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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DLASSQ 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DLASSQ + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER INCX, N 00025 * DOUBLE PRECISION SCALE, SUMSQ 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION X( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DLASSQ returns the values scl and smsq such that 00038 *> 00039 *> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, 00040 *> 00041 *> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is 00042 *> assumed to be non-negative and scl returns the value 00043 *> 00044 *> scl = max( scale, abs( x( i ) ) ). 00045 *> 00046 *> scale and sumsq must be supplied in SCALE and SUMSQ and 00047 *> scl and smsq are overwritten on SCALE and SUMSQ respectively. 00048 *> 00049 *> The routine makes only one pass through the vector x. 00050 *> \endverbatim 00051 * 00052 * Arguments: 00053 * ========== 00054 * 00055 *> \param[in] N 00056 *> \verbatim 00057 *> N is INTEGER 00058 *> The number of elements to be used from the vector X. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] X 00062 *> \verbatim 00063 *> X is DOUBLE PRECISION array, dimension (N) 00064 *> The vector for which a scaled sum of squares is computed. 00065 *> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] INCX 00069 *> \verbatim 00070 *> INCX is INTEGER 00071 *> The increment between successive values of the vector X. 00072 *> INCX > 0. 00073 *> \endverbatim 00074 *> 00075 *> \param[in,out] SCALE 00076 *> \verbatim 00077 *> SCALE is DOUBLE PRECISION 00078 *> On entry, the value scale in the equation above. 00079 *> On exit, SCALE is overwritten with scl , the scaling factor 00080 *> for the sum of squares. 00081 *> \endverbatim 00082 *> 00083 *> \param[in,out] SUMSQ 00084 *> \verbatim 00085 *> SUMSQ is DOUBLE PRECISION 00086 *> On entry, the value sumsq in the equation above. 00087 *> On exit, SUMSQ is overwritten with smsq , the basic sum of 00088 *> squares from which scl has been factored out. 00089 *> \endverbatim 00090 * 00091 * Authors: 00092 * ======== 00093 * 00094 *> \author Univ. of Tennessee 00095 *> \author Univ. of California Berkeley 00096 *> \author Univ. of Colorado Denver 00097 *> \author NAG Ltd. 00098 * 00099 *> \date November 2011 00100 * 00101 *> \ingroup auxOTHERauxiliary 00102 * 00103 * ===================================================================== 00104 SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) 00105 * 00106 * -- LAPACK auxiliary routine (version 3.4.0) -- 00107 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00108 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00109 * November 2011 00110 * 00111 * .. Scalar Arguments .. 00112 INTEGER INCX, N 00113 DOUBLE PRECISION SCALE, SUMSQ 00114 * .. 00115 * .. Array Arguments .. 00116 DOUBLE PRECISION X( * ) 00117 * .. 00118 * 00119 * ===================================================================== 00120 * 00121 * .. Parameters .. 00122 DOUBLE PRECISION ZERO 00123 PARAMETER ( ZERO = 0.0D+0 ) 00124 * .. 00125 * .. Local Scalars .. 00126 INTEGER IX 00127 DOUBLE PRECISION ABSXI 00128 * .. 00129 * .. Intrinsic Functions .. 00130 INTRINSIC ABS 00131 * .. 00132 * .. Executable Statements .. 00133 * 00134 IF( N.GT.0 ) THEN 00135 DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX 00136 IF( X( IX ).NE.ZERO ) THEN 00137 ABSXI = ABS( X( IX ) ) 00138 IF( SCALE.LT.ABSXI ) THEN 00139 SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 00140 SCALE = ABSXI 00141 ELSE 00142 SUMSQ = SUMSQ + ( ABSXI / SCALE )**2 00143 END IF 00144 END IF 00145 10 CONTINUE 00146 END IF 00147 RETURN 00148 * 00149 * End of DLASSQ 00150 * 00151 END