Add graph references
This commit is contained in:
Abdelrahman Said
+512
@@ -0,0 +1,512 @@
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/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* > \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix.
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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> \htmlonly
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> Download DLASR + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f
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">
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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/dlasr.f
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">
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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/dlasr.f
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">
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> [TXT]</a>
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> \endhtmlonly
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Definition:
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===========
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SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
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CHARACTER DIRECT, PIVOT, SIDE
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INTEGER LDA, M, N
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DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
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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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> DLASR applies a sequence of plane rotations to a real matrix A,
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> from either the left or the right.
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>
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> When SIDE = 'L', the transformation takes the form
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>
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> A := P*A
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>
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> and when SIDE = 'R', the transformation takes the form
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>
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> A := A*P**T
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>
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> where P is an orthogonal matrix consisting of a sequence of z plane
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> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
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> and P**T is the transpose of P.
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>
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> When DIRECT = 'F' (Forward sequence), then
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>
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> P = P(z-1) * ... * P(2) * P(1)
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>
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> and when DIRECT = 'B' (Backward sequence), then
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>
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> P = P(1) * P(2) * ... * P(z-1)
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>
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> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
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>
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> R(k) = ( c(k) s(k) )
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> = ( -s(k) c(k) ).
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>
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> When PIVOT = 'V' (Variable pivot), the rotation is performed
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> for the plane (k,k+1), i.e., P(k) has the form
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>
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> P(k) = ( 1 )
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> ( ... )
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> ( 1 )
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> ( c(k) s(k) )
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> ( -s(k) c(k) )
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> ( 1 )
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> ( ... )
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> ( 1 )
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>
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> where R(k) appears as a rank-2 modification to the identity matrix in
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> rows and columns k and k+1.
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>
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> When PIVOT = 'T' (Top pivot), the rotation is performed for the
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> plane (1,k+1), so P(k) has the form
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>
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> P(k) = ( c(k) s(k) )
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> ( 1 )
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> ( ... )
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> ( 1 )
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> ( -s(k) c(k) )
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> ( 1 )
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> ( ... )
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> ( 1 )
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>
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> where R(k) appears in rows and columns 1 and k+1.
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>
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> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
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> performed for the plane (k,z), giving P(k) the form
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>
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> P(k) = ( 1 )
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> ( ... )
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> ( 1 )
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> ( c(k) s(k) )
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> ( 1 )
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> ( ... )
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> ( 1 )
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> ( -s(k) c(k) )
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>
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> where R(k) appears in rows and columns k and z. The rotations are
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> performed without ever forming P(k) explicitly.
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> \endverbatim
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Arguments:
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==========
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> \param[in] SIDE
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> \verbatim
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> SIDE is CHARACTER*1
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> Specifies whether the plane rotation matrix P is applied to
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> A on the left or the right.
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> = 'L': Left, compute A := P*A
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> = 'R': Right, compute A:= A*P**T
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> \endverbatim
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>
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> \param[in] PIVOT
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> \verbatim
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> PIVOT is CHARACTER*1
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> Specifies the plane for which P(k) is a plane rotation
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> matrix.
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> = 'V': Variable pivot, the plane (k,k+1)
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> = 'T': Top pivot, the plane (1,k+1)
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> = 'B': Bottom pivot, the plane (k,z)
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> \endverbatim
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>
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> \param[in] DIRECT
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> \verbatim
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> DIRECT is CHARACTER*1
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> Specifies whether P is a forward or backward sequence of
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> plane rotations.
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> = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
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> = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
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> \endverbatim
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>
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> \param[in] M
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> \verbatim
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> M is INTEGER
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> The number of rows of the matrix A. If m <= 1, an immediate
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> return is effected.
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> \endverbatim
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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 columns of the matrix A. If n <= 1, an
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> immediate return is effected.
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> \endverbatim
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>
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> \param[in] C
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> \verbatim
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> C is DOUBLE PRECISION array, dimension
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> (M-1) if SIDE = 'L'
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> (N-1) if SIDE = 'R'
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> The cosines c(k) of the plane rotations.
