Annotation of rpl/lapack/lapack/dlanhs.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLANHS
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLANHS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanhs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanhs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanhs.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER NORM
! 25: * INTEGER LDA, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION A( LDA, * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DLANHS returns the value of the one norm, or the Frobenius norm, or
! 38: *> the infinity norm, or the element of largest absolute value of a
! 39: *> Hessenberg matrix A.
! 40: *> \endverbatim
! 41: *>
! 42: *> \return DLANHS
! 43: *> \verbatim
! 44: *>
! 45: *> DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 46: *> (
! 47: *> ( norm1(A), NORM = '1', 'O' or 'o'
! 48: *> (
! 49: *> ( normI(A), NORM = 'I' or 'i'
! 50: *> (
! 51: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 52: *>
! 53: *> where norm1 denotes the one norm of a matrix (maximum column sum),
! 54: *> normI denotes the infinity norm of a matrix (maximum row sum) and
! 55: *> normF denotes the Frobenius norm of a matrix (square root of sum of
! 56: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 57: *> \endverbatim
! 58: *
! 59: * Arguments:
! 60: * ==========
! 61: *
! 62: *> \param[in] NORM
! 63: *> \verbatim
! 64: *> NORM is CHARACTER*1
! 65: *> Specifies the value to be returned in DLANHS as described
! 66: *> above.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] N
! 70: *> \verbatim
! 71: *> N is INTEGER
! 72: *> The order of the matrix A. N >= 0. When N = 0, DLANHS is
! 73: *> set to zero.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] A
! 77: *> \verbatim
! 78: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 79: *> The n by n upper Hessenberg matrix A; the part of A below the
! 80: *> first sub-diagonal is not referenced.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] LDA
! 84: *> \verbatim
! 85: *> LDA is INTEGER
! 86: *> The leading dimension of the array A. LDA >= max(N,1).
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[out] WORK
! 90: *> \verbatim
! 91: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 92: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
! 93: *> referenced.
! 94: *> \endverbatim
! 95: *
! 96: * Authors:
! 97: * ========
! 98: *
! 99: *> \author Univ. of Tennessee
! 100: *> \author Univ. of California Berkeley
! 101: *> \author Univ. of Colorado Denver
! 102: *> \author NAG Ltd.
! 103: *
! 104: *> \date November 2011
! 105: *
! 106: *> \ingroup doubleOTHERauxiliary
! 107: *
! 108: * =====================================================================
1.1 bertrand 109: DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
110: *
1.8 ! bertrand 111: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 112: * -- LAPACK is a software package provided by Univ. of Tennessee, --
113: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 114: * November 2011
1.1 bertrand 115: *
116: * .. Scalar Arguments ..
117: CHARACTER NORM
118: INTEGER LDA, N
119: * ..
120: * .. Array Arguments ..
121: DOUBLE PRECISION A( LDA, * ), WORK( * )
122: * ..
123: *
124: * =====================================================================
125: *
126: * .. Parameters ..
127: DOUBLE PRECISION ONE, ZERO
128: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
129: * ..
130: * .. Local Scalars ..
131: INTEGER I, J
132: DOUBLE PRECISION SCALE, SUM, VALUE
133: * ..
134: * .. External Subroutines ..
135: EXTERNAL DLASSQ
136: * ..
137: * .. External Functions ..
138: LOGICAL LSAME
139: EXTERNAL LSAME
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC ABS, MAX, MIN, SQRT
143: * ..
144: * .. Executable Statements ..
145: *
146: IF( N.EQ.0 ) THEN
147: VALUE = ZERO
148: ELSE IF( LSAME( NORM, 'M' ) ) THEN
149: *
150: * Find max(abs(A(i,j))).
151: *
152: VALUE = ZERO
153: DO 20 J = 1, N
154: DO 10 I = 1, MIN( N, J+1 )
155: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
156: 10 CONTINUE
157: 20 CONTINUE
158: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
159: *
160: * Find norm1(A).
161: *
162: VALUE = ZERO
163: DO 40 J = 1, N
164: SUM = ZERO
165: DO 30 I = 1, MIN( N, J+1 )
166: SUM = SUM + ABS( A( I, J ) )
167: 30 CONTINUE
168: VALUE = MAX( VALUE, SUM )
169: 40 CONTINUE
170: ELSE IF( LSAME( NORM, 'I' ) ) THEN
171: *
172: * Find normI(A).
173: *
174: DO 50 I = 1, N
175: WORK( I ) = ZERO
176: 50 CONTINUE
177: DO 70 J = 1, N
178: DO 60 I = 1, MIN( N, J+1 )
179: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
180: 60 CONTINUE
181: 70 CONTINUE
182: VALUE = ZERO
183: DO 80 I = 1, N
184: VALUE = MAX( VALUE, WORK( I ) )
185: 80 CONTINUE
186: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
187: *
188: * Find normF(A).
189: *
190: SCALE = ZERO
191: SUM = ONE
192: DO 90 J = 1, N
193: CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
194: 90 CONTINUE
195: VALUE = SCALE*SQRT( SUM )
196: END IF
197: *
198: DLANHS = VALUE
199: RETURN
200: *
201: * End of DLANHS
202: *
203: END
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