LAPACK 3.3.1 Linear Algebra PACKage

# sget54.f

Go to the documentation of this file.
```00001       SUBROUTINE SGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
00002      \$                   LDV, WORK, RESULT )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            LDA, LDB, LDS, LDT, LDU, LDV, N
00010       REAL               RESULT
00011 *     ..
00012 *     .. Array Arguments ..
00013       REAL               A( LDA, * ), B( LDB, * ), S( LDS, * ),
00014      \$                   T( LDT, * ), U( LDU, * ), V( LDV, * ),
00015      \$                   WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  SGET54 checks a generalized decomposition of the form
00022 *
00023 *           A = U*S*V'  and B = U*T* V'
00024 *
00025 *  where ' means transpose and U and V are orthogonal.
00026 *
00027 *  Specifically,
00028 *
00029 *   RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *  N       (input) INTEGER
00035 *          The size of the matrix.  If it is zero, SGET54 does nothing.
00036 *          It must be at least zero.
00037 *
00038 *  A       (input) REAL array, dimension (LDA, N)
00039 *          The original (unfactored) matrix A.
00040 *
00041 *  LDA     (input) INTEGER
00042 *          The leading dimension of A.  It must be at least 1
00043 *          and at least N.
00044 *
00045 *  B       (input) REAL array, dimension (LDB, N)
00046 *          The original (unfactored) matrix B.
00047 *
00048 *  LDB     (input) INTEGER
00049 *          The leading dimension of B.  It must be at least 1
00050 *          and at least N.
00051 *
00052 *  S       (input) REAL array, dimension (LDS, N)
00053 *          The factored matrix S.
00054 *
00055 *  LDS     (input) INTEGER
00056 *          The leading dimension of S.  It must be at least 1
00057 *          and at least N.
00058 *
00059 *  T       (input) REAL array, dimension (LDT, N)
00060 *          The factored matrix T.
00061 *
00062 *  LDT     (input) INTEGER
00063 *          The leading dimension of T.  It must be at least 1
00064 *          and at least N.
00065 *
00066 *  U       (input) REAL array, dimension (LDU, N)
00067 *          The orthogonal matrix on the left-hand side in the
00068 *          decomposition.
00069 *
00070 *  LDU     (input) INTEGER
00071 *          The leading dimension of U.  LDU must be at least N and
00072 *          at least 1.
00073 *
00074 *  V       (input) REAL array, dimension (LDV, N)
00075 *          The orthogonal matrix on the left-hand side in the
00076 *          decomposition.
00077 *
00078 *  LDV     (input) INTEGER
00079 *          The leading dimension of V.  LDV must be at least N and
00080 *          at least 1.
00081 *
00082 *  WORK    (workspace) REAL array, dimension (3*N**2)
00083 *
00084 *  RESULT  (output) REAL
00085 *          The value RESULT, It is currently limited to 1/ulp, to
00086 *          avoid overflow. Errors are flagged by RESULT=10/ulp.
00087 *
00088 *  =====================================================================
00089 *
00090 *     .. Parameters ..
00091       REAL               ZERO, ONE
00092       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00093 *     ..
00094 *     .. Local Scalars ..
00095       REAL               ABNORM, ULP, UNFL, WNORM
00096 *     ..
00097 *     .. Local Arrays ..
00098       REAL               DUM( 1 )
00099 *     ..
00100 *     .. External Functions ..
00101       REAL               SLAMCH, SLANGE
00102       EXTERNAL           SLAMCH, SLANGE
00103 *     ..
00104 *     .. External Subroutines ..
00105       EXTERNAL           SGEMM, SLACPY
00106 *     ..
00107 *     .. Intrinsic Functions ..
00108       INTRINSIC          MAX, MIN, REAL
00109 *     ..
00110 *     .. Executable Statements ..
00111 *
00112       RESULT = ZERO
00113       IF( N.LE.0 )
00114      \$   RETURN
00115 *
00116 *     Constants
00117 *
00118       UNFL = SLAMCH( 'Safe minimum' )
00119       ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
00120 *
00121 *     compute the norm of (A,B)
00122 *
00123       CALL SLACPY( 'Full', N, N, A, LDA, WORK, N )
00124       CALL SLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N )
00125       ABNORM = MAX( SLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL )
00126 *
00127 *     Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
00128 *
00129       CALL SLACPY( ' ', N, N, A, LDA, WORK, N )
00130       CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, S, LDS, ZERO,
00131      \$            WORK( N*N+1 ), N )
00132 *
00133       CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( N*N+1 ), N, V, LDV,
00134      \$            ONE, WORK, N )
00135 *
00136 *     Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
00137 *
00138       CALL SLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N )
00139       CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, T, LDT, ZERO,
00140      \$            WORK( 2*N*N+1 ), N )
00141 *
00142       CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( 2*N*N+1 ), N, V, LDV,
00143      \$            ONE, WORK( N*N+1 ), N )
00144 *
00145 *     Compute norm(W)/ ( ulp*norm((A,B)) )
00146 *
00147       WNORM = SLANGE( '1', N, 2*N, WORK, N, DUM )
00148 *
00149       IF( ABNORM.GT.WNORM ) THEN
00150          RESULT = ( WNORM / ABNORM ) / ( 2*N*ULP )
00151       ELSE
00152          IF( ABNORM.LT.ONE ) THEN
00153             RESULT = ( MIN( WNORM, 2*N*ABNORM ) / ABNORM ) / ( 2*N*ULP )
00154          ELSE
00155             RESULT = MIN( WNORM / ABNORM, REAL( 2*N ) ) / ( 2*N*ULP )
00156          END IF
00157       END IF
00158 *
00159       RETURN
00160 *
00161 *     End of SGET54
00162 *
00163       END
```