LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtzt02.f
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00001 *> \brief \b DTZT02
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       DOUBLE PRECISION FUNCTION DTZT02( M, N, AF, LDA, TAU, WORK,
00012 *                        LWORK )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       INTEGER            LDA, LWORK, M, N
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       DOUBLE PRECISION   AF( LDA, * ), TAU( * ), WORK( LWORK )
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> DTZT02 returns
00028 *>      || I - Q'*Q || / ( M * eps)
00029 *> where the matrix Q is defined by the Householder transformations
00030 *> generated by DTZRQF.
00031 *> \endverbatim
00032 *
00033 *  Arguments:
00034 *  ==========
00035 *
00036 *> \param[in] M
00037 *> \verbatim
00038 *>          M is INTEGER
00039 *>          The number of rows of the matrix AF.
00040 *> \endverbatim
00041 *>
00042 *> \param[in] N
00043 *> \verbatim
00044 *>          N is INTEGER
00045 *>          The number of columns of the matrix AF.
00046 *> \endverbatim
00047 *>
00048 *> \param[in] AF
00049 *> \verbatim
00050 *>          AF is DOUBLE PRECISION array, dimension (LDA,N)
00051 *>          The output of DTZRQF.
00052 *> \endverbatim
00053 *>
00054 *> \param[in] LDA
00055 *> \verbatim
00056 *>          LDA is INTEGER
00057 *>          The leading dimension of the array AF.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] TAU
00061 *> \verbatim
00062 *>          TAU is DOUBLE PRECISION array, dimension (M)
00063 *>          Details of the Householder transformations as returned by
00064 *>          DTZRQF.
00065 *> \endverbatim
00066 *>
00067 *> \param[out] WORK
00068 *> \verbatim
00069 *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
00070 *> \endverbatim
00071 *>
00072 *> \param[in] LWORK
00073 *> \verbatim
00074 *>          LWORK is INTEGER
00075 *>          length of WORK array. Must be >= N*N+N
00076 *> \endverbatim
00077 *
00078 *  Authors:
00079 *  ========
00080 *
00081 *> \author Univ. of Tennessee 
00082 *> \author Univ. of California Berkeley 
00083 *> \author Univ. of Colorado Denver 
00084 *> \author NAG Ltd. 
00085 *
00086 *> \date November 2011
00087 *
00088 *> \ingroup double_lin
00089 *
00090 *  =====================================================================
00091       DOUBLE PRECISION FUNCTION DTZT02( M, N, AF, LDA, TAU, WORK,
00092      $                 LWORK )
00093 *
00094 *  -- LAPACK test routine (version 3.4.0) --
00095 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00096 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00097 *     November 2011
00098 *
00099 *     .. Scalar Arguments ..
00100       INTEGER            LDA, LWORK, M, N
00101 *     ..
00102 *     .. Array Arguments ..
00103       DOUBLE PRECISION   AF( LDA, * ), TAU( * ), WORK( LWORK )
00104 *     ..
00105 *
00106 *  =====================================================================
00107 *
00108 *     .. Parameters ..
00109       DOUBLE PRECISION   ZERO, ONE
00110       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00111 *     ..
00112 *     .. Local Scalars ..
00113       INTEGER            I
00114 *     ..
00115 *     .. Local Arrays ..
00116       DOUBLE PRECISION   RWORK( 1 )
00117 *     ..
00118 *     .. External Functions ..
00119       DOUBLE PRECISION   DLAMCH, DLANGE
00120       EXTERNAL           DLAMCH, DLANGE
00121 *     ..
00122 *     .. External Subroutines ..
00123       EXTERNAL           DLASET, DLATZM, XERBLA
00124 *     ..
00125 *     .. Intrinsic Functions ..
00126       INTRINSIC          DBLE, MAX
00127 *     ..
00128 *     .. Executable Statements ..
00129 *
00130       DTZT02 = ZERO
00131 *
00132       IF( LWORK.LT.N*N+N ) THEN
00133          CALL XERBLA( 'DTZT02', 7 )
00134          RETURN
00135       END IF
00136 *
00137 *     Quick return if possible
00138 *
00139       IF( M.LE.0 .OR. N.LE.0 )
00140      $   RETURN
00141 *
00142 *     Q := I
00143 *
00144       CALL DLASET( 'Full', N, N, ZERO, ONE, WORK, N )
00145 *
00146 *     Q := P(1) * ... * P(m) * Q
00147 *
00148       DO 10 I = M, 1, -1
00149          CALL DLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
00150      $                WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
00151    10 CONTINUE
00152 *
00153 *     Q := P(m) * ... * P(1) * Q
00154 *
00155       DO 20 I = 1, M
00156          CALL DLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
00157      $                WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
00158    20 CONTINUE
00159 *
00160 *     Q := Q - I
00161 *
00162       DO 30 I = 1, N
00163          WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE
00164    30 CONTINUE
00165 *
00166       DTZT02 = DLANGE( 'One-norm', N, N, WORK, N, RWORK ) /
00167      $         ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
00168       RETURN
00169 *
00170 *     End of DTZT02
00171 *
00172       END
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