---
name: "sgehd2.f"
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/sgehd2.f"
---

# sgehd2.f(3)

## NAME

SRC/sgehd2.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgehd2** (n, ilo, ihi, a, lda, tau, work, info)\
 **SGEHD2** reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine sgehd2 (integer n, integer ilo, integer ihi, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer info)

**SGEHD2** reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

**Purpose:**

```
!>
!> SGEHD2 reduces a real general matrix A to upper Hessenberg form H by
!> an orthogonal similarity transformation:  Q**T * A * Q = H .
!>
```

**Parameters**

*N*

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

*ILO*

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

*IHI*

```
!>          IHI is INTEGER
!>
!>          It is assumed that A is already upper triangular in rows
!>          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
!>          set by a previous call to SGEBAL; otherwise they should be
!>          set to 1 and N respectively. See Further Details.
!>          1 <= ILO <= IHI <= max(1,N).
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the n by n general matrix to be reduced.
!>          On exit, the upper triangle and the first subdiagonal of A
!>          are overwritten with the upper Hessenberg matrix H, and the
!>          elements below the first subdiagonal, with the array TAU,
!>          represent the orthogonal matrix Q as a product of elementary
!>          reflectors. See Further Details.
!>
```

*LDA*

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

*TAU*

```
!>          TAU is REAL array, dimension (N-1)
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (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 Q is represented as a product of (ihi-ilo) elementary
!>  reflectors
!>
!>     Q = H(ilo) H(ilo+1) . . . H(ihi-1).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**T
!>
!>  where tau is a real scalar, and v is a real vector with
!>  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
!>  exit in A(i+2:ihi,i), and tau in TAU(i).
!>
!>  The contents of A are illustrated by the following example, with
!>  n = 7, ilo = 2 and ihi = 6:
!>
!>  on entry,                        on exit,
!>
!>  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
!>  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
!>  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
!>  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
!>  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
!>  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
!>  (                         a )    (                          a )
!>
!>  where a denotes an element of the original matrix A, h denotes a
!>  modified element of the upper Hessenberg matrix H, and vi denotes an
!>  element of the vector defining H(i).
!>
```

Definition at line **148** of file **sgehd2.f**.

## Author

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