Annotation of rpl/lapack/lapack/zlarnv.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLARNV
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLARNV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarnv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarnv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarnv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER IDIST, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER ISEED( 4 )
! 28: * COMPLEX*16 X( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZLARNV returns a vector of n random complex numbers from a uniform or
! 38: *> normal distribution.
! 39: *> \endverbatim
! 40: *
! 41: * Arguments:
! 42: * ==========
! 43: *
! 44: *> \param[in] IDIST
! 45: *> \verbatim
! 46: *> IDIST is INTEGER
! 47: *> Specifies the distribution of the random numbers:
! 48: *> = 1: real and imaginary parts each uniform (0,1)
! 49: *> = 2: real and imaginary parts each uniform (-1,1)
! 50: *> = 3: real and imaginary parts each normal (0,1)
! 51: *> = 4: uniformly distributed on the disc abs(z) < 1
! 52: *> = 5: uniformly distributed on the circle abs(z) = 1
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in,out] ISEED
! 56: *> \verbatim
! 57: *> ISEED is INTEGER array, dimension (4)
! 58: *> On entry, the seed of the random number generator; the array
! 59: *> elements must be between 0 and 4095, and ISEED(4) must be
! 60: *> odd.
! 61: *> On exit, the seed is updated.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] N
! 65: *> \verbatim
! 66: *> N is INTEGER
! 67: *> The number of random numbers to be generated.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[out] X
! 71: *> \verbatim
! 72: *> X is COMPLEX*16 array, dimension (N)
! 73: *> The generated random numbers.
! 74: *> \endverbatim
! 75: *
! 76: * Authors:
! 77: * ========
! 78: *
! 79: *> \author Univ. of Tennessee
! 80: *> \author Univ. of California Berkeley
! 81: *> \author Univ. of Colorado Denver
! 82: *> \author NAG Ltd.
! 83: *
! 84: *> \date November 2011
! 85: *
! 86: *> \ingroup complex16OTHERauxiliary
! 87: *
! 88: *> \par Further Details:
! 89: * =====================
! 90: *>
! 91: *> \verbatim
! 92: *>
! 93: *> This routine calls the auxiliary routine DLARUV to generate random
! 94: *> real numbers from a uniform (0,1) distribution, in batches of up to
! 95: *> 128 using vectorisable code. The Box-Muller method is used to
! 96: *> transform numbers from a uniform to a normal distribution.
! 97: *> \endverbatim
! 98: *>
! 99: * =====================================================================
1.1 bertrand 100: SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
101: *
1.8 ! bertrand 102: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 103: * -- LAPACK is a software package provided by Univ. of Tennessee, --
104: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 105: * November 2011
1.1 bertrand 106: *
107: * .. Scalar Arguments ..
108: INTEGER IDIST, N
109: * ..
110: * .. Array Arguments ..
111: INTEGER ISEED( 4 )
112: COMPLEX*16 X( * )
113: * ..
114: *
115: * =====================================================================
116: *
117: * .. Parameters ..
118: DOUBLE PRECISION ZERO, ONE, TWO
119: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
120: INTEGER LV
121: PARAMETER ( LV = 128 )
122: DOUBLE PRECISION TWOPI
123: PARAMETER ( TWOPI = 6.2831853071795864769252867663D+0 )
124: * ..
125: * .. Local Scalars ..
126: INTEGER I, IL, IV
127: * ..
128: * .. Local Arrays ..
129: DOUBLE PRECISION U( LV )
130: * ..
131: * .. Intrinsic Functions ..
132: INTRINSIC DCMPLX, EXP, LOG, MIN, SQRT
133: * ..
134: * .. External Subroutines ..
135: EXTERNAL DLARUV
136: * ..
137: * .. Executable Statements ..
138: *
139: DO 60 IV = 1, N, LV / 2
140: IL = MIN( LV / 2, N-IV+1 )
141: *
142: * Call DLARUV to generate 2*IL real numbers from a uniform (0,1)
143: * distribution (2*IL <= LV)
144: *
145: CALL DLARUV( ISEED, 2*IL, U )
146: *
147: IF( IDIST.EQ.1 ) THEN
148: *
149: * Copy generated numbers
150: *
151: DO 10 I = 1, IL
152: X( IV+I-1 ) = DCMPLX( U( 2*I-1 ), U( 2*I ) )
153: 10 CONTINUE
154: ELSE IF( IDIST.EQ.2 ) THEN
155: *
156: * Convert generated numbers to uniform (-1,1) distribution
157: *
158: DO 20 I = 1, IL
159: X( IV+I-1 ) = DCMPLX( TWO*U( 2*I-1 )-ONE,
160: $ TWO*U( 2*I )-ONE )
161: 20 CONTINUE
162: ELSE IF( IDIST.EQ.3 ) THEN
163: *
164: * Convert generated numbers to normal (0,1) distribution
165: *
166: DO 30 I = 1, IL
167: X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )*
168: $ EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
169: 30 CONTINUE
170: ELSE IF( IDIST.EQ.4 ) THEN
171: *
172: * Convert generated numbers to complex numbers uniformly
173: * distributed on the unit disk
174: *
175: DO 40 I = 1, IL
176: X( IV+I-1 ) = SQRT( U( 2*I-1 ) )*
177: $ EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
178: 40 CONTINUE
179: ELSE IF( IDIST.EQ.5 ) THEN
180: *
181: * Convert generated numbers to complex numbers uniformly
182: * distributed on the unit circle
183: *
184: DO 50 I = 1, IL
185: X( IV+I-1 ) = EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
186: 50 CONTINUE
187: END IF
188: 60 CONTINUE
189: RETURN
190: *
191: * End of ZLARNV
192: *
193: END
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