LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
 All Files Functions Typedefs Macros
dsbt21.f File Reference

Go to the source code of this file.

Functions/Subroutines

subroutine dsbt21 (UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RESULT)
 DSBT21 More...
 

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'

 where ' 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' | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU' | / ( n ulp )
Parameters
[in]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.
[in]N
          N is INTEGER
          The size of the matrix.  If it is zero, DSBT21 does nothing.
          It must be at least zero.
[in]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.
[in]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.
[in]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.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 1
          and at least min( KA, N-1 ).
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal of the (symmetric tri-) diagonal matrix S.
[in]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.
[in]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.)
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  LDU must be at least N and
          at least 1.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N**2+N)
[out]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.
Date
November 2011

Definition at line 146 of file dsbt21.f.

Here is the call graph for this function:

Here is the caller graph for this function: