|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 |
SUBROUTINE ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
$ RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER KBAND, LDU, N * .. * .. Array Arguments .. DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ), $ SD( * ), SE( * ) COMPLEX*16 U( LDU, * ), WORK( * ) * .. * * Purpose * ======= * * ZSTT21 checks a decomposition of the form * * A = U S U* * * where * means conjugate transpose, A is real symmetric tridiagonal, * U is unitary, and S is real and diagonal (if KBAND=0) or symmetric * tridiagonal (if KBAND=1). Two tests are performed: * * RESULT(1) = | A - U S U* | / ( |A| n ulp ) * * RESULT(2) = | I - UU* | / ( n ulp ) * * Arguments * ========= * * N (input) INTEGER * The size of the matrix. If it is zero, ZSTT21 does nothing. * It must be at least zero. * * KBAND (input) INTEGER * The bandwidth of the matrix S. It may only be zero or one. * If zero, then S is diagonal, and SE is not referenced. If * one, then S is symmetric tri-diagonal. * * AD (input) DOUBLE PRECISION array, dimension (N) * The diagonal of the original (unfactored) matrix A. A is * assumed to be real symmetric tridiagonal. * * AE (input) DOUBLE PRECISION array, dimension (N-1) * The off-diagonal of the original (unfactored) matrix A. A * is assumed to be symmetric tridiagonal. AE(1) is the (1,2) * and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc. * * SD (input) DOUBLE PRECISION array, dimension (N) * The diagonal of the real (symmetric tri-) diagonal matrix S. * * SE (input) DOUBLE PRECISION array, dimension (N-1) * The off-diagonal of the (symmetric tri-) diagonal matrix S. * Not referenced if KBSND=0. If KBAND=1, then AE(1) is the * (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) * element, etc. * * U (input) COMPLEX*16 array, dimension (LDU, N) * The unitary matrix in the decomposition. * * LDU (input) INTEGER * The leading dimension of U. LDU must be at least N. * * WORK (workspace) COMPLEX*16 array, dimension (N**2) * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESULT (output) 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. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE EXTERNAL DLAMCH, ZLANGE, ZLANHE * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZHER, ZHER2, ZLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN * .. * .. Executable Statements .. * * 1) Constants * RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO IF( N.LE.0 ) $ RETURN * UNFL = DLAMCH( 'Safe minimum' ) ULP = DLAMCH( 'Precision' ) * * Do Test 1 * * Copy A & Compute its 1-Norm: * CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N ) * ANORM = ZERO TEMP1 = ZERO * DO 10 J = 1, N - 1 WORK( ( N+1 )*( J-1 )+1 ) = AD( J ) WORK( ( N+1 )*( J-1 )+2 ) = AE( J ) TEMP2 = ABS( AE( J ) ) ANORM = MAX( ANORM, ABS( AD( J ) )+TEMP1+TEMP2 ) TEMP1 = TEMP2 10 CONTINUE * WORK( N**2 ) = AD( N ) ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL ) * * Norm of A - USU* * DO 20 J = 1, N CALL ZHER( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N ) 20 CONTINUE * IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN DO 30 J = 1, N - 1 CALL ZHER2( 'L', N, -DCMPLX( SE( J ) ), U( 1, J ), 1, $ U( 1, J+1 ), 1, WORK, N ) 30 CONTINUE END IF * WNORM = ZLANHE( '1', 'L', N, WORK, N, RWORK ) * IF( ANORM.GT.WNORM ) THEN RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP ) ELSE IF( ANORM.LT.ONE ) THEN RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP ) ELSE RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP ) END IF END IF * * Do Test 2 * * Compute UU* - I * CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK, $ N ) * DO 40 J = 1, N WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE 40 CONTINUE * RESULT( 2 ) = MIN( DBLE( N ), ZLANGE( '1', N, N, WORK, N, $ RWORK ) ) / ( N*ULP ) * RETURN * * End of ZSTT21 * END |