# dstt21.f - Man Page

TESTING/EIG/dstt21.f

## Synopsis

### Functions/Subroutines

subroutine **dstt21** (n, kband, ad, ae, sd, se, u, ldu, work, result)**DSTT21**

## Function/Subroutine Documentation

### subroutine dstt21 (integer n, integer kband, double precision, dimension( * ) ad, double precision, dimension( * ) ae, double precision, dimension( * ) sd, double precision, dimension( * ) se, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) work, double precision, dimension( 2 ) result)

**DSTT21**

**Purpose:**

DSTT21 checks a decomposition of the form A = U S U' where ' means transpose, A is symmetric tridiagonal, U is orthogonal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Two tests are performed: RESULT(1) = | A - U S U' | / ( |A| n ulp ) RESULT(2) = | I - UU' | / ( n ulp )

**Parameters***N*N is INTEGER The size of the matrix. If it is zero, DSTT21 does nothing. It must be at least zero.

*KBAND*KBAND is INTEGER The bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and SE is not referenced. If one, then S is symmetric tri-diagonal.

*AD*AD is DOUBLE PRECISION array, dimension (N) The diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal.

*AE*AE is DOUBLE PRECISION array, dimension (N-1) The off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.

*SD*SD is DOUBLE PRECISION array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix S.

*SE*SE is DOUBLE PRECISION array, dimension (N-1) The off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc.

*U*U is DOUBLE PRECISION array, dimension (LDU, N) The orthogonal matrix in the decomposition.

*LDU*LDU is INTEGER The leading dimension of U. LDU must be at least N.

*WORK*WORK is DOUBLE PRECISION array, dimension (N*(N+1))

*RESULT*RESULT is DOUBLE PRECISION 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **125** of file **dstt21.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dstt21(3) is an alias of dstt21.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK