LAPACK 3.3.1 Linear Algebra PACKage

# spbt01.f

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```00001       SUBROUTINE SPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
00002      \$                   RESID )
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       CHARACTER          UPLO
00010       INTEGER            KD, LDA, LDAFAC, N
00011       REAL               RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  SPBT01 reconstructs a symmetric positive definite band matrix A from
00021 *  its L*L' or U'*U factorization and computes the residual
00022 *     norm( L*L' - A ) / ( N * norm(A) * EPS ) or
00023 *     norm( U'*U - A ) / ( N * norm(A) * EPS ),
00024 *  where EPS is the machine epsilon, L' is the conjugate transpose of
00025 *  L, and U' is the conjugate transpose of U.
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  UPLO    (input) CHARACTER*1
00031 *          Specifies whether the upper or lower triangular part of the
00032 *          symmetric matrix A is stored:
00033 *          = 'U':  Upper triangular
00034 *          = 'L':  Lower triangular
00035 *
00036 *  N       (input) INTEGER
00037 *          The number of rows and columns of the matrix A.  N >= 0.
00038 *
00039 *  KD      (input) INTEGER
00040 *          The number of super-diagonals of the matrix A if UPLO = 'U',
00041 *          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
00042 *
00043 *  A       (input) REAL array, dimension (LDA,N)
00044 *          The original symmetric band matrix A.  If UPLO = 'U', the
00045 *          upper triangular part of A is stored as a band matrix; if
00046 *          UPLO = 'L', the lower triangular part of A is stored.  The
00047 *          columns of the appropriate triangle are stored in the columns
00048 *          of A and the diagonals of the triangle are stored in the rows
00049 *          of A.  See SPBTRF for further details.
00050 *
00051 *  LDA     (input) INTEGER.
00052 *          The leading dimension of the array A.  LDA >= max(1,KD+1).
00053 *
00054 *  AFAC    (input) REAL array, dimension (LDAFAC,N)
00055 *          The factored form of the matrix A.  AFAC contains the factor
00056 *          L or U from the L*L' or U'*U factorization in band storage
00057 *          format, as computed by SPBTRF.
00058 *
00059 *  LDAFAC  (input) INTEGER
00060 *          The leading dimension of the array AFAC.
00061 *          LDAFAC >= max(1,KD+1).
00062 *
00063 *  RWORK   (workspace) REAL array, dimension (N)
00064 *
00065 *  RESID   (output) REAL
00066 *          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
00067 *          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
00068 *
00069 *  =====================================================================
00070 *
00071 *
00072 *     .. Parameters ..
00073       REAL               ZERO, ONE
00074       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00075 *     ..
00076 *     .. Local Scalars ..
00077       INTEGER            I, J, K, KC, KLEN, ML, MU
00078       REAL               ANORM, EPS, T
00079 *     ..
00080 *     .. External Functions ..
00081       LOGICAL            LSAME
00082       REAL               SDOT, SLAMCH, SLANSB
00083       EXTERNAL           LSAME, SDOT, SLAMCH, SLANSB
00084 *     ..
00085 *     .. External Subroutines ..
00086       EXTERNAL           SSCAL, SSYR, STRMV
00087 *     ..
00088 *     .. Intrinsic Functions ..
00089       INTRINSIC          MAX, MIN, REAL
00090 *     ..
00091 *     .. Executable Statements ..
00092 *
00093 *     Quick exit if N = 0.
00094 *
00095       IF( N.LE.0 ) THEN
00096          RESID = ZERO
00097          RETURN
00098       END IF
00099 *
00100 *     Exit with RESID = 1/EPS if ANORM = 0.
00101 *
00102       EPS = SLAMCH( 'Epsilon' )
00103       ANORM = SLANSB( '1', UPLO, N, KD, A, LDA, RWORK )
00104       IF( ANORM.LE.ZERO ) THEN
00105          RESID = ONE / EPS
00106          RETURN
00107       END IF
00108 *
00109 *     Compute the product U'*U, overwriting U.
00110 *
00111       IF( LSAME( UPLO, 'U' ) ) THEN
00112          DO 10 K = N, 1, -1
00113             KC = MAX( 1, KD+2-K )
00114             KLEN = KD + 1 - KC
00115 *
00116 *           Compute the (K,K) element of the result.
00117 *
00118             T = SDOT( KLEN+1, AFAC( KC, K ), 1, AFAC( KC, K ), 1 )
00119             AFAC( KD+1, K ) = T
00120 *
00121 *           Compute the rest of column K.
00122 *
00123             IF( KLEN.GT.0 )
00124      \$         CALL STRMV( 'Upper', 'Transpose', 'Non-unit', KLEN,
00125      \$                     AFAC( KD+1, K-KLEN ), LDAFAC-1,
00126      \$                     AFAC( KC, K ), 1 )
00127 *
00128    10    CONTINUE
00129 *
00130 *     UPLO = 'L':  Compute the product L*L', overwriting L.
00131 *
00132       ELSE
00133          DO 20 K = N, 1, -1
00134             KLEN = MIN( KD, N-K )
00135 *
00136 *           Add a multiple of column K of the factor L to each of
00137 *           columns K+1 through N.
00138 *
00139             IF( KLEN.GT.0 )
00140      \$         CALL SSYR( 'Lower', KLEN, ONE, AFAC( 2, K ), 1,
00141      \$                    AFAC( 1, K+1 ), LDAFAC-1 )
00142 *
00143 *           Scale column K by the diagonal element.
00144 *
00145             T = AFAC( 1, K )
00146             CALL SSCAL( KLEN+1, T, AFAC( 1, K ), 1 )
00147 *
00148    20    CONTINUE
00149       END IF
00150 *
00151 *     Compute the difference  L*L' - A  or  U'*U - A.
00152 *
00153       IF( LSAME( UPLO, 'U' ) ) THEN
00154          DO 40 J = 1, N
00155             MU = MAX( 1, KD+2-J )
00156             DO 30 I = MU, KD + 1
00157                AFAC( I, J ) = AFAC( I, J ) - A( I, J )
00158    30       CONTINUE
00159    40    CONTINUE
00160       ELSE
00161          DO 60 J = 1, N
00162             ML = MIN( KD+1, N-J+1 )
00163             DO 50 I = 1, ML
00164                AFAC( I, J ) = AFAC( I, J ) - A( I, J )
00165    50       CONTINUE
00166    60    CONTINUE
00167       END IF
00168 *
00169 *     Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
00170 *
00171       RESID = SLANSB( 'I', UPLO, N, KD, AFAC, LDAFAC, RWORK )
00172 *
00173       RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
00174 *
00175       RETURN
00176 *
00177 *     End of SPBT01
00178 *
00179       END
```