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256 lines
7.6 KiB
256 lines
7.6 KiB
2 years ago
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*> \brief \b SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SLANSB + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slansb.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slansb.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slansb.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB,
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* WORK )
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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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* REAL AB( LDAB, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLANSB 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 symmetric band matrix A, with k super-diagonals.
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*> \endverbatim
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*>
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*> \return SLANSB
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*> \verbatim
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*>
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*> SLANSB = ( 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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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NORM
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*> \verbatim
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*> NORM is CHARACTER*1
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*> Specifies the value to be returned in SLANSB as described
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*> above.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is 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 part is supplied
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*> = 'L': Lower triangular part is supplied
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0. When N = 0, SLANSB is
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*> set to zero.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is 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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*> \endverbatim
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*>
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*> \param[in] AB
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*> \verbatim
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*> AB is REAL array, dimension (LDAB,N)
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*> The upper or lower triangle of the symmetric 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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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= K+1.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL 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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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup realOTHERauxiliary
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*
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* =====================================================================
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REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB,
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$ WORK )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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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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REAL AB( LDAB, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, L
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REAL ABSA, SCALE, SUM, VALUE
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* ..
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* .. External Subroutines ..
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EXTERNAL SLASSQ
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* ..
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* .. External Functions ..
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LOGICAL LSAME, SISNAN
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EXTERNAL LSAME, SISNAN
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, 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 + 1
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SUM = ABS( AB( I, J ) )
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IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
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10 CONTINUE
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20 CONTINUE
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ELSE
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DO 40 J = 1, N
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DO 30 I = 1, MIN( N+1-J, K+1 )
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SUM = ABS( AB( I, J ) )
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IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
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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 symmetric).
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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( AB( K+1, J ) )
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60 CONTINUE
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DO 70 I = 1, N
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SUM = WORK( I )
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IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
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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( 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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IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) 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 SLASSQ( 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 SLASSQ( 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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CALL SLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
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VALUE = SCALE*SQRT( SUM )
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END IF
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*
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SLANSB = VALUE
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RETURN
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*
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* End of SLANSB
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*
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END
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