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version 1.16, 2017/06/17 11:06:27
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*> \brief \b DLASSQ updates a sum of squares represented in scaled form. |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DLASSQ + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INCX, N |
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* DOUBLE PRECISION SCALE, SUMSQ |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION X( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DLASSQ returns the values scl and smsq such that |
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*> |
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*> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, |
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*> |
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*> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is |
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*> assumed to be non-negative and scl returns the value |
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*> |
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*> scl = max( scale, abs( x( i ) ) ). |
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*> |
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*> scale and sumsq must be supplied in SCALE and SUMSQ and |
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*> scl and smsq are overwritten on SCALE and SUMSQ respectively. |
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*> |
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*> The routine makes only one pass through the vector x. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of elements to be used from the vector X. |
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*> \endverbatim |
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*> |
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*> \param[in] X |
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*> \verbatim |
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*> X is DOUBLE PRECISION array, dimension (N) |
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*> The vector for which a scaled sum of squares is computed. |
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*> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. |
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*> \endverbatim |
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*> |
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*> \param[in] INCX |
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*> \verbatim |
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*> INCX is INTEGER |
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*> The increment between successive values of the vector X. |
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*> INCX > 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] SCALE |
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*> \verbatim |
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*> SCALE is DOUBLE PRECISION |
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*> On entry, the value scale in the equation above. |
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*> On exit, SCALE is overwritten with scl , the scaling factor |
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*> for the sum of squares. |
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*> \endverbatim |
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*> |
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*> \param[in,out] SUMSQ |
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*> \verbatim |
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*> SUMSQ is DOUBLE PRECISION |
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*> On entry, the value sumsq in the equation above. |
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*> On exit, SUMSQ is overwritten with smsq , the basic sum of |
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*> squares from which scl has been factored out. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date December 2016 |
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* |
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*> \ingroup OTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) |
SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INCX, N |
INTEGER INCX, N |
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DOUBLE PRECISION X( * ) |
DOUBLE PRECISION X( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLASSQ returns the values scl and smsq such that |
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* |
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* ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, |
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* |
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* where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is |
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* assumed to be non-negative and scl returns the value |
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* |
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* scl = max( scale, abs( x( i ) ) ). |
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* |
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* scale and sumsq must be supplied in SCALE and SUMSQ and |
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* scl and smsq are overwritten on SCALE and SUMSQ respectively. |
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* |
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* The routine makes only one pass through the vector x. |
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* |
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* Arguments |
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* ========= |
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* |
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* N (input) INTEGER |
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* The number of elements to be used from the vector X. |
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* |
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* X (input) DOUBLE PRECISION array, dimension (N) |
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* The vector for which a scaled sum of squares is computed. |
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* x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. |
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* |
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* INCX (input) INTEGER |
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* The increment between successive values of the vector X. |
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* INCX > 0. |
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* |
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* SCALE (input/output) DOUBLE PRECISION |
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* On entry, the value scale in the equation above. |
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* On exit, SCALE is overwritten with scl , the scaling factor |
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* for the sum of squares. |
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* |
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* SUMSQ (input/output) DOUBLE PRECISION |
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* On entry, the value sumsq in the equation above. |
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* On exit, SUMSQ is overwritten with smsq , the basic sum of |
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* squares from which scl has been factored out. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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INTEGER IX |
INTEGER IX |
DOUBLE PRECISION ABSXI |
DOUBLE PRECISION ABSXI |
* .. |
* .. |
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* .. External Functions .. |
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LOGICAL DISNAN |
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EXTERNAL DISNAN |
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* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS |
INTRINSIC ABS |
* .. |
* .. |
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* |
* |
IF( N.GT.0 ) THEN |
IF( N.GT.0 ) THEN |
DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX |
DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX |
IF( X( IX ).NE.ZERO ) THEN |
ABSXI = ABS( X( IX ) ) |
ABSXI = ABS( X( IX ) ) |
IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN |
IF( SCALE.LT.ABSXI ) THEN |
IF( SCALE.LT.ABSXI ) THEN |
SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 |
SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 |
SCALE = ABSXI |
SCALE = ABSXI |