root / src / lapack / double / dlanst.f @ 1
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| 1 | 1 | equemene | DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK auxiliary routine (version 3.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * November 2006 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | CHARACTER NORM |
| 10 | 1 | equemene | INTEGER N |
| 11 | 1 | equemene | * .. |
| 12 | 1 | equemene | * .. Array Arguments .. |
| 13 | 1 | equemene | DOUBLE PRECISION D( * ), E( * ) |
| 14 | 1 | equemene | * .. |
| 15 | 1 | equemene | * |
| 16 | 1 | equemene | * Purpose |
| 17 | 1 | equemene | * ======= |
| 18 | 1 | equemene | * |
| 19 | 1 | equemene | * DLANST returns the value of the one norm, or the Frobenius norm, or |
| 20 | 1 | equemene | * the infinity norm, or the element of largest absolute value of a |
| 21 | 1 | equemene | * real symmetric tridiagonal matrix A. |
| 22 | 1 | equemene | * |
| 23 | 1 | equemene | * Description |
| 24 | 1 | equemene | * =========== |
| 25 | 1 | equemene | * |
| 26 | 1 | equemene | * DLANST returns the value |
| 27 | 1 | equemene | * |
| 28 | 1 | equemene | * DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
| 29 | 1 | equemene | * ( |
| 30 | 1 | equemene | * ( norm1(A), NORM = '1', 'O' or 'o' |
| 31 | 1 | equemene | * ( |
| 32 | 1 | equemene | * ( normI(A), NORM = 'I' or 'i' |
| 33 | 1 | equemene | * ( |
| 34 | 1 | equemene | * ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
| 35 | 1 | equemene | * |
| 36 | 1 | equemene | * where norm1 denotes the one norm of a matrix (maximum column sum), |
| 37 | 1 | equemene | * normI denotes the infinity norm of a matrix (maximum row sum) and |
| 38 | 1 | equemene | * normF denotes the Frobenius norm of a matrix (square root of sum of |
| 39 | 1 | equemene | * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. |
| 40 | 1 | equemene | * |
| 41 | 1 | equemene | * Arguments |
| 42 | 1 | equemene | * ========= |
| 43 | 1 | equemene | * |
| 44 | 1 | equemene | * NORM (input) CHARACTER*1 |
| 45 | 1 | equemene | * Specifies the value to be returned in DLANST as described |
| 46 | 1 | equemene | * above. |
| 47 | 1 | equemene | * |
| 48 | 1 | equemene | * N (input) INTEGER |
| 49 | 1 | equemene | * The order of the matrix A. N >= 0. When N = 0, DLANST is |
| 50 | 1 | equemene | * set to zero. |
| 51 | 1 | equemene | * |
| 52 | 1 | equemene | * D (input) DOUBLE PRECISION array, dimension (N) |
| 53 | 1 | equemene | * The diagonal elements of A. |
| 54 | 1 | equemene | * |
| 55 | 1 | equemene | * E (input) DOUBLE PRECISION array, dimension (N-1) |
| 56 | 1 | equemene | * The (n-1) sub-diagonal or super-diagonal elements of A. |
| 57 | 1 | equemene | * |
| 58 | 1 | equemene | * ===================================================================== |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * .. Parameters .. |
| 61 | 1 | equemene | DOUBLE PRECISION ONE, ZERO |
| 62 | 1 | equemene | PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
| 63 | 1 | equemene | * .. |
| 64 | 1 | equemene | * .. Local Scalars .. |
| 65 | 1 | equemene | INTEGER I |
| 66 | 1 | equemene | DOUBLE PRECISION ANORM, SCALE, SUM |
| 67 | 1 | equemene | * .. |
| 68 | 1 | equemene | * .. External Functions .. |
| 69 | 1 | equemene | LOGICAL LSAME |
| 70 | 1 | equemene | EXTERNAL LSAME |
| 71 | 1 | equemene | * .. |
| 72 | 1 | equemene | * .. External Subroutines .. |
| 73 | 1 | equemene | EXTERNAL DLASSQ |
| 74 | 1 | equemene | * .. |
| 75 | 1 | equemene | * .. Intrinsic Functions .. |
| 76 | 1 | equemene | INTRINSIC ABS, MAX, SQRT |
| 77 | 1 | equemene | * .. |
| 78 | 1 | equemene | * .. Executable Statements .. |
| 79 | 1 | equemene | * |
| 80 | 1 | equemene | IF( N.LE.0 ) THEN |
| 81 | 1 | equemene | ANORM = ZERO |
| 82 | 1 | equemene | ELSE IF( LSAME( NORM, 'M' ) ) THEN |
| 83 | 1 | equemene | * |
| 84 | 1 | equemene | * Find max(abs(A(i,j))). |
| 85 | 1 | equemene | * |
| 86 | 1 | equemene | ANORM = ABS( D( N ) ) |
| 87 | 1 | equemene | DO 10 I = 1, N - 1 |
| 88 | 1 | equemene | ANORM = MAX( ANORM, ABS( D( I ) ) ) |
| 89 | 1 | equemene | ANORM = MAX( ANORM, ABS( E( I ) ) ) |
| 90 | 1 | equemene | 10 CONTINUE |
| 91 | 1 | equemene | ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. |
| 92 | 1 | equemene | $ LSAME( NORM, 'I' ) ) THEN |
| 93 | 1 | equemene | * |
| 94 | 1 | equemene | * Find norm1(A). |
| 95 | 1 | equemene | * |
| 96 | 1 | equemene | IF( N.EQ.1 ) THEN |
| 97 | 1 | equemene | ANORM = ABS( D( 1 ) ) |
| 98 | 1 | equemene | ELSE |
| 99 | 1 | equemene | ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), |
| 100 | 1 | equemene | $ ABS( E( N-1 ) )+ABS( D( N ) ) ) |
| 101 | 1 | equemene | DO 20 I = 2, N - 1 |
| 102 | 1 | equemene | ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+ |
| 103 | 1 | equemene | $ ABS( E( I-1 ) ) ) |
| 104 | 1 | equemene | 20 CONTINUE |
| 105 | 1 | equemene | END IF |
| 106 | 1 | equemene | ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
| 107 | 1 | equemene | * |
| 108 | 1 | equemene | * Find normF(A). |
| 109 | 1 | equemene | * |
| 110 | 1 | equemene | SCALE = ZERO |
| 111 | 1 | equemene | SUM = ONE |
| 112 | 1 | equemene | IF( N.GT.1 ) THEN |
| 113 | 1 | equemene | CALL DLASSQ( N-1, E, 1, SCALE, SUM ) |
| 114 | 1 | equemene | SUM = 2*SUM |
| 115 | 1 | equemene | END IF |
| 116 | 1 | equemene | CALL DLASSQ( N, D, 1, SCALE, SUM ) |
| 117 | 1 | equemene | ANORM = SCALE*SQRT( SUM ) |
| 118 | 1 | equemene | END IF |
| 119 | 1 | equemene | * |
| 120 | 1 | equemene | DLANST = ANORM |
| 121 | 1 | equemene | RETURN |
| 122 | 1 | equemene | * |
| 123 | 1 | equemene | * End of DLANST |
| 124 | 1 | equemene | * |
| 125 | 1 | equemene | END |