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version 1.19, 2023/08/07 08:39:29
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*> \brief \b ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form. |
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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 ZLANHP + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhp.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/zlanhp.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/zlanhp.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 ZLANHP( NORM, UPLO, N, AP, WORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER NORM, UPLO |
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* INTEGER N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION WORK( * ) |
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* COMPLEX*16 AP( * ) |
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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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*> ZLANHP 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, supplied in packed form. |
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*> \endverbatim |
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*> |
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*> \return ZLANHP |
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*> \verbatim |
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*> |
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*> ZLANHP = ( 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 ZLANHP 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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*> hermitian matrix A is supplied. |
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*> = 'U': Upper triangular part of A is supplied |
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*> = 'L': Lower triangular part of A 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, ZLANHP is |
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*> set to zero. |
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*> \endverbatim |
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*> |
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*> \param[in] AP |
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*> \verbatim |
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*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) |
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*> The upper or lower triangle of the hermitian matrix A, packed |
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*> columnwise in a linear array. The j-th column of A is stored |
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*> in the array AP as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
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*> Note that the imaginary parts of the diagonal elements need |
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*> not be set and are assumed to be zero. |
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*> \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 (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 complex16OTHERauxiliary |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK ) |
DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine -- |
* -- 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..-- |
* November 2006 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM, UPLO |
CHARACTER NORM, UPLO |
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COMPLEX*16 AP( * ) |
COMPLEX*16 AP( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLANHP 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, supplied in packed form. |
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* |
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* Description |
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* =========== |
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* |
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* ZLANHP returns the value |
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* |
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* ZLANHP = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
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* ( |
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* ( norm1(A), NORM = '1', 'O' or 'o' |
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* ( |
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* ( normI(A), NORM = 'I' or 'i' |
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* ( |
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* ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
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* |
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* where norm1 denotes the one norm of a matrix (maximum column sum), |
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* normI denotes the infinity norm of a matrix (maximum row sum) and |
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* normF denotes the Frobenius norm of a matrix (square root of sum of |
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* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. |
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* |
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* Arguments |
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* ========= |
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* |
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* NORM (input) CHARACTER*1 |
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* Specifies the value to be returned in ZLANHP as described |
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* above. |
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* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the upper or lower triangular part of the |
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* hermitian matrix A is supplied. |
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* = 'U': Upper triangular part of A is supplied |
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* = 'L': Lower triangular part of A is supplied |
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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, ZLANHP is |
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* set to zero. |
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* |
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* AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) |
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* The upper or lower triangle of the hermitian matrix A, packed |
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* columnwise in a linear array. The j-th column of A is stored |
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* in the array AP as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
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* Note that the imaginary parts of the diagonal elements need |
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* not be set and are assumed to be zero. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), |
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* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, |
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* WORK is not referenced. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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DOUBLE PRECISION ABSA, SCALE, SUM, VALUE |
DOUBLE PRECISION ABSA, SCALE, SUM, VALUE |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME |
EXTERNAL LSAME, DISNAN |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZLASSQ |
EXTERNAL ZLASSQ |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, MAX, SQRT |
INTRINSIC ABS, DBLE, SQRT |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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K = 0 |
K = 0 |
DO 20 J = 1, N |
DO 20 J = 1, N |
DO 10 I = K + 1, K + J - 1 |
DO 10 I = K + 1, K + J - 1 |
VALUE = MAX( VALUE, ABS( AP( I ) ) ) |
SUM = ABS( AP( I ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
10 CONTINUE |
10 CONTINUE |
K = K + J |
K = K + J |
VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) ) |
SUM = ABS( DBLE( AP( K ) ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
20 CONTINUE |
20 CONTINUE |
ELSE |
ELSE |
K = 1 |
K = 1 |
DO 40 J = 1, N |
DO 40 J = 1, N |
VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) ) |
SUM = ABS( DBLE( AP( K ) ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
DO 30 I = K + 1, K + N - J |
DO 30 I = K + 1, K + N - J |
VALUE = MAX( VALUE, ABS( AP( I ) ) ) |
SUM = ABS( AP( I ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
30 CONTINUE |
30 CONTINUE |
K = K + N - J + 1 |
K = K + N - J + 1 |
40 CONTINUE |
40 CONTINUE |
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K = K + 1 |
K = K + 1 |
60 CONTINUE |
60 CONTINUE |
DO 70 I = 1, N |
DO 70 I = 1, N |
VALUE = MAX( VALUE, WORK( I ) ) |
SUM = WORK( I ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
70 CONTINUE |
70 CONTINUE |
ELSE |
ELSE |
DO 80 I = 1, N |
DO 80 I = 1, N |
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WORK( I ) = WORK( I ) + ABSA |
WORK( I ) = WORK( I ) + ABSA |
K = K + 1 |
K = K + 1 |
90 CONTINUE |
90 CONTINUE |
VALUE = MAX( VALUE, SUM ) |
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
100 CONTINUE |
100 CONTINUE |
END IF |
END IF |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |