Annotation of rpl/lapack/lapack/zlangb.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLANGB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLANGB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLANGB( 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 WORK( * )
! 30: * COMPLEX*16 AB( LDAB, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.
! 42: *> \endverbatim
! 43: *>
! 44: *> \return ZLANGB
! 45: *> \verbatim
! 46: *>
! 47: *> ZLANGB = ( 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 ZLANGB as described
! 68: *> above.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] N
! 72: *> \verbatim
! 73: *> N is INTEGER
! 74: *> The order of the matrix A. N >= 0. When N = 0, ZLANGB is
! 75: *> set to zero.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] KL
! 79: *> \verbatim
! 80: *> KL is INTEGER
! 81: *> The number of sub-diagonals of the matrix A. KL >= 0.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] KU
! 85: *> \verbatim
! 86: *> KU is INTEGER
! 87: *> The number of super-diagonals of the matrix A. KU >= 0.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] AB
! 91: *> \verbatim
! 92: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 93: *> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
! 94: *> column of A is stored in the j-th column of the array AB as
! 95: *> follows:
! 96: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] LDAB
! 100: *> \verbatim
! 101: *> LDAB is INTEGER
! 102: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] WORK
! 106: *> \verbatim
! 107: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 108: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
! 109: *> referenced.
! 110: *> \endverbatim
! 111: *
! 112: * Authors:
! 113: * ========
! 114: *
! 115: *> \author Univ. of Tennessee
! 116: *> \author Univ. of California Berkeley
! 117: *> \author Univ. of Colorado Denver
! 118: *> \author NAG Ltd.
! 119: *
! 120: *> \date November 2011
! 121: *
! 122: *> \ingroup complex16GBauxiliary
! 123: *
! 124: * =====================================================================
1.1 bertrand 125: DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
126: $ WORK )
127: *
1.8 ! bertrand 128: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 131: * November 2011
1.1 bertrand 132: *
133: * .. Scalar Arguments ..
134: CHARACTER NORM
135: INTEGER KL, KU, LDAB, N
136: * ..
137: * .. Array Arguments ..
138: DOUBLE PRECISION WORK( * )
139: COMPLEX*16 AB( LDAB, * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Parameters ..
145: DOUBLE PRECISION ONE, ZERO
146: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
147: * ..
148: * .. Local Scalars ..
149: INTEGER I, J, K, L
150: DOUBLE PRECISION SCALE, SUM, VALUE
151: * ..
152: * .. External Functions ..
153: LOGICAL LSAME
154: EXTERNAL LSAME
155: * ..
156: * .. External Subroutines ..
157: EXTERNAL ZLASSQ
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC ABS, MAX, MIN, SQRT
161: * ..
162: * .. Executable Statements ..
163: *
164: IF( N.EQ.0 ) THEN
165: VALUE = ZERO
166: ELSE IF( LSAME( NORM, 'M' ) ) THEN
167: *
168: * Find max(abs(A(i,j))).
169: *
170: VALUE = ZERO
171: DO 20 J = 1, N
172: DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
173: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
174: 10 CONTINUE
175: 20 CONTINUE
176: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
177: *
178: * Find norm1(A).
179: *
180: VALUE = ZERO
181: DO 40 J = 1, N
182: SUM = ZERO
183: DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
184: SUM = SUM + ABS( AB( I, J ) )
185: 30 CONTINUE
186: VALUE = MAX( VALUE, SUM )
187: 40 CONTINUE
188: ELSE IF( LSAME( NORM, 'I' ) ) THEN
189: *
190: * Find normI(A).
191: *
192: DO 50 I = 1, N
193: WORK( I ) = ZERO
194: 50 CONTINUE
195: DO 70 J = 1, N
196: K = KU + 1 - J
197: DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
198: WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
199: 60 CONTINUE
200: 70 CONTINUE
201: VALUE = ZERO
202: DO 80 I = 1, N
203: VALUE = MAX( VALUE, WORK( I ) )
204: 80 CONTINUE
205: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
206: *
207: * Find normF(A).
208: *
209: SCALE = ZERO
210: SUM = ONE
211: DO 90 J = 1, N
212: L = MAX( 1, J-KU )
213: K = KU + 1 - J + L
214: CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
215: 90 CONTINUE
216: VALUE = SCALE*SQRT( SUM )
217: END IF
218: *
219: ZLANGB = VALUE
220: RETURN
221: *
222: * End of ZLANGB
223: *
224: END
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