|
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 STPT01( 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 REAL RCOND, RESID * .. * .. Array Arguments .. REAL AINVP( * ), AP( * ), WORK( * ) * .. * * Purpose * ======= * * STPT01 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) REAL 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) REAL 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) REAL * The reciprocal condition number of A, computed as * 1/(norm(A) * norm(AINV)). * * WORK (workspace) REAL array, dimension (N) * * RESID (output) REAL * norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL UNITD INTEGER J, JC REAL AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANTP EXTERNAL LSAME, SLAMCH, SLANTP * .. * .. External Subroutines .. EXTERNAL STPMV * .. * .. Intrinsic Functions .. INTRINSIC REAL * .. * .. 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 = SLAMCH( 'Epsilon' ) ANORM = SLANTP( '1', UPLO, DIAG, N, AP, WORK ) AINVNM = SLANTP( '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 STPMV( '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 STPMV( '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 = SLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK ) * RESID = ( ( RESID*RCOND ) / REAL( N ) ) / EPS * RETURN * * End of STPT01 * END |