LAPACK 3.3.1 Linear Algebra PACKage

# slanst.f

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```00001       REAL             FUNCTION SLANST( NORM, N, D, E )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          NORM
00010       INTEGER            N
00011 *     ..
00012 *     .. Array Arguments ..
00013       REAL               D( * ), E( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  SLANST  returns the value of the one norm,  or the Frobenius norm, or
00020 *  the  infinity norm,  or the  element of  largest absolute value  of a
00021 *  real symmetric tridiagonal matrix A.
00022 *
00023 *  Description
00024 *  ===========
00025 *
00026 *  SLANST returns the value
00027 *
00028 *     SLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00029 *              (
00030 *              ( norm1(A),         NORM = '1', 'O' or 'o'
00031 *              (
00032 *              ( normI(A),         NORM = 'I' or 'i'
00033 *              (
00034 *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00035 *
00036 *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
00037 *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00038 *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
00039 *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00040 *
00041 *  Arguments
00042 *  =========
00043 *
00044 *  NORM    (input) CHARACTER*1
00045 *          Specifies the value to be returned in SLANST as described
00046 *          above.
00047 *
00048 *  N       (input) INTEGER
00049 *          The order of the matrix A.  N >= 0.  When N = 0, SLANST is
00050 *          set to zero.
00051 *
00052 *  D       (input) REAL array, dimension (N)
00053 *          The diagonal elements of A.
00054 *
00055 *  E       (input) REAL array, dimension (N-1)
00056 *          The (n-1) sub-diagonal or super-diagonal elements of A.
00057 *
00058 *  =====================================================================
00059 *
00060 *     .. Parameters ..
00061       REAL               ONE, ZERO
00062       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00063 *     ..
00064 *     .. Local Scalars ..
00065       INTEGER            I
00066       REAL               ANORM, SCALE, SUM
00067 *     ..
00068 *     .. External Functions ..
00069       LOGICAL            LSAME
00070       EXTERNAL           LSAME
00071 *     ..
00072 *     .. External Subroutines ..
00073       EXTERNAL           SLASSQ
00074 *     ..
00075 *     .. Intrinsic Functions ..
00076       INTRINSIC          ABS, MAX, SQRT
00077 *     ..
00078 *     .. Executable Statements ..
00079 *
00080       IF( N.LE.0 ) THEN
00081          ANORM = ZERO
00082       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00083 *
00084 *        Find max(abs(A(i,j))).
00085 *
00086          ANORM = ABS( D( N ) )
00087          DO 10 I = 1, N - 1
00088             ANORM = MAX( ANORM, ABS( D( I ) ) )
00089             ANORM = MAX( ANORM, ABS( E( I ) ) )
00090    10    CONTINUE
00091       ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
00092      \$         LSAME( NORM, 'I' ) ) THEN
00093 *
00094 *        Find norm1(A).
00095 *
00096          IF( N.EQ.1 ) THEN
00097             ANORM = ABS( D( 1 ) )
00098          ELSE
00099             ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
00100      \$              ABS( E( N-1 ) )+ABS( D( N ) ) )
00101             DO 20 I = 2, N - 1
00102                ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
00103      \$                 ABS( E( I-1 ) ) )
00104    20       CONTINUE
00105          END IF
00106       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00107 *
00108 *        Find normF(A).
00109 *
00110          SCALE = ZERO
00111          SUM = ONE
00112          IF( N.GT.1 ) THEN
00113             CALL SLASSQ( N-1, E, 1, SCALE, SUM )
00114             SUM = 2*SUM
00115          END IF
00116          CALL SLASSQ( N, D, 1, SCALE, SUM )
00117          ANORM = SCALE*SQRT( SUM )
00118       END IF
00119 *
00120       SLANST = ANORM
00121       RETURN
00122 *
00123 *     End of SLANST
00124 *
00125       END
```