965 lines
32 KiB
Fortran
965 lines
32 KiB
Fortran
*> \brief \b SLANSF
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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 SLANSF + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slansf.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/slansf.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/slansf.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 SLANSF( NORM, TRANSR, UPLO, N, A, WORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER NORM, TRANSR, UPLO
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* INTEGER N
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* ..
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* .. Array Arguments ..
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* REAL A( 0: * ), WORK( 0: * )
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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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*> SLANSF 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 a
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*> real symmetric matrix A in RFP format.
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*> \endverbatim
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*>
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*> \return SLANSF
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*> \verbatim
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*>
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*> SLANSF = ( 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 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 SLANSF as described
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*> above.
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*> \endverbatim
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*>
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*> \param[in] TRANSR
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*> \verbatim
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*> TRANSR is CHARACTER*1
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*> Specifies whether the RFP format of A is normal or
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*> transposed format.
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*> = 'N': RFP format is Normal;
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*> = 'T': RFP format is Transpose.
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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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*> On entry, UPLO specifies whether the RFP matrix A came from
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*> an upper or lower triangular matrix as follows:
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*> = 'U': RFP A came from an upper triangular matrix;
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*> = 'L': RFP A came from a lower triangular matrix.
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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, SLANSF is
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*> set to zero.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension ( N*(N+1)/2 );
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*> On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
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*> part of the symmetric matrix A stored in RFP format. See the
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*> "Notes" below for more details.
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*> Unchanged on exit.
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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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*> \date September 2012
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*
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*> \ingroup realOTHERcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> We first consider Rectangular Full Packed (RFP) Format when N is
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*> even. We give an example where N = 6.
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*>
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*> AP is Upper AP is Lower
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*>
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*> 00 01 02 03 04 05 00
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*> 11 12 13 14 15 10 11
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*> 22 23 24 25 20 21 22
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*> 33 34 35 30 31 32 33
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*> 44 45 40 41 42 43 44
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*> 55 50 51 52 53 54 55
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*>
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*>
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*> Let TRANSR = 'N'. RFP holds AP as follows:
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*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
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*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
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*> the transpose of the first three columns of AP upper.
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*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
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*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
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*> the transpose of the last three columns of AP lower.
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*> This covers the case N even and TRANSR = 'N'.
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*>
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*> RFP A RFP A
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*>
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*> 03 04 05 33 43 53
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*> 13 14 15 00 44 54
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*> 23 24 25 10 11 55
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*> 33 34 35 20 21 22
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*> 00 44 45 30 31 32
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*> 01 11 55 40 41 42
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*> 02 12 22 50 51 52
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*>
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*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
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*> transpose of RFP A above. One therefore gets:
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*>
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*>
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*> RFP A RFP A
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*>
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*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
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*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
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*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
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*>
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*>
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*> We then consider Rectangular Full Packed (RFP) Format when N is
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*> odd. We give an example where N = 5.
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*>
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*> AP is Upper AP is Lower
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*>
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*> 00 01 02 03 04 00
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*> 11 12 13 14 10 11
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*> 22 23 24 20 21 22
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*> 33 34 30 31 32 33
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*> 44 40 41 42 43 44
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*>
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*>
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*> Let TRANSR = 'N'. RFP holds AP as follows:
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*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
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*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
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*> the transpose of the first two columns of AP upper.
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*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
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*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
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*> the transpose of the last two columns of AP lower.
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*> This covers the case N odd and TRANSR = 'N'.
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*>
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*> RFP A RFP A
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*>
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*> 02 03 04 00 33 43
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*> 12 13 14 10 11 44
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*> 22 23 24 20 21 22
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*> 00 33 34 30 31 32
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*> 01 11 44 40 41 42
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*>
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*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
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*> transpose of RFP A above. One therefore gets:
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*>
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*> RFP A RFP A
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*>
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*> 02 12 22 00 01 00 10 20 30 40 50
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*> 03 13 23 33 11 33 11 21 31 41 51
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*> 04 14 24 34 44 43 44 22 32 42 52
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*> \endverbatim
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*
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* =====================================================================
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REAL FUNCTION SLANSF( NORM, TRANSR, UPLO, N, A, WORK )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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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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* September 2012
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*
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* .. Scalar Arguments ..
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CHARACTER NORM, TRANSR, UPLO
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INTEGER N
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* ..
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* .. Array Arguments ..
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REAL A( 0: * ), WORK( 0: * )
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* ..
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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, IFM, ILU, NOE, N1, K, L, LDA
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REAL SCALE, S, VALUE, AA, TEMP
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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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* .. External Subroutines ..
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EXTERNAL SLASSQ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, 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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SLANSF = ZERO
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RETURN
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ELSE IF( N.EQ.1 ) THEN
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SLANSF = ABS( A(0) )
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RETURN
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END IF
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*
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* set noe = 1 if n is odd. if n is even set noe=0
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*
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NOE = 1
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IF( MOD( N, 2 ).EQ.0 )
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$ NOE = 0
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*
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* set ifm = 0 when form='T or 't' and 1 otherwise
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*
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IFM = 1
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IF( LSAME( TRANSR, 'T' ) )
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$ IFM = 0
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*
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* set ilu = 0 when uplo='U or 'u' and 1 otherwise
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*
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ILU = 1
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IF( LSAME( UPLO, 'U' ) )
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$ ILU = 0
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*
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* set lda = (n+1)/2 when ifm = 0
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* set lda = n when ifm = 1 and noe = 1
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* set lda = n+1 when ifm = 1 and noe = 0
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*
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IF( IFM.EQ.1 ) THEN
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IF( NOE.EQ.1 ) THEN
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LDA = N
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ELSE
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* noe=0
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LDA = N + 1
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END IF
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ELSE
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* ifm=0
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LDA = ( N+1 ) / 2
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END IF
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*
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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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K = ( N+1 ) / 2
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VALUE = ZERO
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IF( NOE.EQ.1 ) THEN
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* n is odd
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IF( IFM.EQ.1 ) THEN
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* A is n by k
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DO J = 0, K - 1
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DO I = 0, N - 1
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TEMP = ABS( A( I+J*LDA ) )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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END DO
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ELSE
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* xpose case; A is k by n
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DO J = 0, N - 1
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DO I = 0, K - 1
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TEMP = ABS( A( I+J*LDA ) )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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END DO
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END IF
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ELSE
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* n is even
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IF( IFM.EQ.1 ) THEN
