version 1.5, 2011/07/22 07:38:17
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version 1.6, 2011/11/21 20:43:15
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DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) |
*> \brief \b ZLANHF |
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* |
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* =========== DOCUMENTATION =========== |
* |
* |
* -- LAPACK routine (version 3.3.1) -- |
* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
* |
* |
* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- |
*> \htmlonly |
* -- April 2009 -- |
*> Download ZLANHF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhf.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/zlanhf.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/zlanhf.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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* DOUBLE PRECISION FUNCTION ZLANHF( 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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* DOUBLE PRECISION WORK( 0: * ) |
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* COMPLEX*16 A( 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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*> ZLANHF 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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*> complex Hermitian matrix A in RFP format. |
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*> \endverbatim |
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*> |
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*> \return ZLANHF |
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*> \verbatim |
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*> |
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*> ZLANHF = ( 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 |
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*> Specifies the value to be returned in ZLANHF 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 |
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*> Specifies whether the RFP format of A is normal or |
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*> conjugate-transposed format. |
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*> = 'N': RFP format is Normal |
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*> = 'C': RFP format is Conjugate-transposed |
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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 |
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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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*> |
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*> UPLO = 'U' or 'u' RFP A came from an upper triangular |
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*> matrix |
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*> |
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*> UPLO = 'L' or 'l' RFP A came from a lower triangular |
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*> 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, ZLANHF 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 COMPLEX*16 array, dimension ( N*(N+1)/2 ); |
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*> On entry, the matrix A in RFP Format. |
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*> RFP Format is described by TRANSR, UPLO and N as follows: |
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*> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; |
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*> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If |
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*> TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A |
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*> as defined when TRANSR = 'N'. The contents of RFP A are |
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*> defined by UPLO as follows: If UPLO = 'U' the RFP A |
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*> contains the ( N*(N+1)/2 ) elements of upper packed A |
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*> either in normal or conjugate-transpose Format. If |
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*> UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements |
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*> of lower packed A either in normal or conjugate-transpose |
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*> Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When |
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*> TRANSR is 'N' the LDA is N+1 when N is even and is N when |
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*> is odd. See the Note 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 DOUBLE PRECISION array, dimension (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 November 2011 |
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* |
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*> \ingroup complex16OTHERcomputational |
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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 Standard Packed Format when N is even. |
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*> 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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*> conjugate-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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*> conjugate-transpose of the last three columns of AP lower. |
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*> To denote conjugate we place -- above the element. This covers the |
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*> 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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*> -- -- -- |
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*> 03 04 05 33 43 53 |
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*> -- -- |
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*> 13 14 15 00 44 54 |
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*> -- |
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*> 23 24 25 10 11 55 |
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*> |
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*> 33 34 35 20 21 22 |
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*> -- |
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*> 00 44 45 30 31 32 |
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*> -- -- |
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*> 01 11 55 40 41 42 |
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*> -- -- -- |
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*> 02 12 22 50 51 52 |
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*> |
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*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- |
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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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*> -- -- -- -- -- -- -- -- -- -- |
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*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 |
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*> -- -- -- -- -- -- -- -- -- -- |
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*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 |
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*> -- -- -- -- -- -- -- -- -- -- |
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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 next consider Standard Packed Format when N is odd. |
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*> 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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*> conjugate-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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*> conjugate-transpose of the last two columns of AP lower. |
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*> To denote conjugate we place -- above the element. This covers the |
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*> 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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*> -- -- |
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*> 02 03 04 00 33 43 |
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*> -- |
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*> 12 13 14 10 11 44 |
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*> |
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*> 22 23 24 20 21 22 |
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*> -- |
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*> 00 33 34 30 31 32 |
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*> -- -- |
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*> 01 11 44 40 41 42 |
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*> |
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*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- |
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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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*> -- -- -- -- -- -- -- -- -- |
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*> 02 12 22 00 01 00 10 20 30 40 50 |
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*> -- -- -- -- -- -- -- -- -- |
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*> 03 13 23 33 11 33 11 21 31 41 51 |
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*> -- -- -- -- -- -- -- -- -- |
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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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DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) |
