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*> \brief \b ZSPT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
* RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER LDW, N
* DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( * ), AINV( * ), WORK( LDW, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSPT03 computes the residual for a complex symmetric packed matrix
*> times its inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> complex symmetric matrix A is stored:
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (N*(N+1)/2)
*> The original complex symmetric matrix A, stored as a packed
*> triangular matrix.
*> \endverbatim
*>
*> \param[in] AINV
*> \verbatim
*> AINV is COMPLEX*16 array, dimension (N*(N+1)/2)
*> The (symmetric) inverse of the matrix A, stored as a packed
*> triangular matrix.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LDW,N)
*> \endverbatim
*>
*> \param[in] LDW
*> \verbatim
*> LDW is INTEGER
*> The leading dimension of the array WORK. LDW >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is DOUBLE PRECISION
*> The reciprocal of the condition number of A, computed as
*> ( 1/norm(A) ) / norm(AINV).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
$ RESID )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDW, N
DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), AINV( * ), WORK( LDW, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, ICOL, J, JCOL, K, KCOL, NALL
DOUBLE PRECISION AINVNM, ANORM, EPS
COMPLEX*16 T
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSP
COMPLEX*16 ZDOTU
EXTERNAL LSAME, DLAMCH, ZLANGE, ZLANSP, ZDOTU
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RCOND = ONE
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANSP( '1', UPLO, N, A, RWORK )
AINVNM = ZLANSP( '1', UPLO, N, AINV, RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCOND = ZERO
RESID = ONE / EPS
RETURN
END IF
RCOND = ( ONE / ANORM ) / AINVNM
*
* Case where both A and AINV are upper triangular:
* Each element of - A * AINV is computed by taking the dot product
* of a row of A with a column of AINV.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 70 I = 1, N
ICOL = ( ( I-1 )*I ) / 2 + 1
*
* Code when J <= I
*
DO 30 J = 1, I
JCOL = ( ( J-1 )*J ) / 2 + 1
T = ZDOTU( J, A( ICOL ), 1, AINV( JCOL ), 1 )
JCOL = JCOL + 2*J - 1
KCOL = ICOL - 1
DO 10 K = J + 1, I
T = T + A( KCOL+K )*AINV( JCOL )
JCOL = JCOL + K
10 CONTINUE
KCOL = KCOL + 2*I
DO 20 K = I + 1, N
T = T + A( KCOL )*AINV( JCOL )
KCOL = KCOL + K
JCOL = JCOL + K
20 CONTINUE
WORK( I, J ) = -T
30 CONTINUE
*
* Code when J > I
*
DO 60 J = I + 1, N
JCOL = ( ( J-1 )*J ) / 2 + 1
T = ZDOTU( I, A( ICOL ), 1, AINV( JCOL ), 1 )
JCOL = JCOL - 1
KCOL = ICOL + 2*I - 1
DO 40 K = I + 1, J
T = T + A( KCOL )*AINV( JCOL+K )
KCOL = KCOL + K
40 CONTINUE
JCOL = JCOL + 2*J
DO 50 K = J + 1, N
T = T + A( KCOL )*AINV( JCOL )
KCOL = KCOL + K
JCOL = JCOL + K
50 CONTINUE
WORK( I, J ) = -T
60 CONTINUE
70 CONTINUE
ELSE
*
* Case where both A and AINV are lower triangular
*
NALL = ( N*( N+1 ) ) / 2
DO 140 I = 1, N
*
* Code when J <= I
*
ICOL = NALL - ( ( N-I+1 )*( N-I+2 ) ) / 2 + 1
DO 100 J = 1, I
JCOL = NALL - ( ( N-J )*( N-J+1 ) ) / 2 - ( N-I )
T = ZDOTU( N-I+1, A( ICOL ), 1, AINV( JCOL ), 1 )
KCOL = I
JCOL = J
DO 80 K = 1, J - 1
T = T + A( KCOL )*AINV( JCOL )
JCOL = JCOL + N - K
KCOL = KCOL + N - K
80 CONTINUE
JCOL = JCOL - J
DO 90 K = J, I - 1
T = T + A( KCOL )*AINV( JCOL+K )
KCOL = KCOL + N - K
90 CONTINUE
WORK( I, J ) = -T
100 CONTINUE
*
* Code when J > I
*
ICOL = NALL - ( ( N-I )*( N-I+1 ) ) / 2
DO 130 J = I + 1, N
JCOL = NALL - ( ( N-J+1 )*( N-J+2 ) ) / 2 + 1
T = ZDOTU( N-J+1, A( ICOL-N+J ), 1, AINV( JCOL ), 1 )
KCOL = I
JCOL = J
DO 110 K = 1, I - 1
T = T + A( KCOL )*AINV( JCOL )
JCOL = JCOL + N - K
KCOL = KCOL + N - K
110 CONTINUE
KCOL = KCOL - I
DO 120 K = I, J - 1
T = T + A( KCOL+K )*AINV( JCOL )
JCOL = JCOL + N - K
120 CONTINUE
WORK( I, J ) = -T
130 CONTINUE
140 CONTINUE
END IF
*
* Add the identity matrix to WORK .
*
DO 150 I = 1, N
WORK( I, I ) = WORK( I, I ) + ONE
150 CONTINUE
*
* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
RESID = ZLANGE( '1', N, N, WORK, LDW, RWORK )
*
RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
*
RETURN
*
* End of ZSPT03
*
END
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