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> \endverbatim
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>
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> \param[in] S
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> \verbatim
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> S is DOUBLE PRECISION array, dimension
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> (M-1) if SIDE = 'L'
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> (N-1) if SIDE = 'R'
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> The sines s(k) of the plane rotations. The 2-by-2 plane
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> rotation part of the matrix P(k), R(k), has the form
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> R(k) = ( c(k) s(k) )
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> ( -s(k) c(k) ).
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> \endverbatim
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>
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> \param[in,out] A
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> \verbatim
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> A is DOUBLE PRECISION array, dimension (LDA,N)
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> The M-by-N matrix A. On exit, A is overwritten by P*A if
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> SIDE = 'R' or by A*P**T if SIDE = 'L'.
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> \endverbatim
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>
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> \param[in] LDA
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> \verbatim
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> LDA is INTEGER
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> The leading dimension of the array A. LDA >= max(1,M).
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> \endverbatim
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Authors:
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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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> \date September 2012
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> \ingroup auxOTHERauxiliary
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=====================================================================
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Subroutine */ int igraphdlasr_(char *side, char *pivot, char *direct, integer *m,
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integer *n, doublereal *c__, doublereal *s, doublereal *a, integer *
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lda)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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/* Local variables */
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integer i__, j, info;
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doublereal temp;
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extern logical igraphlsame_(char *, char *);
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doublereal ctemp, stemp;
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extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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-- LAPACK is a software package provided by Univ. of Tennessee, --
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-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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September 2012
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=====================================================================
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Test the input parameters
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Parameter adjustments */
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--c__;
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--s;
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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/* Function Body */
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info = 0;
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if (! (igraphlsame_(side, "L") || igraphlsame_(side, "R"))) {
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info = 1;
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} else if (! (igraphlsame_(pivot, "V") || igraphlsame_(pivot,
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"T") || igraphlsame_(pivot, "B"))) {
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info = 2;
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} else if (! (igraphlsame_(direct, "F") || igraphlsame_(direct,
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"B"))) {
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info = 3;
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} else if (*m < 0) {
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info = 4;
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} else if (*n < 0) {
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info = 5;
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} else if (*lda < max(1,*m)) {
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info = 9;
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}
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if (info != 0) {
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igraphxerbla_("DLASR ", &info, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*m == 0 || *n == 0) {
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return 0;
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}
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if (igraphlsame_(side, "L")) {
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/* Form P * A */
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if (igraphlsame_(pivot, "V")) {
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if (igraphlsame_(direct, "F")) {
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i__1 = *m - 1;
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for (j = 1; j <= i__1; ++j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1. || stemp != 0.) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[j + 1 + i__ * a_dim1];
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a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp *
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a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j