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* A is n+1 by k
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DO J = 0, K - 1
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DO I = 0, N
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TEMP = ABS( A( I+J*LDA ) )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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END DO
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ELSE
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* xpose case; A is k by n+1
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DO J = 0, N
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DO I = 0, K - 1
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TEMP = ABS( A( I+J*LDA ) )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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END DO
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END IF
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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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IF( IFM.EQ.1 ) THEN
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K = N / 2
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IF( NOE.EQ.1 ) THEN
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* n is odd
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IF( ILU.EQ.0 ) THEN
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DO I = 0, K - 1
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WORK( I ) = ZERO
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END DO
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DO J = 0, K
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S = ZERO
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DO I = 0, K + J - 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(i,j+k)
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S = S + AA
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WORK( I ) = WORK( I ) + AA
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END DO
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AA = ABS( A( I+J*LDA ) )
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* -> A(j+k,j+k)
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WORK( J+K ) = S + AA
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IF( I.EQ.K+K )
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$ GO TO 10
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(j,j)
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WORK( J ) = WORK( J ) + AA
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S = ZERO
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DO L = J + 1, K - 1
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(l,j)
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S = S + AA
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WORK( L ) = WORK( L ) + AA
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END DO
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WORK( J ) = WORK( J ) + S
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END DO
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10 CONTINUE
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VALUE = WORK( 0 )
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DO I = 1, N-1
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TEMP = WORK( I )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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ELSE
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* ilu = 1
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K = K + 1
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* k=(n+1)/2 for n odd and ilu=1
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DO I = K, N - 1
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WORK( I ) = ZERO
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END DO
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DO J = K - 1, 0, -1
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S = ZERO
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DO I = 0, J - 2
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AA = ABS( A( I+J*LDA ) )
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* -> A(j+k,i+k)
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S = S + AA
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WORK( I+K ) = WORK( I+K ) + AA
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END DO
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IF( J.GT.0 ) THEN
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AA = ABS( A( I+J*LDA ) )
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* -> A(j+k,j+k)
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S = S + AA
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WORK( I+K ) = WORK( I+K ) + S
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* i=j
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I = I + 1
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END IF
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AA = ABS( A( I+J*LDA ) )
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* -> A(j,j)
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WORK( J ) = AA
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S = ZERO
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DO L = J + 1, N - 1
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(l,j)
