Annotation of rpl/lapack/lapack/zlansb.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLANSB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLANSB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlansb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlansb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlansb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLANSB( 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 WORK( * )
! 30: * COMPLEX*16 AB( LDAB, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZLANSB returns the value of the one norm, or the Frobenius norm, or
! 40: *> the infinity norm, or the element of largest absolute value of an
! 41: *> n by n symmetric band matrix A, with k super-diagonals.
! 42: *> \endverbatim
! 43: *>
! 44: *> \return ZLANSB
! 45: *> \verbatim
! 46: *>
! 47: *> ZLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 48: *> (
! 49: *> ( norm1(A), NORM = '1', 'O' or 'o'
! 50: *> (
! 51: *> ( normI(A), NORM = 'I' or 'i'
! 52: *> (
! 53: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 54: *>
! 55: *> where norm1 denotes the one norm of a matrix (maximum column sum),
! 56: *> normI denotes the infinity norm of a matrix (maximum row sum) and
! 57: *> normF denotes the Frobenius norm of a matrix (square root of sum of
! 58: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 59: *> \endverbatim
! 60: *
! 61: * Arguments:
! 62: * ==========
! 63: *
! 64: *> \param[in] NORM
! 65: *> \verbatim
! 66: *> NORM is CHARACTER*1
! 67: *> Specifies the value to be returned in ZLANSB as described
! 68: *> above.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] UPLO
! 72: *> \verbatim
! 73: *> UPLO is CHARACTER*1
! 74: *> Specifies whether the upper or lower triangular part of the
! 75: *> band matrix A is supplied.
! 76: *> = 'U': Upper triangular part is supplied
! 77: *> = 'L': Lower triangular part is supplied
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] N
! 81: *> \verbatim
! 82: *> N is INTEGER
! 83: *> The order of the matrix A. N >= 0. When N = 0, ZLANSB is
! 84: *> set to zero.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] K
! 88: *> \verbatim
! 89: *> K is INTEGER
! 90: *> The number of super-diagonals or sub-diagonals of the
! 91: *> band matrix A. K >= 0.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in] AB
! 95: *> \verbatim
! 96: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 97: *> The upper or lower triangle of the symmetric band matrix A,
! 98: *> stored in the first K+1 rows of AB. The j-th column of A is
! 99: *> stored in the j-th column of the array AB as follows:
! 100: *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
! 101: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[in] LDAB
! 105: *> \verbatim
! 106: *> LDAB is INTEGER
! 107: *> The leading dimension of the array AB. LDAB >= K+1.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[out] WORK
! 111: *> \verbatim
! 112: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 113: *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 114: *> WORK is not referenced.
! 115: *> \endverbatim
! 116: *
! 117: * Authors:
! 118: * ========
! 119: *
! 120: *> \author Univ. of Tennessee
! 121: *> \author Univ. of California Berkeley
! 122: *> \author Univ. of Colorado Denver
! 123: *> \author NAG Ltd.
! 124: *
! 125: *> \date November 2011
! 126: *
! 127: *> \ingroup complex16OTHERauxiliary
! 128: *
! 129: * =====================================================================
1.1 bertrand 130: DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
131: $ WORK )
132: *
1.8 ! bertrand 133: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 136: * November 2011
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER NORM, UPLO
140: INTEGER K, LDAB, N
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION WORK( * )
144: COMPLEX*16 AB( LDAB, * )
145: * ..
146: *
147: * =====================================================================
148: *
149: * .. Parameters ..
150: DOUBLE PRECISION ONE, ZERO
151: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
152: * ..
153: * .. Local Scalars ..
154: INTEGER I, J, L
155: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME
159: EXTERNAL LSAME
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL ZLASSQ
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC ABS, MAX, MIN, SQRT
166: * ..
167: * .. Executable Statements ..
168: *
169: IF( N.EQ.0 ) THEN
170: VALUE = ZERO
171: ELSE IF( LSAME( NORM, 'M' ) ) THEN
172: *
173: * Find max(abs(A(i,j))).
174: *
175: VALUE = ZERO
176: IF( LSAME( UPLO, 'U' ) ) THEN
177: DO 20 J = 1, N
178: DO 10 I = MAX( K+2-J, 1 ), K + 1
179: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
180: 10 CONTINUE
181: 20 CONTINUE
182: ELSE
183: DO 40 J = 1, N
184: DO 30 I = 1, MIN( N+1-J, K+1 )
185: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
186: 30 CONTINUE
187: 40 CONTINUE
188: END IF
189: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
190: $ ( NORM.EQ.'1' ) ) THEN
191: *
192: * Find normI(A) ( = norm1(A), since A is symmetric).
193: *
194: VALUE = ZERO
195: IF( LSAME( UPLO, 'U' ) ) THEN
196: DO 60 J = 1, N
197: SUM = ZERO
198: L = K + 1 - J
199: DO 50 I = MAX( 1, J-K ), J - 1
200: ABSA = ABS( AB( L+I, J ) )
201: SUM = SUM + ABSA
202: WORK( I ) = WORK( I ) + ABSA
203: 50 CONTINUE
204: WORK( J ) = SUM + ABS( AB( K+1, J ) )
205: 60 CONTINUE
206: DO 70 I = 1, N
207: VALUE = MAX( VALUE, WORK( I ) )
208: 70 CONTINUE
209: ELSE
210: DO 80 I = 1, N
211: WORK( I ) = ZERO
212: 80 CONTINUE
213: DO 100 J = 1, N
214: SUM = WORK( J ) + ABS( AB( 1, J ) )
215: L = 1 - J
216: DO 90 I = J + 1, MIN( N, J+K )
217: ABSA = ABS( AB( L+I, J ) )
218: SUM = SUM + ABSA
219: WORK( I ) = WORK( I ) + ABSA
220: 90 CONTINUE
221: VALUE = MAX( VALUE, SUM )
222: 100 CONTINUE
223: END IF
224: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
225: *
226: * Find normF(A).
227: *
228: SCALE = ZERO
229: SUM = ONE
230: IF( K.GT.0 ) THEN
231: IF( LSAME( UPLO, 'U' ) ) THEN
232: DO 110 J = 2, N
233: CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
234: $ 1, SCALE, SUM )
235: 110 CONTINUE
236: L = K + 1
237: ELSE
238: DO 120 J = 1, N - 1
239: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
240: $ SUM )
241: 120 CONTINUE
242: L = 1
243: END IF
244: SUM = 2*SUM
245: ELSE
246: L = 1
247: END IF
248: CALL ZLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
249: VALUE = SCALE*SQRT( SUM )
250: END IF
251: *
252: ZLANSB = VALUE
253: RETURN
254: *
255: * End of ZLANSB
256: *
257: END
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