# tzrzf - Man Page

tzrzf: RZ factor

## Synopsis

### Functions

subroutine **ctzrzf** (m, n, a, lda, tau, work, lwork, info)**CTZRZF**

subroutine **dtzrzf** (m, n, a, lda, tau, work, lwork, info)**DTZRZF**

subroutine **stzrzf** (m, n, a, lda, tau, work, lwork, info)**STZRZF**

subroutine **ztzrzf** (m, n, a, lda, tau, work, lwork, info)**ZTZRZF**

## Detailed Description

## Function Documentation

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

**CTZRZF**

**Purpose:**

CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

**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 >= M.

*A*A is COMPLEX array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors.

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

*TAU*TAU is COMPLEX array, dimension (M) The scalar factors of the elementary reflectors.

*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 had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

**Further Details:**

The N-by-N matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each N-by-N Z(k) is given by Z(k) = I - tau(k)*v(k)*v(k)**H with v(k) is the kth row vector of the M-by-N matrix V = ( I A(:,M+1:N) ) I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from CTZRZF, and tau(k) is the kth element of the array TAU.

Definition at line **150** of file **ctzrzf.f**.

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

**DTZRZF**

**Purpose:**

DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

**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 >= M.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the orthogonal matrix Z as a product of M elementary reflectors.

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

*TAU*TAU is DOUBLE PRECISION array, dimension (M) The scalar factors of the elementary reflectors.

*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 had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

**Further Details:**

The N-by-N matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each N-by-N Z(k) is given by Z(k) = I - tau(k)*v(k)*v(k)**T with v(k) is the kth row vector of the M-by-N matrix V = ( I A(:,M+1:N) ) I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from DTZRZF, and tau(k) is the kth element of the array TAU.

Definition at line **150** of file **dtzrzf.f**.

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

**STZRZF**

**Purpose:**

STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

**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 >= M.

*A*A is REAL array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the orthogonal matrix Z as a product of M elementary reflectors.

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

*TAU*TAU is REAL array, dimension (M) The scalar factors of the elementary reflectors.

*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 had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

**Further Details:**

The N-by-N matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each N-by-N Z(k) is given by Z(k) = I - tau(k)*v(k)*v(k)**T with v(k) is the kth row vector of the M-by-N matrix V = ( I A(:,M+1:N) ) I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from STZRZF, and tau(k) is the kth element of the array TAU.

Definition at line **150** of file **stzrzf.f**.

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

**ZTZRZF**

**Purpose:**

ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

**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 >= M.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors.

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

*TAU*TAU is COMPLEX*16 array, dimension (M) The scalar factors of the elementary reflectors.

*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 had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

**Further Details:**

The N-by-N matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each N-by-N Z(k) is given by Z(k) = I - tau(k)*v(k)*v(k)**H with v(k) is the kth row vector of the M-by-N matrix V = ( I A(:,M+1:N) ) I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from ZTZRZF, and tau(k) is the kth element of the array TAU.

Definition at line **150** of file **ztzrzf.f**.

## Author

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