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S = S + AA
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WORK( L ) = WORK( L ) + AA
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END DO
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WORK( J ) = WORK( J ) + S
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END DO
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VALUE = WORK( 0 )
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DO I = 1, N-1
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TEMP = WORK( I )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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END IF
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ELSE
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* n is even
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IF( ILU.EQ.0 ) THEN
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DO I = 0, K - 1
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WORK( I ) = ZERO
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END DO
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DO J = 0, K - 1
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S = ZERO
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DO I = 0, K + J - 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(i,j+k)
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S = S + AA
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WORK( I ) = WORK( I ) + AA
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END DO
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AA = ABS( A( I+J*LDA ) )
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* -> A(j+k,j+k)
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WORK( J+K ) = S + AA
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(j,j)
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WORK( J ) = WORK( J ) + AA
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S = ZERO
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DO L = J + 1, K - 1
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(l,j)
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S = S + AA
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WORK( L ) = WORK( L ) + AA
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END DO
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WORK( J ) = WORK( J ) + S
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END DO
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VALUE = WORK( 0 )
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DO I = 1, N-1
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TEMP = WORK( I )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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ELSE
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* ilu = 1
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DO I = K, N - 1
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WORK( I ) = ZERO
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END DO
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DO J = K - 1, 0, -1
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S = ZERO
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DO I = 0, J - 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(j+k,i+k)
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S = S + AA
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WORK( I+K ) = WORK( I+K ) + AA
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END DO
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AA = ABS( A( I+J*LDA ) )
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* -> A(j+k,j+k)
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S = S + AA
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WORK( I+K ) = WORK( I+K ) + S
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* i=j
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(j,j)
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WORK( J ) = AA
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S = ZERO
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DO L = J + 1, N - 1
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I = I + 1
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AA = ABS( A( I+J*LDA ) )
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* -> A(l,j)
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S = S + AA
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WORK( L ) = WORK( L ) + AA
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END DO
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WORK( J ) = WORK( J ) + S
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END DO
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VALUE = WORK( 0 )
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DO I = 1, N-1
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TEMP = WORK( I )
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IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
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$ VALUE = TEMP
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END DO
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END IF
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END IF
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ELSE
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* ifm=0
