Annotation of rpl/lapack/lapack/zlange.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANGE( 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 WORK( * )
! 14: COMPLEX*16 A( LDA, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLANGE returns the value of the one norm, or the Frobenius norm, or
! 21: * the infinity norm, or the element of largest absolute value of a
! 22: * complex matrix A.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANGE returns the value
! 28: *
! 29: * ZLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 30: * (
! 31: * ( norm1(A), NORM = '1', 'O' or 'o'
! 32: * (
! 33: * ( normI(A), NORM = 'I' or 'i'
! 34: * (
! 35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 36: *
! 37: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 38: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 39: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 41: *
! 42: * Arguments
! 43: * =========
! 44: *
! 45: * NORM (input) CHARACTER*1
! 46: * Specifies the value to be returned in ZLANGE as described
! 47: * above.
! 48: *
! 49: * M (input) INTEGER
! 50: * The number of rows of the matrix A. M >= 0. When M = 0,
! 51: * ZLANGE is set to zero.
! 52: *
! 53: * N (input) INTEGER
! 54: * The number of columns of the matrix A. N >= 0. When N = 0,
! 55: * ZLANGE is set to zero.
! 56: *
! 57: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 58: * The m by n matrix A.
! 59: *
! 60: * LDA (input) INTEGER
! 61: * The leading dimension of the array A. LDA >= max(M,1).
! 62: *
! 63: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 64: * where LWORK >= M when NORM = 'I'; otherwise, WORK is not
! 65: * referenced.
! 66: *
! 67: * =====================================================================
! 68: *
! 69: * .. Parameters ..
! 70: DOUBLE PRECISION ONE, ZERO
! 71: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 72: * ..
! 73: * .. Local Scalars ..
! 74: INTEGER I, J
! 75: DOUBLE PRECISION SCALE, SUM, VALUE
! 76: * ..
! 77: * .. External Functions ..
! 78: LOGICAL LSAME
! 79: EXTERNAL LSAME
! 80: * ..
! 81: * .. External Subroutines ..
! 82: EXTERNAL ZLASSQ
! 83: * ..
! 84: * .. Intrinsic Functions ..
! 85: INTRINSIC ABS, MAX, MIN, SQRT
! 86: * ..
! 87: * .. Executable Statements ..
! 88: *
! 89: IF( MIN( M, N ).EQ.0 ) THEN
! 90: VALUE = ZERO
! 91: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 92: *
! 93: * Find max(abs(A(i,j))).
! 94: *
! 95: VALUE = ZERO
! 96: DO 20 J = 1, N
! 97: DO 10 I = 1, M
! 98: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 99: 10 CONTINUE
! 100: 20 CONTINUE
! 101: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
! 102: *
! 103: * Find norm1(A).
! 104: *
! 105: VALUE = ZERO
! 106: DO 40 J = 1, N
! 107: SUM = ZERO
! 108: DO 30 I = 1, M
! 109: SUM = SUM + ABS( A( I, J ) )
! 110: 30 CONTINUE
! 111: VALUE = MAX( VALUE, SUM )
! 112: 40 CONTINUE
! 113: ELSE IF( LSAME( NORM, 'I' ) ) THEN
! 114: *
! 115: * Find normI(A).
! 116: *
! 117: DO 50 I = 1, M
! 118: WORK( I ) = ZERO
! 119: 50 CONTINUE
! 120: DO 70 J = 1, N
! 121: DO 60 I = 1, M
! 122: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
! 123: 60 CONTINUE
! 124: 70 CONTINUE
! 125: VALUE = ZERO
! 126: DO 80 I = 1, M
! 127: VALUE = MAX( VALUE, WORK( I ) )
! 128: 80 CONTINUE
! 129: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 130: *
! 131: * Find normF(A).
! 132: *
! 133: SCALE = ZERO
! 134: SUM = ONE
! 135: DO 90 J = 1, N
! 136: CALL ZLASSQ( M, A( 1, J ), 1, SCALE, SUM )
! 137: 90 CONTINUE
! 138: VALUE = SCALE*SQRT( SUM )
! 139: END IF
! 140: *
! 141: ZLANGE = VALUE
! 142: RETURN
! 143: *
! 144: * End of ZLANGE
! 145: *
! 146: END
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