julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
143 lines
3.9 KiB
FortranFixed
143 lines
3.9 KiB
FortranFixed
DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
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*
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* -- LAPACK auxiliary routine (version 3.2) --
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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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* November 2006
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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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* 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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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION SCALE, SUM, VALUE
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* ..
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* .. External Subroutines ..
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EXTERNAL DLASSQ
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, 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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VALUE = ZERO
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ELSE 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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VALUE = ZERO
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DO 20 J = 1, N
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DO 10 I = 1, MIN( N, J+1 )
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VALUE = MAX( VALUE, ABS( A( I, J ) ) )
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10 CONTINUE
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20 CONTINUE
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ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
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*
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* Find norm1(A).
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*
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VALUE = ZERO
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DO 40 J = 1, N
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SUM = ZERO
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DO 30 I = 1, MIN( N, J+1 )
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SUM = SUM + ABS( A( I, J ) )
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30 CONTINUE
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VALUE = MAX( VALUE, SUM )
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40 CONTINUE
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ELSE IF( LSAME( NORM, 'I' ) ) THEN
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*
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* Find normI(A).
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*
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DO 50 I = 1, N
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WORK( I ) = ZERO
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50 CONTINUE
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DO 70 J = 1, N
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DO 60 I = 1, MIN( N, J+1 )
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WORK( I ) = WORK( I ) + ABS( A( I, J ) )
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60 CONTINUE
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70 CONTINUE
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VALUE = ZERO
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DO 80 I = 1, N
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VALUE = MAX( VALUE, WORK( I ) )
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80 CONTINUE
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
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*
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* Find normF(A).
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*
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SCALE = ZERO
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SUM = ONE
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DO 90 J = 1, N
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CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
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90 CONTINUE
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VALUE = SCALE*SQRT( SUM )
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END IF
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*
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DLANHS = VALUE
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RETURN
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*
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* End of DLANHS
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*
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END
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