Annotation of rpl/lapack/lapack/zlange.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLANGE
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLANGE + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlange.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlange.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlange.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER NORM
! 25: * INTEGER LDA, M, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION WORK( * )
! 29: * COMPLEX*16 A( LDA, * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZLANGE returns the value of the one norm, or the Frobenius norm, or
! 39: *> the infinity norm, or the element of largest absolute value of a
! 40: *> complex matrix A.
! 41: *> \endverbatim
! 42: *>
! 43: *> \return ZLANGE
! 44: *> \verbatim
! 45: *>
! 46: *> ZLANGE = ( 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 ZLANGE as described
! 67: *> above.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] M
! 71: *> \verbatim
! 72: *> M is INTEGER
! 73: *> The number of rows of the matrix A. M >= 0. When M = 0,
! 74: *> ZLANGE is set to zero.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] N
! 78: *> \verbatim
! 79: *> N is INTEGER
! 80: *> The number of columns of the matrix A. N >= 0. When N = 0,
! 81: *> ZLANGE is set to zero.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] A
! 85: *> \verbatim
! 86: *> A is COMPLEX*16 array, dimension (LDA,N)
! 87: *> The m by n matrix A.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] LDA
! 91: *> \verbatim
! 92: *> LDA is INTEGER
! 93: *> The leading dimension of the array A. LDA >= max(M,1).
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[out] WORK
! 97: *> \verbatim
! 98: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 99: *> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
! 100: *> referenced.
! 101: *> \endverbatim
! 102: *
! 103: * Authors:
! 104: * ========
! 105: *
! 106: *> \author Univ. of Tennessee
! 107: *> \author Univ. of California Berkeley
! 108: *> \author Univ. of Colorado Denver
! 109: *> \author NAG Ltd.
! 110: *
! 111: *> \date November 2011
! 112: *
! 113: *> \ingroup complex16GEauxiliary
! 114: *
! 115: * =====================================================================
1.1 bertrand 116: DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK )
117: *
1.8 ! bertrand 118: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 119: * -- LAPACK is a software package provided by Univ. of Tennessee, --
120: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 121: * November 2011
1.1 bertrand 122: *
123: * .. Scalar Arguments ..
124: CHARACTER NORM
125: INTEGER LDA, M, N
126: * ..
127: * .. Array Arguments ..
128: DOUBLE PRECISION WORK( * )
129: COMPLEX*16 A( LDA, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ONE, ZERO
136: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
137: * ..
138: * .. Local Scalars ..
139: INTEGER I, J
140: DOUBLE PRECISION SCALE, SUM, VALUE
141: * ..
142: * .. External Functions ..
143: LOGICAL LSAME
144: EXTERNAL LSAME
145: * ..
146: * .. External Subroutines ..
147: EXTERNAL ZLASSQ
148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC ABS, MAX, MIN, SQRT
151: * ..
152: * .. Executable Statements ..
153: *
154: IF( MIN( M, N ).EQ.0 ) THEN
155: VALUE = ZERO
156: ELSE IF( LSAME( NORM, 'M' ) ) THEN
157: *
158: * Find max(abs(A(i,j))).
159: *
160: VALUE = ZERO
161: DO 20 J = 1, N
162: DO 10 I = 1, M
163: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
164: 10 CONTINUE
165: 20 CONTINUE
166: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
167: *
168: * Find norm1(A).
169: *
170: VALUE = ZERO
171: DO 40 J = 1, N
172: SUM = ZERO
173: DO 30 I = 1, M
174: SUM = SUM + ABS( A( I, J ) )
175: 30 CONTINUE
176: VALUE = MAX( VALUE, SUM )
177: 40 CONTINUE
178: ELSE IF( LSAME( NORM, 'I' ) ) THEN
179: *
180: * Find normI(A).
181: *
182: DO 50 I = 1, M
183: WORK( I ) = ZERO
184: 50 CONTINUE
185: DO 70 J = 1, N
186: DO 60 I = 1, M
187: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
188: 60 CONTINUE
189: 70 CONTINUE
190: VALUE = ZERO
191: DO 80 I = 1, M
192: VALUE = MAX( VALUE, WORK( I ) )
193: 80 CONTINUE
194: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
195: *
196: * Find normF(A).
197: *
198: SCALE = ZERO
199: SUM = ONE
200: DO 90 J = 1, N
201: CALL ZLASSQ( M, A( 1, J ), 1, SCALE, SUM )
202: 90 CONTINUE
203: VALUE = SCALE*SQRT( SUM )
204: END IF
205: *
206: ZLANGE = VALUE
207: RETURN
208: *
209: * End of ZLANGE
210: *
211: END
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