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version 1.19, 2023/08/07 08:38:55
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*> \brief \b DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DLANHS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanhs.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/dlanhs.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/dlanhs.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 DLANHS( NORM, N, A, LDA, WORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER NORM |
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* INTEGER LDA, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DLANHS 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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*> Hessenberg matrix A. |
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*> \endverbatim |
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*> |
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*> \return DLANHS |
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*> \verbatim |
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*> |
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*> DLANHS = ( 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 DLANHS as described |
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*> above. |
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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, DLANHS 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 DOUBLE PRECISION array, dimension (LDA,N) |
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*> The n by n upper Hessenberg matrix A; the part of A below the |
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*> first sub-diagonal is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(N,1). |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), |
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*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not |
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*> 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 doubleOTHERauxiliary |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK ) |
DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, 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 |
CHARACTER NORM |
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DOUBLE PRECISION A( LDA, * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLANHS 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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* Hessenberg matrix A. |
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* |
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* Description |
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* =========== |
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* |
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* DLANHS returns the value |
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* |
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* DLANHS = ( 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 DLANHS as described |
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* above. |
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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, DLANHS is |
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* set to zero. |
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* |
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* A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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* The n by n upper Hessenberg matrix A; the part of A below the |
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* first sub-diagonal is not referenced. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(N,1). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), |
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* where LWORK >= N when NORM = 'I'; otherwise, WORK is not |
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* referenced. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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EXTERNAL DLASSQ |
EXTERNAL DLASSQ |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME |
EXTERNAL LSAME, DISNAN |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, MAX, MIN, SQRT |
INTRINSIC ABS, MIN, SQRT |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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VALUE = ZERO |
VALUE = ZERO |
DO 20 J = 1, N |
DO 20 J = 1, N |
DO 10 I = 1, MIN( N, J+1 ) |
DO 10 I = 1, MIN( N, J+1 ) |
VALUE = MAX( VALUE, ABS( A( I, J ) ) ) |
SUM = ABS( A( I, J ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
10 CONTINUE |
10 CONTINUE |
20 CONTINUE |
20 CONTINUE |
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN |
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN |
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DO 30 I = 1, MIN( N, J+1 ) |
DO 30 I = 1, MIN( N, J+1 ) |
SUM = SUM + ABS( A( I, J ) ) |
SUM = SUM + ABS( A( I, J ) ) |
30 CONTINUE |
30 CONTINUE |
VALUE = MAX( VALUE, SUM ) |
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
40 CONTINUE |
40 CONTINUE |
ELSE IF( LSAME( NORM, 'I' ) ) THEN |
ELSE IF( LSAME( NORM, 'I' ) ) THEN |
* |
* |
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70 CONTINUE |
70 CONTINUE |
VALUE = ZERO |
VALUE = ZERO |
DO 80 I = 1, N |
DO 80 I = 1, N |
VALUE = MAX( VALUE, WORK( I ) ) |
SUM = WORK( I ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
80 CONTINUE |
80 CONTINUE |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
* |
* |