|
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 |
SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
* * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * ) * .. * * Purpose * ======= * * DTPT01 computes the residual for a triangular matrix A times its * inverse when A is stored in packed format: * RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the matrix A is upper or lower triangular. * = 'U': Upper triangular * = 'L': Lower triangular * * DIAG (input) CHARACTER*1 * Specifies whether or not the matrix A is unit triangular. * = 'N': Non-unit triangular * = 'U': Unit triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) * The original upper or lower triangular matrix A, packed * columnwise in a linear array. The j-th column of A is stored * in the array AP as follows: * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; * if UPLO = 'L', * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. * * AINVP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) * On entry, the (triangular) inverse of the matrix A, packed * columnwise in a linear array as in AP. * On exit, the contents of AINVP are destroyed. * * RCOND (output) DOUBLE PRECISION * The reciprocal condition number of A, computed as * 1/(norm(A) * norm(AINV)). * * WORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UNITD INTEGER J, JC DOUBLE PRECISION AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANTP EXTERNAL LSAME, DLAMCH, DLANTP * .. * .. External Subroutines .. EXTERNAL DTPMV * .. * .. 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 = DLANTP( '1', UPLO, DIAG, N, AP, WORK ) AINVNM = DLANTP( '1', UPLO, DIAG, N, AINVP, WORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Compute A * AINV, overwriting AINV. * UNITD = LSAME( DIAG, 'U' ) IF( LSAME( UPLO, 'U' ) ) THEN JC = 1 DO 10 J = 1, N IF( UNITD ) $ AINVP( JC+J-1 ) = ONE * * Form the j-th column of A*AINV * CALL DTPMV( 'Upper', 'No transpose', DIAG, J, AP, $ AINVP( JC ), 1 ) * * Subtract 1 from the diagonal * AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE JC = JC + J 10 CONTINUE ELSE JC = 1 DO 20 J = 1, N IF( UNITD ) $ AINVP( JC ) = ONE * * Form the j-th column of A*AINV * CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ), $ AINVP( JC ), 1 ) * * Subtract 1 from the diagonal * AINVP( JC ) = AINVP( JC ) - ONE JC = JC + N - J + 1 20 CONTINUE END IF * * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) * RESID = DLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK ) * RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS * RETURN * * End of DTPT01 * END |