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K = N / 2
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IF( NOE.EQ.1 ) THEN
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* n is odd
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IF( ILU.EQ.0 ) THEN
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|
N1 = K
|
|
* n/2
|
|
K = K + 1
|
|
* k is the row size and lda
|
|
DO I = N1, N - 1
|
|
WORK( I ) = ZERO
|
|
END DO
|
|
DO J = 0, N1 - 1
|
|
S = ZERO
|
|
DO I = 0, K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,n1+i)
|
|
WORK( I+N1 ) = WORK( I+N1 ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = S
|
|
END DO
|
|
* j=n1=k-1 is special
|
|
S = ABS( A( 0+J*LDA ) )
|
|
* A(k-1,k-1)
|
|
DO I = 1, K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k-1,i+n1)
|
|
WORK( I+N1 ) = WORK( I+N1 ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = WORK( J ) + S
|
|
DO J = K, N - 1
|
|
S = ZERO
|
|
DO I = 0, J - K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(i,j-k)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
* i=j-k
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j-k,j-k)
|
|
S = S + AA
|
|
WORK( J-K ) = WORK( J-K ) + S
|
|
I = I + 1
|
|
S = ABS( A( I+J*LDA ) )
|
|
* A(j,j)
|
|
DO L = J + 1, N - 1
|
|
I = I + 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,l)
|
|
WORK( L ) = WORK( L ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = WORK( J ) + S
|
|
END DO
|
|
VALUE = WORK( 0 )
|
|
DO I = 1, N-1
|
|
TEMP = WORK( I )
|
|
IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
|
|
$ VALUE = TEMP
|
|
END DO
|
|
ELSE
|
|
* ilu=1
|
|
K = K + 1
|
|
* k=(n+1)/2 for n odd and ilu=1
|
|
DO I = K, N - 1
|
|
WORK( I ) = ZERO
|
|
END DO
|
|
DO J = 0, K - 2
|
|
* process
|
|
S = ZERO
|
|
DO I = 0, J - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,i)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* i=j so process of A(j,j)
|
|
S = S + AA
|
|
WORK( J ) = S
|
|
* is initialised here
|
|
I = I + 1
|
|
* i=j process A(j+k,j+k)
|
|
AA = ABS( A( I+J*LDA ) )
|
|
S = AA
|
|
DO L = K + J + 1, N - 1
|
|
I = I + 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(l,k+j)
|
|
S = S + AA
|
|
WORK( L ) = WORK( L ) + AA
|
|
END DO
|
|
WORK( K+J ) = WORK( K+J ) + S
|
|
END DO
|
|
* j=k-1 is special :process col A(k-1,0:k-1)
|
|
S = ZERO
|
|
DO I = 0, K - 2
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k,i)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
* i=k-1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k-1,k-1)
|
|
S = S + AA
|
|
WORK( I ) = S
|
|
* done with col j=k+1
|
|
DO J = K, N - 1
|
|
* process col j of A = A(j,0:k-1)
|
|
S = ZERO
|
|
DO I = 0, K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,i)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = WORK( J ) + S
|
|
END DO
|
|
VALUE = WORK( 0 )
|
|
DO I = 1, N-1
|
|
TEMP = WORK( I )
|
|
IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
|
|
$ VALUE = TEMP
|
|
END DO
|
|
END IF
|
|
ELSE
|
|
* n is even
|
|
IF( ILU.EQ.0 ) THEN
|
|
DO I = K, N - 1
|
|
WORK( I ) = ZERO
|
|
END DO
|
|
DO J = 0, K - 1
|
|
S = ZERO
|
|
DO I = 0, K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,i+k)
|
|
WORK( I+K ) = WORK( I+K ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = S
|
|
END DO
|
|
* j=k
|
|
AA = ABS( A( 0+J*LDA ) )
|
|
* A(k,k)
|
|
S = AA
|
|
DO I = 1, K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k,k+i)
|
|
WORK( I+K ) = WORK( I+K ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = WORK( J ) + S
|
|
DO J = K + 1, N - 1
|
|
S = ZERO
|
|
DO I = 0, J - 2 - K
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(i,j-k-1)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
* i=j-1-k
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j-k-1,j-k-1)
|
|
S = S + AA
|
|
WORK( J-K-1 ) = WORK( J-K-1 ) + S
|
|
I = I + 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,j)
|
|
S = AA
|
|
DO L = J + 1, N - 1
|
|
I = I + 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j,l)
|
|
WORK( L ) = WORK( L ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J ) = WORK( J ) + S
|
|
END DO
|
|
* j=n
|
|
S = ZERO
|
|
DO I = 0, K - 2
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(i,k-1)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
* i=k-1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k-1,k-1)
|
|
S = S + AA
|
|
WORK( I ) = WORK( I ) + S
|
|
VALUE = WORK ( 0 )
|
|
DO I = 1, N-1
|
|
TEMP = WORK( I )
|
|
IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
|
|
$ VALUE = TEMP
|
|
END DO
|
|
ELSE
|
|
* ilu=1
|
|
DO I = K, N - 1
|
|
WORK( I ) = ZERO
|
|
END DO
|
|
* j=0 is special :process col A(k:n-1,k)
|
|
S = ABS( A( 0 ) )
|
|
* A(k,k)
|
|
DO I = 1, K - 1
|
|
AA = ABS( A( I ) )
|
|
* A(k+i,k)
|
|
WORK( I+K ) = WORK( I+K ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( K ) = WORK( K ) + S
|
|
DO J = 1, K - 1
|
|
* process
|
|
S = ZERO
|
|
DO I = 0, J - 2
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j-1,i)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* i=j-1 so process of A(j-1,j-1)
|
|
S = S + AA
|
|
WORK( J-1 ) = S
|
|
* is initialised here
|
|
I = I + 1
|
|
* i=j process A(j+k,j+k)
|
|
AA = ABS( A( I+J*LDA ) )
|
|
S = AA
|
|
DO L = K + J + 1, N - 1
|
|
I = I + 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(l,k+j)
|
|
S = S + AA
|
|
WORK( L ) = WORK( L ) + AA
|
|
END DO
|
|
WORK( K+J ) = WORK( K+J ) + S
|
|
END DO
|
|
* j=k is special :process col A(k,0:k-1)
|
|
S = ZERO
|
|
DO I = 0, K - 2
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k,i)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
* i=k-1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(k-1,k-1)
|
|
S = S + AA
|
|
WORK( I ) = S
|
|
* done with col j=k+1
|
|
DO J = K + 1, N
|
|
* process col j-1 of A = A(j-1,0:k-1)
|
|
S = ZERO
|
|
DO I = 0, K - 1
|
|
AA = ABS( A( I+J*LDA ) )
|
|
* A(j-1,i)
|
|
WORK( I ) = WORK( I ) + AA
|
|
S = S + AA
|
|
END DO
|
|
WORK( J-1 ) = WORK( J-1 ) + S
|
|
END DO
|
|
VALUE = WORK( 0 )
|
|
DO I = 1, N-1
|
|
TEMP = WORK( I )
|
|
IF( VALUE .LT. TEMP .OR. SISNAN( TEMP ) )
|
|
$ VALUE = TEMP
|
|
END DO
|
|
END IF
|
|
END IF
|
|
END IF
|
|
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
|
|
*
|
|
* Find normF(A).
|
|
*
|
|
K = ( N+1 ) / 2
|
|
SCALE = ZERO
|
|
S = ONE
|
|
IF( NOE.EQ.1 ) THEN
|
|
* n is odd
|
|
IF( IFM.EQ.1 ) THEN
|
|
* A is normal
|
|
IF( ILU.EQ.0 ) THEN
|
|
* A is upper
|
|
DO J = 0, K - 3
|
|
CALL SLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S )
|
|
* L at A(k,0)
|
|
END DO
|
|
DO J = 0, K - 1
|
|
CALL SLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S )
|
|
* trap U at A(0,0)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K-1, A( K ), LDA+1, SCALE, S )
|
|
* tri L at A(k,0)
|
|
CALL SLASSQ( K, A( K-1 ), LDA+1, SCALE, S )
|
|
* tri U at A(k-1,0)
|
|
ELSE
|
|
* ilu=1 & A is lower
|
|
DO J = 0, K - 1
|
|
CALL SLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S )
|
|
* trap L at A(0,0)
|
|
END DO
|
|
DO J = 0, K - 2
|
|
CALL SLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S )
|
|
* U at A(0,1)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S )
|
|
* tri L at A(0,0)
|
|
CALL SLASSQ( K-1, A( 0+LDA ), LDA+1, SCALE, S )
|
|
* tri U at A(0,1)
|
|
END IF
|
|
ELSE
|
|
* A is xpose
|
|
IF( ILU.EQ.0 ) THEN
|
|
* A**T is upper
|
|
DO J = 1, K - 2
|
|
CALL SLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S )
|
|
* U at A(0,k)
|
|
END DO
|
|
DO J = 0, K - 2
|
|
CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
|
|
* k by k-1 rect. at A(0,0)
|
|
END DO
|
|
DO J = 0, K - 2
|
|
CALL SLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1,
|
|
$ SCALE, S )
|
|
* L at A(0,k-1)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K-1, A( 0+K*LDA ), LDA+1, SCALE, S )
|
|
* tri U at A(0,k)
|
|
CALL SLASSQ( K, A( 0+( K-1 )*LDA ), LDA+1, SCALE, S )
|
|
* tri L at A(0,k-1)
|
|
ELSE
|
|
* A**T is lower
|
|
DO J = 1, K - 1
|
|
CALL SLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
|
|
* U at A(0,0)
|
|
END DO
|
|
DO J = K, N - 1
|
|
CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
|
|
* k by k-1 rect. at A(0,k)
|
|
END DO
|
|
DO J = 0, K - 3
|
|
CALL SLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S )
|
|
* L at A(1,0)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S )
|
|
* tri U at A(0,0)
|
|
CALL SLASSQ( K-1, A( 1 ), LDA+1, SCALE, S )
|
|
* tri L at A(1,0)
|
|
END IF
|
|
END IF
|
|
ELSE
|
|
* n is even
|
|
IF( IFM.EQ.1 ) THEN
|
|
* A is normal
|
|
IF( ILU.EQ.0 ) THEN
|
|
* A is upper
|
|
DO J = 0, K - 2
|
|
CALL SLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S )
|
|
* L at A(k+1,0)
|
|
END DO
|
|
DO J = 0, K - 1
|
|
CALL SLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S )
|
|
* trap U at A(0,0)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K, A( K+1 ), LDA+1, SCALE, S )
|
|
* tri L at A(k+1,0)
|
|
CALL SLASSQ( K, A( K ), LDA+1, SCALE, S )
|
|
* tri U at A(k,0)
|
|
ELSE
|
|
* ilu=1 & A is lower
|
|
DO J = 0, K - 1
|
|
CALL SLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S )
|
|
* trap L at A(1,0)
|
|
END DO
|
|
DO J = 1, K - 1
|
|
CALL SLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
|
|
* U at A(0,0)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K, A( 1 ), LDA+1, SCALE, S )
|
|
* tri L at A(1,0)
|
|
CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S )
|
|
* tri U at A(0,0)
|
|
END IF
|
|
ELSE
|
|
* A is xpose
|
|
IF( ILU.EQ.0 ) THEN
|
|
* A**T is upper
|
|
DO J = 1, K - 1
|
|
CALL SLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S )
|
|
* U at A(0,k+1)
|
|
END DO
|
|
DO J = 0, K - 1
|
|
CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
|
|
* k by k rect. at A(0,0)
|
|
END DO
|
|
DO J = 0, K - 2
|
|
CALL SLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE,
|
|
$ S )
|
|
* L at A(0,k)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K, A( 0+( K+1 )*LDA ), LDA+1, SCALE, S )
|
|
* tri U at A(0,k+1)
|
|
CALL SLASSQ( K, A( 0+K*LDA ), LDA+1, SCALE, S )
|
|
* tri L at A(0,k)
|
|
ELSE
|
|
* A**T is lower
|
|
DO J = 1, K - 1
|
|
CALL SLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S )
|
|
* U at A(0,1)
|
|
END DO
|
|
DO J = K + 1, N
|
|
CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
|
|
* k by k rect. at A(0,k+1)
|
|
END DO
|
|
DO J = 0, K - 2
|
|
CALL SLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S )
|
|
* L at A(0,0)
|
|
END DO
|
|
S = S + S
|
|
* double s for the off diagonal elements
|
|
CALL SLASSQ( K, A( LDA ), LDA+1, SCALE, S )
|
|
* tri L at A(0,1)
|
|
CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S )
|
|
* tri U at A(0,0)
|
|
END IF
|
|
END IF
|
|
END IF
|
|
VALUE = SCALE*SQRT( S )
|
|
END IF
|
|
*
|
|
SLANSF = VALUE
|
|
RETURN
|
|
*
|
|
* End of SLANSF
|
|
*
|
|
END
|