# ungtr - Man Page

{un,or}gtr: generate Q from hetrd

## Synopsis

### Functions

subroutine **cungtr** (uplo, n, a, lda, tau, work, lwork, info)**CUNGTR**

subroutine **dorgtr** (uplo, n, a, lda, tau, work, lwork, info)**DORGTR**

subroutine **sorgtr** (uplo, n, a, lda, tau, work, lwork, info)**SORGTR**

subroutine **zungtr** (uplo, n, a, lda, tau, work, lwork, info)**ZUNGTR**

## Detailed Description

## Function Documentation

### subroutine cungtr (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

**CUNGTR**

**Purpose:**

CUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from CHETRD; = 'L': Lower triangle of A contains elementary reflectors from CHETRD.

*N*N is INTEGER The order of the matrix Q. N >= 0.

*A*A is COMPLEX array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by CHETRD. On exit, the N-by-N unitary matrix Q.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= N.

*TAU*TAU is COMPLEX array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD.

*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 >= N-1. For optimum performance LWORK >= (N-1)*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.

Definition at line **122** of file **cungtr.f**.

### subroutine dorgtr (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

**DORGTR**

**Purpose:**

DORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors from DSYTRD.

*N*N is INTEGER The order of the matrix Q. N >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DSYTRD. On exit, the N-by-N orthogonal matrix Q.

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

*TAU*TAU is DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.

*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,N-1). For optimum performance LWORK >= (N-1)*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.

Definition at line **122** of file **dorgtr.f**.

### subroutine sorgtr (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

**SORGTR**

**Purpose:**

SORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from SSYTRD; = 'L': Lower triangle of A contains elementary reflectors from SSYTRD.

*N*N is INTEGER The order of the matrix Q. N >= 0.

*A*A is REAL array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by SSYTRD. On exit, the N-by-N orthogonal matrix Q.

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

*TAU*TAU is REAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.

*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,N-1). For optimum performance LWORK >= (N-1)*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.

Definition at line **122** of file **sorgtr.f**.

### subroutine zungtr (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

**ZUNGTR**

**Purpose:**

ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from ZHETRD; = 'L': Lower triangle of A contains elementary reflectors from ZHETRD.

*N*N is INTEGER The order of the matrix Q. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by ZHETRD. On exit, the N-by-N unitary matrix Q.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= N.

*TAU*TAU is COMPLEX*16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.

*WORK*WORK is COMPLEX*16 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 >= N-1. For optimum performance LWORK >= (N-1)*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.

Definition at line **122** of file **zungtr.f**.

## Author

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