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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID ) 00002 * 00003 * -- LAPACK test routine (version 3.1) -- 00004 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00005 * November 2006 00006 * 00007 * .. Scalar Arguments .. 00008 INTEGER LDB, LDC, LDU, M, N 00009 REAL RESID 00010 * .. 00011 * .. Array Arguments .. 00012 REAL B( LDB, * ), C( LDC, * ), U( LDU, * ), 00013 $ WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SBDT02 tests the change of basis C = U' * B by computing the residual 00020 * 00021 * RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ), 00022 * 00023 * where B and C are M by N matrices, U is an M by M orthogonal matrix, 00024 * and EPS is the machine precision. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * M (input) INTEGER 00030 * The number of rows of the matrices B and C and the order of 00031 * the matrix Q. 00032 * 00033 * N (input) INTEGER 00034 * The number of columns of the matrices B and C. 00035 * 00036 * B (input) REAL array, dimension (LDB,N) 00037 * The m by n matrix B. 00038 * 00039 * LDB (input) INTEGER 00040 * The leading dimension of the array B. LDB >= max(1,M). 00041 * 00042 * C (input) REAL array, dimension (LDC,N) 00043 * The m by n matrix C, assumed to contain U' * B. 00044 * 00045 * LDC (input) INTEGER 00046 * The leading dimension of the array C. LDC >= max(1,M). 00047 * 00048 * U (input) REAL array, dimension (LDU,M) 00049 * The m by m orthogonal matrix U. 00050 * 00051 * LDU (input) INTEGER 00052 * The leading dimension of the array U. LDU >= max(1,M). 00053 * 00054 * WORK (workspace) REAL array, dimension (M) 00055 * 00056 * RESID (output) REAL 00057 * RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ), 00058 * 00059 * ====================================================================== 00060 * 00061 * .. Parameters .. 00062 REAL ZERO, ONE 00063 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00064 * .. 00065 * .. Local Scalars .. 00066 INTEGER J 00067 REAL BNORM, EPS, REALMN 00068 * .. 00069 * .. External Functions .. 00070 REAL SASUM, SLAMCH, SLANGE 00071 EXTERNAL SASUM, SLAMCH, SLANGE 00072 * .. 00073 * .. External Subroutines .. 00074 EXTERNAL SCOPY, SGEMV 00075 * .. 00076 * .. Intrinsic Functions .. 00077 INTRINSIC MAX, MIN, REAL 00078 * .. 00079 * .. Executable Statements .. 00080 * 00081 * Quick return if possible 00082 * 00083 RESID = ZERO 00084 IF( M.LE.0 .OR. N.LE.0 ) 00085 $ RETURN 00086 REALMN = REAL( MAX( M, N ) ) 00087 EPS = SLAMCH( 'Precision' ) 00088 * 00089 * Compute norm( B - U * C ) 00090 * 00091 DO 10 J = 1, N 00092 CALL SCOPY( M, B( 1, J ), 1, WORK, 1 ) 00093 CALL SGEMV( 'No transpose', M, M, -ONE, U, LDU, C( 1, J ), 1, 00094 $ ONE, WORK, 1 ) 00095 RESID = MAX( RESID, SASUM( M, WORK, 1 ) ) 00096 10 CONTINUE 00097 * 00098 * Compute norm of B. 00099 * 00100 BNORM = SLANGE( '1', M, N, B, LDB, WORK ) 00101 * 00102 IF( BNORM.LE.ZERO ) THEN 00103 IF( RESID.NE.ZERO ) 00104 $ RESID = ONE / EPS 00105 ELSE 00106 IF( BNORM.GE.RESID ) THEN 00107 RESID = ( RESID / BNORM ) / ( REALMN*EPS ) 00108 ELSE 00109 IF( BNORM.LT.ONE ) THEN 00110 RESID = ( MIN( RESID, REALMN*BNORM ) / BNORM ) / 00111 $ ( REALMN*EPS ) 00112 ELSE 00113 RESID = MIN( RESID / BNORM, REALMN ) / ( REALMN*EPS ) 00114 END IF 00115 END IF 00116 END IF 00117 RETURN 00118 * 00119 * End of SBDT02 00120 * 00121 END
1.7.3 
