Annotation of rpl/lapack/lapack/dlansb.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLANSB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLANSB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
! 22: * WORK )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER NORM, UPLO
! 26: * INTEGER K, LDAB, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION AB( LDAB, * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DLANSB 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 symmetric band matrix A, with k super-diagonals.
! 41: *> \endverbatim
! 42: *>
! 43: *> \return DLANSB
! 44: *> \verbatim
! 45: *>
! 46: *> DLANSB = ( 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 DLANSB as described
! 67: *> above.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] UPLO
! 71: *> \verbatim
! 72: *> UPLO is CHARACTER*1
! 73: *> Specifies whether the upper or lower triangular part of the
! 74: *> band matrix A is supplied.
! 75: *> = 'U': Upper triangular part is supplied
! 76: *> = 'L': Lower triangular part is supplied
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] N
! 80: *> \verbatim
! 81: *> N is INTEGER
! 82: *> The order of the matrix A. N >= 0. When N = 0, DLANSB is
! 83: *> set to zero.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] K
! 87: *> \verbatim
! 88: *> K is INTEGER
! 89: *> The number of super-diagonals or sub-diagonals of the
! 90: *> band matrix A. K >= 0.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in] AB
! 94: *> \verbatim
! 95: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
! 96: *> The upper or lower triangle of the symmetric band matrix A,
! 97: *> stored in the first K+1 rows of AB. The j-th column of A is
! 98: *> stored in the j-th column of the array AB as follows:
! 99: *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
! 100: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] LDAB
! 104: *> \verbatim
! 105: *> LDAB is INTEGER
! 106: *> The leading dimension of the array AB. LDAB >= K+1.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[out] WORK
! 110: *> \verbatim
! 111: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 112: *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 113: *> WORK is not referenced.
! 114: *> \endverbatim
! 115: *
! 116: * Authors:
! 117: * ========
! 118: *
! 119: *> \author Univ. of Tennessee
! 120: *> \author Univ. of California Berkeley
! 121: *> \author Univ. of Colorado Denver
! 122: *> \author NAG Ltd.
! 123: *
! 124: *> \date November 2011
! 125: *
! 126: *> \ingroup doubleOTHERauxiliary
! 127: *
! 128: * =====================================================================
1.1 bertrand 129: DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
130: $ WORK )
131: *
1.8 ! bertrand 132: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 133: * -- LAPACK is a software package provided by Univ. of Tennessee, --
134: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 135: * November 2011
1.1 bertrand 136: *
137: * .. Scalar Arguments ..
138: CHARACTER NORM, UPLO
139: INTEGER K, LDAB, N
140: * ..
141: * .. Array Arguments ..
142: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
143: * ..
144: *
145: * =====================================================================
146: *
147: * .. Parameters ..
148: DOUBLE PRECISION ONE, ZERO
149: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
150: * ..
151: * .. Local Scalars ..
152: INTEGER I, J, L
153: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
154: * ..
155: * .. External Subroutines ..
156: EXTERNAL DLASSQ
157: * ..
158: * .. External Functions ..
159: LOGICAL LSAME
160: EXTERNAL LSAME
161: * ..
162: * .. Intrinsic Functions ..
163: INTRINSIC ABS, MAX, MIN, SQRT
164: * ..
165: * .. Executable Statements ..
166: *
167: IF( N.EQ.0 ) THEN
168: VALUE = ZERO
169: ELSE IF( LSAME( NORM, 'M' ) ) THEN
170: *
171: * Find max(abs(A(i,j))).
172: *
173: VALUE = ZERO
174: IF( LSAME( UPLO, 'U' ) ) THEN
175: DO 20 J = 1, N
176: DO 10 I = MAX( K+2-J, 1 ), K + 1
177: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
178: 10 CONTINUE
179: 20 CONTINUE
180: ELSE
181: DO 40 J = 1, N
182: DO 30 I = 1, MIN( N+1-J, K+1 )
183: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
184: 30 CONTINUE
185: 40 CONTINUE
186: END IF
187: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
188: $ ( NORM.EQ.'1' ) ) THEN
189: *
190: * Find normI(A) ( = norm1(A), since A is symmetric).
191: *
192: VALUE = ZERO
193: IF( LSAME( UPLO, 'U' ) ) THEN
194: DO 60 J = 1, N
195: SUM = ZERO
196: L = K + 1 - J
197: DO 50 I = MAX( 1, J-K ), J - 1
198: ABSA = ABS( AB( L+I, J ) )
199: SUM = SUM + ABSA
200: WORK( I ) = WORK( I ) + ABSA
201: 50 CONTINUE
202: WORK( J ) = SUM + ABS( AB( K+1, J ) )
203: 60 CONTINUE
204: DO 70 I = 1, N
205: VALUE = MAX( VALUE, WORK( I ) )
206: 70 CONTINUE
207: ELSE
208: DO 80 I = 1, N
209: WORK( I ) = ZERO
210: 80 CONTINUE
211: DO 100 J = 1, N
212: SUM = WORK( J ) + ABS( AB( 1, J ) )
213: L = 1 - J
214: DO 90 I = J + 1, MIN( N, J+K )
215: ABSA = ABS( AB( L+I, J ) )
216: SUM = SUM + ABSA
217: WORK( I ) = WORK( I ) + ABSA
218: 90 CONTINUE
219: VALUE = MAX( VALUE, SUM )
220: 100 CONTINUE
221: END IF
222: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
223: *
224: * Find normF(A).
225: *
226: SCALE = ZERO
227: SUM = ONE
228: IF( K.GT.0 ) THEN
229: IF( LSAME( UPLO, 'U' ) ) THEN
230: DO 110 J = 2, N
231: CALL DLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
232: $ 1, SCALE, SUM )
233: 110 CONTINUE
234: L = K + 1
235: ELSE
236: DO 120 J = 1, N - 1
237: CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
238: $ SUM )
239: 120 CONTINUE
240: L = 1
241: END IF
242: SUM = 2*SUM
243: ELSE
244: L = 1
245: END IF
246: CALL DLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
247: VALUE = SCALE*SQRT( SUM )
248: END IF
249: *
250: DLANSB = VALUE
251: RETURN
252: *
253: * End of DLANSB
254: *
255: END
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