Annotation of rpl/lapack/lapack/dlanhs.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER NORM
! 10: INTEGER LDA, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION A( LDA, * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DLANHS returns the value of the one norm, or the Frobenius norm, or
! 20: * the infinity norm, or the element of largest absolute value of a
! 21: * Hessenberg matrix A.
! 22: *
! 23: * Description
! 24: * ===========
! 25: *
! 26: * DLANHS returns the value
! 27: *
! 28: * DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 29: * (
! 30: * ( norm1(A), NORM = '1', 'O' or 'o'
! 31: * (
! 32: * ( normI(A), NORM = 'I' or 'i'
! 33: * (
! 34: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 35: *
! 36: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 37: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 38: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 39: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 40: *
! 41: * Arguments
! 42: * =========
! 43: *
! 44: * NORM (input) CHARACTER*1
! 45: * Specifies the value to be returned in DLANHS as described
! 46: * above.
! 47: *
! 48: * N (input) INTEGER
! 49: * The order of the matrix A. N >= 0. When N = 0, DLANHS is
! 50: * set to zero.
! 51: *
! 52: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 53: * The n by n upper Hessenberg matrix A; the part of A below the
! 54: * first sub-diagonal is not referenced.
! 55: *
! 56: * LDA (input) INTEGER
! 57: * The leading dimension of the array A. LDA >= max(N,1).
! 58: *
! 59: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 60: * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
! 61: * referenced.
! 62: *
! 63: * =====================================================================
! 64: *
! 65: * .. Parameters ..
! 66: DOUBLE PRECISION ONE, ZERO
! 67: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 68: * ..
! 69: * .. Local Scalars ..
! 70: INTEGER I, J
! 71: DOUBLE PRECISION SCALE, SUM, VALUE
! 72: * ..
! 73: * .. External Subroutines ..
! 74: EXTERNAL DLASSQ
! 75: * ..
! 76: * .. External Functions ..
! 77: LOGICAL LSAME
! 78: EXTERNAL LSAME
! 79: * ..
! 80: * .. Intrinsic Functions ..
! 81: INTRINSIC ABS, MAX, MIN, SQRT
! 82: * ..
! 83: * .. Executable Statements ..
! 84: *
! 85: IF( N.EQ.0 ) THEN
! 86: VALUE = ZERO
! 87: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 88: *
! 89: * Find max(abs(A(i,j))).
! 90: *
! 91: VALUE = ZERO
! 92: DO 20 J = 1, N
! 93: DO 10 I = 1, MIN( N, J+1 )
! 94: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 95: 10 CONTINUE
! 96: 20 CONTINUE
! 97: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
! 98: *
! 99: * Find norm1(A).
! 100: *
! 101: VALUE = ZERO
! 102: DO 40 J = 1, N
! 103: SUM = ZERO
! 104: DO 30 I = 1, MIN( N, J+1 )
! 105: SUM = SUM + ABS( A( I, J ) )
! 106: 30 CONTINUE
! 107: VALUE = MAX( VALUE, SUM )
! 108: 40 CONTINUE
! 109: ELSE IF( LSAME( NORM, 'I' ) ) THEN
! 110: *
! 111: * Find normI(A).
! 112: *
! 113: DO 50 I = 1, N
! 114: WORK( I ) = ZERO
! 115: 50 CONTINUE
! 116: DO 70 J = 1, N
! 117: DO 60 I = 1, MIN( N, J+1 )
! 118: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 119: 60 CONTINUE
! 120: 70 CONTINUE
! 121: VALUE = ZERO
! 122: DO 80 I = 1, N
! 123: VALUE = MAX( VALUE, WORK( I ) )
! 124: 80 CONTINUE
! 125: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 126: *
! 127: * Find normF(A).
! 128: *
! 129: SCALE = ZERO
! 130: SUM = ONE
! 131: DO 90 J = 1, N
! 132: CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
! 133: 90 CONTINUE
! 134: VALUE = SCALE*SQRT( SUM )
! 135: END IF
! 136: *
! 137: DLANHS = VALUE
! 138: RETURN
! 139: *
! 140: * End of DLANHS
! 141: *
! 142: END
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