# dsbt21.f - Man Page

TESTING/EIG/dsbt21.f

## Synopsis

### Functions/Subroutines

subroutine **dsbt21** (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, result)**DSBT21**

## Function/Subroutine Documentation

### subroutine dsbt21 (character uplo, integer n, integer ka, integer ks, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) work, double precision, dimension( 2 ) result)

**DSBT21**

**Purpose:**

DSBT21 generally checks a decomposition of the form A = U S U**T where **T means transpose, A is symmetric banded, U is orthogonal, and S is diagonal (if KS=0) or symmetric tridiagonal (if KS=1). Specifically: RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and RESULT(2) = | I - U U**T | / ( n ulp )

**Parameters***UPLO*UPLO is CHARACTER If UPLO='U', the upper triangle of A and V will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A and V will be used and the (strictly) upper triangle will not be referenced.

*N*N is INTEGER The size of the matrix. If it is zero, DSBT21 does nothing. It must be at least zero.

*KA*KA is INTEGER The bandwidth of the matrix A. It must be at least zero. If it is larger than N-1, then max( 0, N-1 ) will be used.

*KS*KS is INTEGER The bandwidth of the matrix S. 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.

*A*A is DOUBLE PRECISION 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.

*LDA*LDA is INTEGER The leading dimension of A. It must be at least 1 and at least min( KA, N-1 ).

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

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

*U*U is DOUBLE PRECISION array, dimension (LDU, N) The orthogonal matrix in the decomposition, expressed as a dense matrix (i.e., not as a product of Householder transformations, Givens transformations, etc.)

*LDU*LDU is INTEGER The leading dimension of U. LDU must be at least N and at least 1.

*WORK*WORK is DOUBLE PRECISION array, dimension (N**2+N)

*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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **145** of file **dsbt21.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dsbt21(3) is an alias of dsbt21.f(3).

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