numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/clanhs.f | 5747B | -rw-r--r-- |
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*> \brief \b CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CLANHS + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clanhs.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhs.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhs.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * REAL FUNCTION CLANHS( NORM, N, A, LDA, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER LDA, N * .. * .. Array Arguments .. * REAL WORK( * ) * COMPLEX A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLANHS returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> Hessenberg matrix A. *> \endverbatim *> *> \return CLANHS *> \verbatim *> *> CLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> 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 consistent matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in CLANHS as described *> above. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, CLANHS is *> set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The n by n upper Hessenberg matrix A; the part of A below the *> first sub-diagonal is not referenced. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(N,1). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (MAX(1,LWORK)), *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not *> referenced. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup lanhs * * ===================================================================== REAL FUNCTION CLANHS( NORM, N, A, LDA, WORK ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER NORM INTEGER LDA, N * .. * .. Array Arguments .. REAL WORK( * ) COMPLEX A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL SCALE, SUM, VALUE * .. * .. External Functions .. LOGICAL LSAME, SISNAN EXTERNAL LSAME, SISNAN * .. * .. External Subroutines .. EXTERNAL CLASSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, MIN, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN VALUE = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO DO 20 J = 1, N DO 10 I = 1, MIN( N, J+1 ) SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN * * Find norm1(A). * VALUE = ZERO DO 40 J = 1, N SUM = ZERO DO 30 I = 1, MIN( N, J+1 ) SUM = SUM + ABS( A( I, J ) ) 30 CONTINUE IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 40 CONTINUE ELSE IF( LSAME( NORM, 'I' ) ) THEN * * Find normI(A). * DO 50 I = 1, N WORK( I ) = ZERO 50 CONTINUE DO 70 J = 1, N DO 60 I = 1, MIN( N, J+1 ) WORK( I ) = WORK( I ) + ABS( A( I, J ) ) 60 CONTINUE 70 CONTINUE VALUE = ZERO DO 80 I = 1, N SUM = WORK( I ) IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 80 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. $ ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE DO 90 J = 1, N CALL CLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM ) 90 CONTINUE VALUE = SCALE*SQRT( SUM ) END IF * CLANHS = VALUE RETURN * * End of CLANHS * END