* |
* |
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* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM, TRANSR, UPLO |
CHARACTER NORM, TRANSR, UPLO |
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COMPLEX*16 A( 0: * ) |
COMPLEX*16 A( 0: * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZLANHF returns the value of the one norm, or the Frobenius norm, or |
|
* the infinity norm, or the element of largest absolute value of a |
|
* complex Hermitian matrix A in RFP format. |
|
* |
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* Description |
|
* =========== |
|
* |
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* ZLANHF returns the value |
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* |
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* ZLANHF = ( 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), |
|
* normI denotes the infinity norm of a matrix (maximum row sum) and |
|
* normF denotes the Frobenius norm of a matrix (square root of sum of |
|
* squares). Note that max(abs(A(i,j))) is not a matrix norm. |
|
* |
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* Arguments |
|
* ========= |
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* |
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* NORM (input) CHARACTER |
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* Specifies the value to be returned in ZLANHF as described |
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* above. |
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* |
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* TRANSR (input) CHARACTER |
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* Specifies whether the RFP format of A is normal or |
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* conjugate-transposed format. |
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* = 'N': RFP format is Normal |
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* = 'C': RFP format is Conjugate-transposed |
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* |
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* UPLO (input) CHARACTER |
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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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* |
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* UPLO = 'U' or 'u' RFP A came from an upper triangular |
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* matrix |
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* |
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* UPLO = 'L' or 'l' RFP A came from a lower triangular |
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* matrix |
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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, ZLANHF is |
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* set to zero. |
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* |
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* A (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ); |
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* On entry, the matrix A in RFP Format. |
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* RFP Format is described by TRANSR, UPLO and N as follows: |
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* If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; |
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* K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If |
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* TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A |
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* as defined when TRANSR = 'N'. The contents of RFP A are |
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* defined by UPLO as follows: If UPLO = 'U' the RFP A |
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* contains the ( N*(N+1)/2 ) elements of upper packed A |
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* either in normal or conjugate-transpose Format. If |
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* UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements |
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* of lower packed A either in normal or conjugate-transpose |
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* Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When |
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* TRANSR is 'N' the LDA is N+1 when N is even and is N when |
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* is odd. See the Note below for more details. |
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* Unchanged on exit. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (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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* Further Details |
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* =============== |
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* |
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* We first consider Standard Packed Format when N is even. |
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* 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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* conjugate-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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* conjugate-transpose of the last three columns of AP lower. |
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* To denote conjugate we place -- above the element. This covers the |
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* 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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* -- -- -- |
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* 03 04 05 33 43 53 |
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* -- -- |
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* 13 14 15 00 44 54 |
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* -- |
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* 23 24 25 10 11 55 |
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* |
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* 33 34 35 20 21 22 |
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* -- |
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* 00 44 45 30 31 32 |
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* -- -- |
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* 01 11 55 40 41 42 |
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* -- -- -- |
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* 02 12 22 50 51 52 |
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* |
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* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- |
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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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* -- -- -- -- -- -- -- -- -- -- |
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* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 |
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* -- -- -- -- -- -- -- -- -- -- |
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* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 |
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* -- -- -- -- -- -- -- -- -- -- |
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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 next consider Standard Packed Format when N is odd. |
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* 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 |
|
* three columns of AP upper. The lower triangle A(3:4,0:1) consists of |
|
* conjugate-transpose of the first two columns of AP upper. |
|
* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first |
|
* three columns of AP lower. The upper triangle A(0:1,1:2) consists of |
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* conjugate-transpose of the last two columns of AP lower. |
|
* To denote conjugate we place -- above the element. This covers the |
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* 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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* -- -- |
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* 02 03 04 00 33 43 |
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* -- |
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* 12 13 14 10 11 44 |
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* |
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* 22 23 24 20 21 22 |
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* -- |
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* 00 33 34 30 31 32 |
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* -- -- |
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* 01 11 44 40 41 42 |
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* |
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* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- |
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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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* -- -- -- -- -- -- -- -- -- |
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* 02 12 22 00 01 00 10 20 30 40 50 |
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* -- -- -- -- -- -- -- -- -- |
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* 03 13 23 33 11 33 11 21 31 41 51 |
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* -- -- -- -- -- -- -- -- -- |
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* 04 14 24 34 44 43 44 22 32 42 52 |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |