dsyt22()

subroutine dsyt22	(	integer	itype,
		character	uplo,
		integer	n,
		integer	m,
		integer	kband,
		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( ldv, * )	v,
		integer	ldv,
		double precision, dimension( * )	tau,
		double precision, dimension( * )	work,
		double precision, dimension( 2 )	result )

DSYT22

Purpose:

!>
!>      DSYT22  generally checks a decomposition of the form
!>
!>              A U = U S
!>
!>      where A is symmetric, 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**T A U - S | / ( |A| m ulp ) and
!>              RESULT(2) = | I - U**T 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**T | / ( |A| n ulp )  and
!>             RESULT(2) = | I - U U**T | / ( 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, DSYT22 does nothing.
!>          It must be at least zero.
!>          Not modified.
!>
!>  M       INTEGER
!>          The number of columns of U.  If it is zero, DSYT22 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       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.
!>          Not modified.
!>
!>  LDA     INTEGER
!>          The leading dimension of A.  It must be at least 1
!>          and at least N.
!>          Not modified.
!>
!>  D       DOUBLE PRECISION array, dimension (N)
!>          The diagonal of the (symmetric tri-) diagonal matrix.
!>          Not modified.
!>
!>  E       DOUBLE PRECISION 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       DOUBLE PRECISION array, dimension (LDU, N)
!>          If ITYPE=1 or 3, this contains the orthogonal matrix in
!>          the decomposition, expressed as a dense matrix.  If ITYPE=2,
!>          then it is not referenced.
!>          Not modified.
!>
!>  LDU     INTEGER
!>          The leading dimension of U.  LDU must be at least N and
!>          at least 1.
!>          Not modified.
!>
!>  V       DOUBLE PRECISION 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     DOUBLE PRECISION array, dimension (N)
!>          If ITYPE >= 2, then TAU(j) is the scalar factor of
!>          v(j) v(j)**T 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    DOUBLE PRECISION array, dimension (2*N**2)
!>          Workspace.
!>          Modified.
!>
!>  RESULT  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.  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 155 of file dsyt22.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            ITYPE, KBAND, LDA, LDU, LDV, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), RESULT( 2 ),
     $                   TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d0, one = 1.0d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J, JJ, JJ1, JJ2, NN, NNP1
      DOUBLE PRECISION   ANORM, ULP, UNFL, WNORM
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLANSY
      EXTERNAL           dlamch, dlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dort01, dsymm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, max, min
*     ..
*     .. Executable Statements ..
*
      result( 1 ) = zero
      result( 2 ) = zero
      IF( n.LE.0 .OR. m.LE.0 )
     $   RETURN
*
      unfl = dlamch( 'Safe minimum' )
      ulp = dlamch( 'Precision' )
*
*     Do Test 1
*
*     Norm of A:
*
      anorm = max( dlansy( '1', uplo, n, a, lda, work ), unfl )
*
*     Compute error matrix:
*
*     ITYPE=1: error = U**T A U - S
*
      CALL dsymm( 'L', uplo, n, m, one, a, lda, u, ldu, zero, work, n )
      nn = n*n
      nnp1 = nn + 1
      CALL dgemm( 'T', 'N', m, m, n, one, u, ldu, work, n, zero,
     $            work( nnp1 ), n )
      DO 10 j = 1, m
         jj = nn + ( j-1 )*n + j
         work( jj ) = work( jj ) - d( j )
   10 CONTINUE
      IF( kband.EQ.1 .AND. n.GT.1 ) THEN
         DO 20 j = 2, m
            jj1 = nn + ( j-1 )*n + j - 1
            jj2 = nn + ( j-2 )*n + j
            work( jj1 ) = work( jj1 ) - e( j-1 )
            work( jj2 ) = work( jj2 ) - e( j-1 )
   20    CONTINUE
      END IF
      wnorm = dlansy( '1', uplo, m, work( nnp1 ), n, work( 1 ) )
*
      IF( anorm.GT.wnorm ) THEN
         result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
      ELSE
         IF( anorm.LT.one ) THEN
            result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
         ELSE
            result( 1 ) = min( wnorm / anorm, dble( m ) ) / ( m*ulp )
         END IF
      END IF
*
*     Do Test 2
*
*     Compute  U**T U - I
*
      IF( itype.EQ.1 )
     $   CALL dort01( 'Columns', n, m, u, ldu, work, 2*n*n,
     $                result( 2 ) )
*
      RETURN
*
*     End of DSYT22
*

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