---
name: "chet22.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/chet22.f"
---

# chet22.f(3)

## NAME

TESTING/EIG/chet22.f

## SYNOPSIS

### Functions/Subroutines

subroutine **chet22** (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, rwork, result)\
 **CHET22**

## Function/Subroutine Documentation

### subroutine chet22 (integer itype, character uplo, integer n, integer m, integer kband, complex, dimension( lda, \* ) a, integer lda, real, dimension( \* ) d, real, dimension( \* ) e, complex, dimension( ldu, \* ) u, integer ldu, complex, dimension( ldv, \* ) v, integer ldv, complex, dimension( \* ) tau, complex, dimension( \* ) work, real, dimension( \* ) rwork, real, dimension( 2 ) result)

**CHET22**

**Purpose:**

```
!>
!>      CHET22  generally checks a decomposition of the form
!>
!>              A U = U S
!>
!>      where A is complex Hermitian, the columns of U are orthonormal,
!>      and S is diagonal (if KBAND=0) or symmetric tridiagonal (if
!>      KBAND=1).  If ITYPE=1, then U is represented as a dense matrix,
!>      otherwise the U is expressed as a product of Householder
!>      transformations, whose vectors are stored in the array  and
!>      whose scaling constants are in
 we shall use the letter
!>       to refer to the product of Householder transformations
!>      (which should be equal to U).
!>
!>      Specifically, if ITYPE=1, then:
!>
!>              RESULT(1) = | U**H A U - S | / ( |A| m ulp ) and
!>              RESULT(2) = | I - U**H U | / ( m ulp )
!>
```

```
!>  ITYPE   INTEGER
!>          Specifies the type of tests to be performed.
!>          1: U expressed as a dense orthogonal matrix:
!>             RESULT(1) = | A - U S U**H | / ( |A| n ulp )  and
!>             RESULT(2) = | I - U U**H | / ( n ulp )
!>
!>  UPLO    CHARACTER
!>          If UPLO='U', the upper triangle of A will be used and the
!>          (strictly) lower triangle will not be referenced.  If
!>          UPLO='L', the lower triangle of A will be used and the
!>          (strictly) upper triangle will not be referenced.
!>          Not modified.
!>
!>  N       INTEGER
!>          The size of the matrix.  If it is zero, CHET22 does nothing.
!>          It must be at least zero.
!>          Not modified.
!>
!>  M       INTEGER
!>          The number of columns of U.  If it is zero, CHET22 does
!>          nothing.  It must be at least zero.
!>          Not modified.
!>
!>  KBAND   INTEGER
!>          The bandwidth of the matrix.  It may only be zero or one.
!>          If zero, then S is diagonal, and E is not referenced.  If
!>          one, then S is symmetric tri-diagonal.
!>          Not modified.
!>
!>  A       COMPLEX array, dimension (LDA , N)
!>          The original (unfactored) matrix.  It is assumed to be
!>          symmetric, and only the upper (UPLO='U') or only the lower
!>          (UPLO='L') will be referenced.
!>          Not modified.
!>
!>  LDA     INTEGER
!>          The leading dimension of A.  It must be at least 1
!>          and at least N.
!>          Not modified.
!>
!>  D       REAL array, dimension (N)
!>          The diagonal of the (symmetric tri-) diagonal matrix.
!>          Not modified.
!>
!>  E       REAL array, dimension (N)
!>          The off-diagonal of the (symmetric tri-) diagonal matrix.
!>          E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc.
!>          Not referenced if KBAND=0.
!>          Not modified.
!>
!>  U       COMPLEX array, dimension (LDU, N)
!>          If ITYPE=1, this contains the orthogonal matrix in
!>          the decomposition, expressed as a dense matrix.
!>          Not modified.
!>
!>  LDU     INTEGER
!>          The leading dimension of U.  LDU must be at least N and
!>          at least 1.
!>          Not modified.
!>
!>  V       COMPLEX array, dimension (LDV, N)
!>          If ITYPE=2 or 3, the lower triangle of this array contains
!>          the Householder vectors used to describe the orthogonal
!>          matrix in the decomposition.  If ITYPE=1, then it is not
!>          referenced.
!>          Not modified.
!>
!>  LDV     INTEGER
!>          The leading dimension of V.  LDV must be at least N and
!>          at least 1.
!>          Not modified.
!>
!>  TAU     COMPLEX array, dimension (N)
!>          If ITYPE >= 2, then TAU(j) is the scalar factor of
!>          v(j) v(j)**H in the Householder transformation H(j) of
!>          the product  U = H(1)...H(n-2)
!>          If ITYPE < 2, then TAU is not referenced.
!>          Not modified.
!>
!>  WORK    COMPLEX array, dimension (2*N**2)
!>          Workspace.
!>          Modified.
!>
!>  RWORK   REAL array, dimension (N)
!>          Workspace.
!>          Modified.
!>
!>  RESULT  REAL array, dimension (2)
!>          The values computed by the two tests described above.  The
!>          values are currently limited to 1/ulp, to avoid overflow.
!>          RESULT(1) is always modified.  RESULT(2) is modified only
!>          if LDU is at least N.
!>          Modified.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **159** of file **chet22.f**.

## Author

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