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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHET22 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE ZHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU, 00012 * V, LDV, TAU, WORK, RWORK, RESULT ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER UPLO 00016 * INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N 00017 * .. 00018 * .. Array Arguments .. 00019 * DOUBLE PRECISION D( * ), E( * ), RESULT( 2 ), RWORK( * ) 00020 * COMPLEX*16 A( LDA, * ), TAU( * ), U( LDU, * ), 00021 * $ V( LDV, * ), WORK( * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> ZHET22 generally checks a decomposition of the form 00031 *> 00032 *> A U = U S 00033 *> 00034 *> where A is complex Hermitian, the columns of U are orthonormal, 00035 *> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if 00036 *> KBAND=1). If ITYPE=1, then U is represented as a dense matrix, 00037 *> otherwise the U is expressed as a product of Householder 00038 *> transformations, whose vectors are stored in the array "V" and 00039 *> whose scaling constants are in "TAU"; we shall use the letter 00040 *> "V" to refer to the product of Householder transformations 00041 *> (which should be equal to U). 00042 *> 00043 *> Specifically, if ITYPE=1, then: 00044 *> 00045 *> RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC> RESULT(2) = | I - U'U | / ( m ulp ) 00046 *> \endverbatim 00047 * 00048 * Arguments: 00049 * ========== 00050 * 00051 *> \verbatim 00052 *> ITYPE INTEGER 00053 *> Specifies the type of tests to be performed. 00054 *> 1: U expressed as a dense orthogonal matrix: 00055 *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) 00056 *> 00057 *> UPLO CHARACTER 00058 *> If UPLO='U', the upper triangle of A will be used and the 00059 *> (strictly) lower triangle will not be referenced. If 00060 *> UPLO='L', the lower triangle of A will be used and the 00061 *> (strictly) upper triangle will not be referenced. 00062 *> Not modified. 00063 *> 00064 *> N INTEGER 00065 *> The size of the matrix. If it is zero, ZHET22 does nothing. 00066 *> It must be at least zero. 00067 *> Not modified. 00068 *> 00069 *> M INTEGER 00070 *> The number of columns of U. If it is zero, ZHET22 does 00071 *> nothing. It must be at least zero. 00072 *> Not modified. 00073 *> 00074 *> KBAND INTEGER 00075 *> The bandwidth of the matrix. It may only be zero or one. 00076 *> If zero, then S is diagonal, and E is not referenced. If 00077 *> one, then S is symmetric tri-diagonal. 00078 *> Not modified. 00079 *> 00080 *> A COMPLEX*16 array, dimension (LDA , N) 00081 *> The original (unfactored) matrix. It is assumed to be 00082 *> symmetric, and only the upper (UPLO='U') or only the lower 00083 *> (UPLO='L') will be referenced. 00084 *> Not modified. 00085 *> 00086 *> LDA INTEGER 00087 *> The leading dimension of A. It must be at least 1 00088 *> and at least N. 00089 *> Not modified. 00090 *> 00091 *> D DOUBLE PRECISION array, dimension (N) 00092 *> The diagonal of the (symmetric tri-) diagonal matrix. 00093 *> Not modified. 00094 *> 00095 *> E DOUBLE PRECISION array, dimension (N) 00096 *> The off-diagonal of the (symmetric tri-) diagonal matrix. 00097 *> E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. 00098 *> Not referenced if KBAND=0. 00099 *> Not modified. 00100 *> 00101 *> U COMPLEX*16 array, dimension (LDU, N) 00102 *> If ITYPE=1, this contains the orthogonal matrix in 00103 *> the decomposition, expressed as a dense matrix. 00104 *> Not modified. 00105 *> 00106 *> LDU INTEGER 00107 *> The leading dimension of U. LDU must be at least N and 00108 *> at least 1. 00109 *> Not modified. 00110 *> 00111 *> V COMPLEX*16 array, dimension (LDV, N) 00112 *> If ITYPE=2 or 3, the lower triangle of this array contains 00113 *> the Householder vectors used to describe the orthogonal 00114 *> matrix in the decomposition. If ITYPE=1, then it is not 00115 *> referenced. 00116 *> Not modified. 00117 *> 00118 *> LDV INTEGER 00119 *> The leading dimension of V. LDV must be at least N and 00120 *> at least 1. 00121 *> Not modified. 