202 lines
6.3 KiB
FortranFixed
202 lines
6.3 KiB
FortranFixed
DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB,
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$ WORK )
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER NORM, UPLO
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INTEGER K, LDAB, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION WORK( * )
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COMPLEX*16 AB( LDAB, * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZLANHB returns the value of the one norm, or the Frobenius norm, or
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* the infinity norm, or the element of largest absolute value of an
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* n by n hermitian band matrix A, with k super-diagonals.
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*
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* Description
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* ===========
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*
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* ZLANHB returns the value
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*
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* ZLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
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* (
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* ( norm1(A), NORM = '1', 'O' or 'o'
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* (
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* ( normI(A), NORM = 'I' or 'i'
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* (
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* ( normF(A), NORM = 'F', 'f', 'E' or 'e'
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*
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* where norm1 denotes the one norm of a matrix (maximum column sum),
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* normI denotes the infinity norm of a matrix (maximum row sum) and
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* normF denotes the Frobenius norm of a matrix (square root of sum of
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* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
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*
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* Arguments
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* =========
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*
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* NORM (input) CHARACTER*1
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* Specifies the value to be returned in ZLANHB as described
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* above.
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*
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* UPLO (input) CHARACTER*1
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* Specifies whether the upper or lower triangular part of the
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* band matrix A is supplied.
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0. When N = 0, ZLANHB is
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* set to zero.
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*
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* K (input) INTEGER
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* The number of super-diagonals or sub-diagonals of the
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* band matrix A. K >= 0.
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*
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* AB (input) COMPLEX*16 array, dimension (LDAB,N)
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* The upper or lower triangle of the hermitian band matrix A,
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* stored in the first K+1 rows of AB. The j-th column of A is
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* stored in the j-th column of the array AB as follows:
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* if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
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* Note that the imaginary parts of the diagonal elements need
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* not be set and are assumed to be zero.
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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDAB >= K+1.
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*
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* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
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* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
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* WORK is not referenced.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, L
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DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL ZLASSQ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, MAX, MIN, SQRT
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* ..
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* .. Executable Statements ..
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*
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IF( N.EQ.0 ) THEN
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VALUE = ZERO
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ELSE IF( LSAME( NORM, 'M' ) ) THEN
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*
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* Find max(abs(A(i,j))).
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*
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VALUE = ZERO
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 20 J = 1, N
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DO 10 I = MAX( K+2-J, 1 ), K
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VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
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10 CONTINUE
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VALUE = MAX( VALUE, ABS( DBLE( AB( K+1, J ) ) ) )
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20 CONTINUE
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ELSE
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DO 40 J = 1, N
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VALUE = MAX( VALUE, ABS( DBLE( AB( 1, J ) ) ) )
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DO 30 I = 2, MIN( N+1-J, K+1 )
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VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
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30 CONTINUE
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40 CONTINUE
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END IF
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ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
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$ ( NORM.EQ.'1' ) ) THEN
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*
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* Find normI(A) ( = norm1(A), since A is hermitian).
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*
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VALUE = ZERO
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 60 J = 1, N
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SUM = ZERO
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L = K + 1 - J
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DO 50 I = MAX( 1, J-K ), J - 1
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ABSA = ABS( AB( L+I, J ) )
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SUM = SUM + ABSA
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WORK( I ) = WORK( I ) + ABSA
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50 CONTINUE
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WORK( J ) = SUM + ABS( DBLE( AB( K+1, J ) ) )
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60 CONTINUE
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DO 70 I = 1, N
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VALUE = MAX( VALUE, WORK( I ) )
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70 CONTINUE
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ELSE
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DO 80 I = 1, N
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WORK( I ) = ZERO
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80 CONTINUE
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DO 100 J = 1, N
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SUM = WORK( J ) + ABS( DBLE( AB( 1, J ) ) )
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L = 1 - J
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DO 90 I = J + 1, MIN( N, J+K )
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ABSA = ABS( AB( L+I, J ) )
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SUM = SUM + ABSA
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WORK( I ) = WORK( I ) + ABSA
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90 CONTINUE
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VALUE = MAX( VALUE, SUM )
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100 CONTINUE
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END IF
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
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*
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* Find normF(A).
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*
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SCALE = ZERO
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SUM = ONE
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IF( K.GT.0 ) THEN
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 110 J = 2, N
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CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
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$ 1, SCALE, SUM )
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110 CONTINUE
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L = K + 1
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ELSE
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DO 120 J = 1, N - 1
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CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
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$ SUM )
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120 CONTINUE
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L = 1
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END IF
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SUM = 2*SUM
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ELSE
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L = 1
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END IF
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DO 130 J = 1, N
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IF( DBLE( AB( L, J ) ).NE.ZERO ) THEN
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ABSA = ABS( DBLE( AB( L, J ) ) )
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IF( SCALE.LT.ABSA ) THEN
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SUM = ONE + SUM*( SCALE / ABSA )**2
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SCALE = ABSA
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ELSE
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SUM = SUM + ( ABSA / SCALE )**2
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END IF
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END IF
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130 CONTINUE
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VALUE = SCALE*SQRT( SUM )
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END IF
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*
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ZLANHB = VALUE
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RETURN
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*
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* End of ZLANHB
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*
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END
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