Annotation of rpl/lapack/lapack/dlangb.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLANGB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLANGB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
! 22: * WORK )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER NORM
! 26: * INTEGER KL, KU, LDAB, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION AB( LDAB, * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DLANGB returns the value of the one norm, or the Frobenius norm, or
! 39: *> the infinity norm, or the element of largest absolute value of an
! 40: *> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
! 41: *> \endverbatim
! 42: *>
! 43: *> \return DLANGB
! 44: *> \verbatim
! 45: *>
! 46: *> DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 47: *> (
! 48: *> ( norm1(A), NORM = '1', 'O' or 'o'
! 49: *> (
! 50: *> ( normI(A), NORM = 'I' or 'i'
! 51: *> (
! 52: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 53: *>
! 54: *> where norm1 denotes the one norm of a matrix (maximum column sum),
! 55: *> normI denotes the infinity norm of a matrix (maximum row sum) and
! 56: *> normF denotes the Frobenius norm of a matrix (square root of sum of
! 57: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 58: *> \endverbatim
! 59: *
! 60: * Arguments:
! 61: * ==========
! 62: *
! 63: *> \param[in] NORM
! 64: *> \verbatim
! 65: *> NORM is CHARACTER*1
! 66: *> Specifies the value to be returned in DLANGB as described
! 67: *> above.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] N
! 71: *> \verbatim
! 72: *> N is INTEGER
! 73: *> The order of the matrix A. N >= 0. When N = 0, DLANGB is
! 74: *> set to zero.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] KL
! 78: *> \verbatim
! 79: *> KL is INTEGER
! 80: *> The number of sub-diagonals of the matrix A. KL >= 0.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] KU
! 84: *> \verbatim
! 85: *> KU is INTEGER
! 86: *> The number of super-diagonals of the matrix A. KU >= 0.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] AB
! 90: *> \verbatim
! 91: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
! 92: *> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
! 93: *> column of A is stored in the j-th column of the array AB as
! 94: *> follows:
! 95: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] LDAB
! 99: *> \verbatim
! 100: *> LDAB is INTEGER
! 101: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[out] WORK
! 105: *> \verbatim
! 106: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 107: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
! 108: *> referenced.
! 109: *> \endverbatim
! 110: *
! 111: * Authors:
! 112: * ========
! 113: *
! 114: *> \author Univ. of Tennessee
! 115: *> \author Univ. of California Berkeley
! 116: *> \author Univ. of Colorado Denver
! 117: *> \author NAG Ltd.
! 118: *
! 119: *> \date November 2011
! 120: *
! 121: *> \ingroup doubleGBauxiliary
! 122: *
! 123: * =====================================================================
1.1 bertrand 124: DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
125: $ WORK )
126: *
1.8 ! bertrand 127: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 130: * November 2011
1.1 bertrand 131: *
132: * .. Scalar Arguments ..
133: CHARACTER NORM
134: INTEGER KL, KU, LDAB, N
135: * ..
136: * .. Array Arguments ..
137: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
138: * ..
139: *
140: * =====================================================================
141: *
142: *
143: * .. Parameters ..
144: DOUBLE PRECISION ONE, ZERO
145: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
146: * ..
147: * .. Local Scalars ..
148: INTEGER I, J, K, L
149: DOUBLE PRECISION SCALE, SUM, VALUE
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL DLASSQ
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: EXTERNAL LSAME
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC ABS, MAX, MIN, SQRT
160: * ..
161: * .. Executable Statements ..
162: *
163: IF( N.EQ.0 ) THEN
164: VALUE = ZERO
165: ELSE IF( LSAME( NORM, 'M' ) ) THEN
166: *
167: * Find max(abs(A(i,j))).
168: *
169: VALUE = ZERO
170: DO 20 J = 1, N
171: DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
172: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
173: 10 CONTINUE
174: 20 CONTINUE
175: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
176: *
177: * Find norm1(A).
178: *
179: VALUE = ZERO
180: DO 40 J = 1, N
181: SUM = ZERO
182: DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
183: SUM = SUM + ABS( AB( I, J ) )
184: 30 CONTINUE
185: VALUE = MAX( VALUE, SUM )
186: 40 CONTINUE
187: ELSE IF( LSAME( NORM, 'I' ) ) THEN
188: *
189: * Find normI(A).
190: *
191: DO 50 I = 1, N
192: WORK( I ) = ZERO
193: 50 CONTINUE
194: DO 70 J = 1, N
195: K = KU + 1 - J
196: DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
197: WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
198: 60 CONTINUE
199: 70 CONTINUE
200: VALUE = ZERO
201: DO 80 I = 1, N
202: VALUE = MAX( VALUE, WORK( I ) )
203: 80 CONTINUE
204: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
205: *
206: * Find normF(A).
207: *
208: SCALE = ZERO
209: SUM = ONE
210: DO 90 J = 1, N
211: L = MAX( 1, J-KU )
212: K = KU + 1 - J + L
213: CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
214: 90 CONTINUE
215: VALUE = SCALE*SQRT( SUM )
216: END IF
217: *
218: DLANGB = VALUE
219: RETURN
220: *
221: * End of DLANGB
222: *
223: END
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