---
name: "unghr"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/unghr"
---

# unghr(3)

{un,or}ghr: generate Q from gehrd

## NAME

unghr - {un,or}ghr: generate Q from gehrd

## SYNOPSIS

### Functions

subroutine **cunghr** (n, ilo, ihi, a, lda, tau, work, lwork, info)\
 **CUNGHR**  subroutine **dorghr** (n, ilo, ihi, a, lda, tau, work, lwork, info)\
 **DORGHR**  subroutine **sorghr** (n, ilo, ihi, a, lda, tau, work, lwork, info)\
 **SORGHR**  subroutine **zunghr** (n, ilo, ihi, a, lda, tau, work, lwork, info)\
 **ZUNGHR**

## Detailed Description

## Function Documentation

### subroutine cunghr (integer n, integer ilo, integer ihi, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer lwork, integer info)

**CUNGHR**

**Purpose:**

```
!>
!> CUNGHR generates a complex unitary matrix Q which is defined as the
!> product of IHI-ILO elementary reflectors of order N, as returned by
!> CGEHRD:
!>
!> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
!>
```

**Parameters**

*N*

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

*ILO*

```
!>          ILO is INTEGER
!>
```

*IHI*

```
!>          IHI is INTEGER
!>
!>          ILO and IHI must have the same values as in the previous call
!>          of CGEHRD. Q is equal to the unit matrix except in the
!>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
!>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
!>
```

*A*

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

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,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 CGEHRD.
!>
```

*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 >= IHI-ILO.
!>          For optimum performance LWORK >= (IHI-ILO)*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 **125** of file **cunghr.f**.

### subroutine dorghr (integer n, integer ilo, integer ihi, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( \* ) work, integer lwork, integer info)

**DORGHR**

**Purpose:**

```
!>
!> DORGHR generates a real orthogonal matrix Q which is defined as the
!> product of IHI-ILO elementary reflectors of order N, as returned by
!> DGEHRD:
!>
!> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
!>
```

**Parameters**

*N*

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

*ILO*

```
!>          ILO is INTEGER
!>
```

*IHI*

```
!>          IHI is INTEGER
!>
!>          ILO and IHI must have the same values as in the previous call
!>          of DGEHRD. Q is equal to the unit matrix except in the
!>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
!>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the vectors which define the elementary reflectors,
!>          as returned by DGEHRD.
!>          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 DGEHRD.
!>
```

*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 >= IHI-ILO.
!>          For optimum performance LWORK >= (IHI-ILO)*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 **125** of file **dorghr.f**.

### subroutine sorghr (integer n, integer ilo, integer ihi, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer lwork, integer info)

**SORGHR**

**Purpose:**

```
!>
!> SORGHR generates a real orthogonal matrix Q which is defined as the
!> product of IHI-ILO elementary reflectors of order N, as returned by
!> SGEHRD:
!>
!> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
!>
```

**Parameters**

*N*

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

*ILO*

```
!>          ILO is INTEGER
!>
```

*IHI*

```
!>          IHI is INTEGER
!>
!>          ILO and IHI must have the same values as in the previous call
!>          of SGEHRD. Q is equal to the unit matrix except in the
!>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
!>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the vectors which define the elementary reflectors,
!>          as returned by SGEHRD.
!>          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 SGEHRD.
!>
```

*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 >= IHI-ILO.
!>          For optimum performance LWORK >= (IHI-ILO)*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 **125** of file **sorghr.f**.

### subroutine zunghr (integer n, integer ilo, integer ihi, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( \* ) work, integer lwork, integer info)

**ZUNGHR**

**Purpose:**

```
!>
!> ZUNGHR generates a complex unitary matrix Q which is defined as the
!> product of IHI-ILO elementary reflectors of order N, as returned by
!> ZGEHRD:
!>
!> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
!>
```

**Parameters**

*N*

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

*ILO*

```
!>          ILO is INTEGER
!>
```

*IHI*

```
!>          IHI is INTEGER
!>
!>          ILO and IHI must have the same values as in the previous call
!>          of ZGEHRD. Q is equal to the unit matrix except in the
!>          submatrix Q(ilo+1:ihi,ilo+1:ihi).
!>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
!>
```

*A*

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

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,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 ZGEHRD.
!>
```

*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 >= IHI-ILO.
!>          For optimum performance LWORK >= (IHI-ILO)*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 **125** of file **zunghr.f**.

## Author

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