1*> \brief \b CRZT02 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* REAL FUNCTION CRZT02( M, N, AF, LDA, TAU, WORK, 12* LWORK ) 13* 14* .. Scalar Arguments .. 15* INTEGER LDA, LWORK, M, N 16* .. 17* .. Array Arguments .. 18* COMPLEX AF( LDA, * ), TAU( * ), WORK( LWORK ) 19* .. 20* 21* 22*> \par Purpose: 23* ============= 24*> 25*> \verbatim 26*> 27*> CRZT02 returns 28*> || I - Q'*Q || / ( M * eps) 29*> where the matrix Q is defined by the Householder transformations 30*> generated by CTZRZF. 31*> \endverbatim 32* 33* Arguments: 34* ========== 35* 36*> \param[in] M 37*> \verbatim 38*> M is INTEGER 39*> The number of rows of the matrix AF. 40*> \endverbatim 41*> 42*> \param[in] N 43*> \verbatim 44*> N is INTEGER 45*> The number of columns of the matrix AF. 46*> \endverbatim 47*> 48*> \param[in] AF 49*> \verbatim 50*> AF is COMPLEX array, dimension (LDA,N) 51*> The output of CTZRZF. 52*> \endverbatim 53*> 54*> \param[in] LDA 55*> \verbatim 56*> LDA is INTEGER 57*> The leading dimension of the array AF. 58*> \endverbatim 59*> 60*> \param[in] TAU 61*> \verbatim 62*> TAU is COMPLEX array, dimension (M) 63*> Details of the Householder transformations as returned by 64*> CTZRZF. 65*> \endverbatim 66*> 67*> \param[out] WORK 68*> \verbatim 69*> WORK is COMPLEX array, dimension (LWORK) 70*> \endverbatim 71*> 72*> \param[in] LWORK 73*> \verbatim 74*> LWORK is INTEGER 75*> Length of WORK array. LWORK >= N*N+N. 76*> \endverbatim 77* 78* Authors: 79* ======== 80* 81*> \author Univ. of Tennessee 82*> \author Univ. of California Berkeley 83*> \author Univ. of Colorado Denver 84*> \author NAG Ltd. 85* 86*> \ingroup complex_lin 87* 88* ===================================================================== 89 REAL FUNCTION CRZT02( M, N, AF, LDA, TAU, WORK, 90 $ LWORK ) 91* 92* -- LAPACK test routine -- 93* -- LAPACK is a software package provided by Univ. of Tennessee, -- 94* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 95* 96* .. Scalar Arguments .. 97 INTEGER LDA, LWORK, M, N 98* .. 99* .. Array Arguments .. 100 COMPLEX AF( LDA, * ), TAU( * ), WORK( LWORK ) 101* .. 102* 103* ===================================================================== 104* 105* .. Parameters .. 106 REAL ZERO, ONE 107 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 108* .. 109* .. Local Scalars .. 110 INTEGER I, INFO 111* .. 112* .. Local Arrays .. 113 REAL RWORK( 1 ) 114* .. 115* .. External Functions .. 116 REAL CLANGE, SLAMCH 117 EXTERNAL CLANGE, SLAMCH 118* .. 119* .. External Subroutines .. 120 EXTERNAL CLASET, CUNMRZ, XERBLA 121* .. 122* .. Intrinsic Functions .. 123 INTRINSIC CMPLX, MAX, REAL 124* .. 125* .. Executable Statements .. 126* 127 CRZT02 = ZERO 128* 129 IF( LWORK.LT.N*N+N ) THEN 130 CALL XERBLA( 'CRZT02', 7 ) 131 RETURN 132 END IF 133* 134* Quick return if possible 135* 136 IF( M.LE.0 .OR. N.LE.0 ) 137 $ RETURN 138* 139* Q := I 140* 141 CALL CLASET( 'Full', N, N, CMPLX( ZERO ), CMPLX( ONE ), WORK, N ) 142* 143* Q := P(1) * ... * P(m) * Q 144* 145 CALL CUNMRZ( 'Left', 'No transpose', N, N, M, N-M, AF, LDA, TAU, 146 $ WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO ) 147* 148* Q := P(m)' * ... * P(1)' * Q 149* 150 CALL CUNMRZ( 'Left', 'Conjugate transpose', N, N, M, N-M, AF, LDA, 151 $ TAU, WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO ) 152* 153* Q := Q - I 154* 155 DO 10 I = 1, N 156 WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE 157 10 CONTINUE 158* 159 CRZT02 = CLANGE( 'One-norm', N, N, WORK, N, RWORK ) / 160 $ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) 161 RETURN 162* 163* End of CRZT02 164* 165 END 166