Annotation of rpl/lapack/lapack/dlange.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION DLANGE( NORM, M, 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, M, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION A( LDA, * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DLANGE 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: * real matrix A.
! 22: *
! 23: * Description
! 24: * ===========
! 25: *
! 26: * DLANGE returns the value
! 27: *
! 28: * DLANGE = ( 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 DLANGE as described
! 46: * above.
! 47: *
! 48: * M (input) INTEGER
! 49: * The number of rows of the matrix A. M >= 0. When M = 0,
! 50: * DLANGE is set to zero.
! 51: *
! 52: * N (input) INTEGER
! 53: * The number of columns of the matrix A. N >= 0. When N = 0,
! 54: * DLANGE is set to zero.
! 55: *
! 56: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 57: * The m by n matrix A.
! 58: *
! 59: * LDA (input) INTEGER
! 60: * The leading dimension of the array A. LDA >= max(M,1).
! 61: *
! 62: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 63: * where LWORK >= M when NORM = 'I'; otherwise, WORK is not
! 64: * referenced.
! 65: *
! 66: * =====================================================================
! 67: *
! 68: * .. Parameters ..
! 69: DOUBLE PRECISION ONE, ZERO
! 70: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 71: * ..
! 72: * .. Local Scalars ..
! 73: INTEGER I, J
! 74: DOUBLE PRECISION SCALE, SUM, VALUE
! 75: * ..
! 76: * .. External Subroutines ..
! 77: EXTERNAL DLASSQ
! 78: * ..
! 79: * .. External Functions ..
! 80: LOGICAL LSAME
! 81: EXTERNAL LSAME
! 82: * ..
! 83: * .. Intrinsic Functions ..
! 84: INTRINSIC ABS, MAX, MIN, SQRT
! 85: * ..
! 86: * .. Executable Statements ..
! 87: *
! 88: IF( MIN( M, N ).EQ.0 ) THEN
! 89: VALUE = ZERO
! 90: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 91: *
! 92: * Find max(abs(A(i,j))).
! 93: *
! 94: VALUE = ZERO
! 95: DO 20 J = 1, N
! 96: DO 10 I = 1, M
! 97: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 98: 10 CONTINUE
! 99: 20 CONTINUE
! 100: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
! 101: *
! 102: * Find norm1(A).
! 103: *
! 104: VALUE = ZERO
! 105: DO 40 J = 1, N
! 106: SUM = ZERO
! 107: DO 30 I = 1, M
! 108: SUM = SUM + ABS( A( I, J ) )
! 109: 30 CONTINUE
! 110: VALUE = MAX( VALUE, SUM )
! 111: 40 CONTINUE
! 112: ELSE IF( LSAME( NORM, 'I' ) ) THEN
! 113: *
! 114: * Find normI(A).
! 115: *
! 116: DO 50 I = 1, M
! 117: WORK( I ) = ZERO
! 118: 50 CONTINUE
! 119: DO 70 J = 1, N
! 120: DO 60 I = 1, M
! 121: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 122: 60 CONTINUE
! 123: 70 CONTINUE
! 124: VALUE = ZERO
! 125: DO 80 I = 1, M
! 126: VALUE = MAX( VALUE, WORK( I ) )
! 127: 80 CONTINUE
! 128: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 129: *
! 130: * Find normF(A).
! 131: *
! 132: SCALE = ZERO
! 133: SUM = ONE
! 134: DO 90 J = 1, N
! 135: CALL DLASSQ( M, A( 1, J ), 1, SCALE, SUM )
! 136: 90 CONTINUE
! 137: VALUE = SCALE*SQRT( SUM )
! 138: END IF
! 139: *
! 140: DLANGE = VALUE
! 141: RETURN
! 142: *
! 143: * End of DLANGE
! 144: *
! 145: END
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