00122 *> 00123 *> TAU COMPLEX*16 array, dimension (N) 00124 *> If ITYPE >= 2, then TAU(j) is the scalar factor of 00125 *> v(j) v(j)' in the Householder transformation H(j) of 00126 *> the product U = H(1)...H(n-2) 00127 *> If ITYPE < 2, then TAU is not referenced. 00128 *> Not modified. 00129 *> 00130 *> WORK COMPLEX*16 array, dimension (2*N**2) 00131 *> Workspace. 00132 *> Modified. 00133 *> 00134 *> RWORK DOUBLE PRECISION array, dimension (N) 00135 *> Workspace. 00136 *> Modified. 00137 *> 00138 *> RESULT DOUBLE PRECISION array, dimension (2) 00139 *> The values computed by the two tests described above. The 00140 *> values are currently limited to 1/ulp, to avoid overflow. 00141 *> RESULT(1) is always modified. RESULT(2) is modified only 00142 *> if LDU is at least N. 00143 *> Modified. 00144 *> \endverbatim 00145 * 00146 * Authors: 00147 * ======== 00148 * 00149 *> \author Univ. of Tennessee 00150 *> \author Univ. of California Berkeley 00151 *> \author Univ. of Colorado Denver 00152 *> \author NAG Ltd. 00153 * 00154 *> \date November 2011 00155 * 00156 *> \ingroup complex16_eig 00157 * 00158 * ===================================================================== 00159 SUBROUTINE ZHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU, 00160 $ V, LDV, TAU, WORK, RWORK, RESULT ) 00161 * 00162 * -- LAPACK test routine (version 3.4.0) -- 00163 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00165 * November 2011 00166 * 00167 * .. Scalar Arguments .. 00168 CHARACTER UPLO 00169 INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N 00170 * .. 00171 * .. Array Arguments .. 00172 DOUBLE PRECISION D( * ), E( * ), RESULT( 2 ), RWORK( * ) 00173 COMPLEX*16 A( LDA, * ), TAU( * ), U( LDU, * ), 00174 $ V( LDV, * ), WORK( * ) 00175 * .. 00176 * 00177 * ===================================================================== 00178 * 00179 * .. Parameters .. 00180 DOUBLE PRECISION ZERO, ONE 00181 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 00182 COMPLEX*16 CZERO, CONE 00183 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), 00184 $ CONE = ( 1.0D0, 0.0D0 ) ) 00185 * .. 00186 * .. Local Scalars .. 00187 INTEGER J, JJ, JJ1, JJ2, NN, NNP1 00188 DOUBLE PRECISION ANORM, ULP, UNFL, WNORM 00189 * .. 00190 * .. External Functions .. 00191 DOUBLE PRECISION DLAMCH, ZLANHE 00192 EXTERNAL DLAMCH, ZLANHE 00193 * .. 00194 * .. External Subroutines .. 00195 EXTERNAL ZGEMM, ZHEMM, ZUNT01 00196 * .. 00197 * .. Intrinsic Functions .. 00198 INTRINSIC DBLE, MAX, MIN 00199 * .. 00200 * .. Executable Statements .. 00201 * 00202 RESULT( 1 ) = ZERO 00203 RESULT( 2 ) = ZERO 00204 IF( N.LE.0 .OR. M.LE.0 ) 00205 $ RETURN 00206 * 00207 UNFL = DLAMCH( 'Safe minimum' ) 00208 ULP = DLAMCH( 'Precision' ) 00209 * 00210 * Do Test 1 00211 * 00212 * Norm of A: 00213 * 00214 ANORM = MAX( ZLANHE( '1', UPLO, N, A, LDA, RWORK ), UNFL ) 00215 * 00216 * Compute error matrix: 00217 * 00218 * ITYPE=1: error = U' A U - S 00219 * 00220 CALL ZHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK, 00221 $ N ) 00222 NN = N*N 00223 NNP1 = NN + 1 00224 CALL ZGEMM( 'C', 'N', M, M, N, CONE, U, LDU, WORK, N, CZERO, 00225 $ WORK( NNP1 ), N ) 00226 DO 10 J = 1, M 00227 JJ = NN + ( J-1 )*N + J 00228 WORK( JJ ) = WORK( JJ ) - D( J ) 00229 10 CONTINUE 00230 IF( KBAND.EQ.1 .AND. N.GT.1 ) THEN 00231 DO 20 J = 2, M 00232 JJ1 = NN + ( J-1 )*N + J - 1 00233 JJ2 = NN + ( J-2 )*N + J 00234 WORK( JJ1 ) = WORK( JJ1 ) - E( J-1 ) 00235 WORK( JJ2 ) = WORK( JJ2 ) - E( J-1 ) 00236 20 CONTINUE 00237 END IF 00238 WNORM = ZLANHE( '1', UPLO, M, WORK( NNP1 ), N, RWORK ) 00239 * 00240 IF( ANORM.GT.WNORM ) THEN 00241 RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP ) 00242 ELSE 00243 IF( ANORM.LT.ONE ) THEN 00244 RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP ) 00245 ELSE 00246 RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( M ) ) / ( M*ULP ) 00247 END IF 00248 END IF 00249 * 00250 * Do Test 2 00251 * 00252 * Compute U'U - I 00253 * 00254 IF( ITYPE.EQ.1 ) 00255 $ CALL ZUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK, 00256 $ RESULT( 2 ) ) 00257 * 00258 RETURN 00259 * 00260 * End of ZHET22 00261 * 00262 END