**.

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

**SGEQRT**

**Purpose:**

SGEQRT computes a blocked 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 >= 0.

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

*NB*NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.

*A*A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

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

*T*T is REAL array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.

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

*WORK*WORK is REAL array, dimension (NB*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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 ... TB).

Definition at line **140** of file **sgeqrt.f**.

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

**ZGEQRT**

**Purpose:**

ZGEQRT computes a blocked 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 >= 0.

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

*NB*NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

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

*T*T is COMPLEX*16 array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.

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

*WORK*WORK is COMPLEX*16 array, dimension (NB*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:**

Definition at line **140** of file **zgeqrt.f**.

## Author

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