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