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+ i__ * a_dim1];
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/* L10: */
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}
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}
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/* L20: */
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}
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} else if (igraphlsame_(direct, "B")) {
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for (j = *m - 1; j >= 1; --j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1. || stemp != 0.) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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temp = a[j + 1 + i__ * a_dim1];
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a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp *
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a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j
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+ i__ * a_dim1];
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/* L30: */
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}
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}
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/* L40: */
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}
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}
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} else if (igraphlsame_(pivot, "T")) {
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if (igraphlsame_(direct, "F")) {
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i__1 = *m;
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for (j = 2; j <= i__1; ++j) {
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ctemp = c__[j - 1];
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stemp = s[j - 1];
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if (ctemp != 1. || stemp != 0.) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[j + i__ * a_dim1];
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||||
a[j + i__ * a_dim1] = ctemp * temp - stemp * a[
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i__ * a_dim1 + 1];
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a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[
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||||
i__ * a_dim1 + 1];
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||||
/* L50: */
|
||||
}
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||||
}
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||||
/* L60: */
|
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}
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} else if (igraphlsame_(direct, "B")) {
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for (j = *m; j >= 2; --j) {
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ctemp = c__[j - 1];
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stemp = s[j - 1];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
temp = a[j + i__ * a_dim1];
|
||||
a[j + i__ * a_dim1] = ctemp * temp - stemp * a[
|
||||
i__ * a_dim1 + 1];
|
||||
a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[
|
||||
i__ * a_dim1 + 1];
|
||||
/* L70: */
|
||||
}
|
||||
}
|
||||
/* L80: */
|
||||
}
|
||||
}
|
||||
} else if (igraphlsame_(pivot, "B")) {
|
||||
if (igraphlsame_(direct, "F")) {
|
||||
i__1 = *m - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
ctemp = c__[j];
|
||||
stemp = s[j];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__2 = *n;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
temp = a[j + i__ * a_dim1];
|
||||
a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1]
|
||||
+ ctemp * temp;
|
||||
a[*m + i__ * a_dim1] = ctemp * a[*m + i__ *
|
||||
a_dim1] - stemp * temp;
|
||||
/* L90: */
|
||||
}
|
||||
}
|
||||
/* L100: */
|
||||
}
|
||||
} else if (igraphlsame_(direct, "B")) {
|
||||
for (j = *m - 1; j >= 1; --j) {
|
||||
ctemp = c__[j];
|
||||
stemp = s[j];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
temp = a[j + i__ * a_dim1];
|
||||
a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1]
|
||||
+ ctemp * temp;
|
||||
a[*m + i__ * a_dim1] = ctemp * a[*m + i__ *
|
||||
a_dim1] - stemp * temp;
|
||||
/* L110: */
|
||||
}
|
||||
}
|
||||
/* L120: */
|
||||
}
|
||||
}
|
||||
}
|
||||
} else if (igraphlsame_(side, "R")) {
|
||||
|
||||
/* Form A * P**T */
|
||||
|
||||
if (igraphlsame_(pivot, "V")) {
|
||||
if (igraphlsame_(direct, "F")) {
|
||||
i__1 = *n - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
ctemp = c__[j];
|
||||
stemp = s[j];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
temp = a[i__ + (j + 1) * a_dim1];
|
||||
a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp *
|
||||
a[i__ + j * a_dim1];
|
||||
a[i__ + j * a_dim1] = stemp * temp + ctemp * a[
|
||||
i__ + j * a_dim1];
|
||||
/* L130: */
|
||||
}
|
||||
}
|
||||
/* L140: */
|
||||
}
|
||||
} else if (igraphlsame_(direct, "B")) {
|
||||
for (j = *n - 1; j >= 1; --j) {
|
||||
ctemp = c__[j];
|
||||
stemp = s[j];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
temp = a[i__ + (j + 1) * a_dim1];
|
||||
a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp *
|
||||
a[i__ + j * a_dim1];
|
||||
a[i__ + j * a_dim1] = stemp * temp + ctemp * a[
|
||||
i__ + j * a_dim1];
|
||||
/* L150: */
|
||||
}
|
||||
}
|
||||
/* L160: */
|
||||
}
|
||||
}
|
||||
} else if (igraphlsame_(pivot, "T")) {
|
||||
if (igraphlsame_(direct, "F")) {
|
||||
i__1 = *n;
|
||||
for (j = 2; j <= i__1; ++j) {
|
||||
ctemp = c__[j - 1];
|
||||
stemp = s[j - 1];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
temp = a[i__ + j * a_dim1];
|
||||
a[i__ + j * a_dim1] = ctemp * temp - stemp * a[
|
||||
i__ + a_dim1];
|
||||
a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ +
|
||||
a_dim1];
|
||||
/* L170: */
|
||||
}
|
||||
}
|
||||
/* L180: */
|
||||
}
|
||||
} else if (igraphlsame_(direct, "B")) {
|
||||
for (j = *n; j >= 2; --j) {
|
||||
ctemp = c__[j - 1];
|
||||
stemp = s[j - 1];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
temp = a[i__ + j * a_dim1];
|
||||
a[i__ + j * a_dim1] = ctemp * temp - stemp * a[
|
||||
i__ + a_dim1];
|
||||
a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ +
|
||||
a_dim1];
|
||||
/* L190: */
|
||||
}
|
||||
}
|
||||
/* L200: */
|
||||
}
|
||||
}
|
||||
} else if (igraphlsame_(pivot, "B")) {
|
||||
if (igraphlsame_(direct, "F")) {
|
||||
i__1 = *n - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
ctemp = c__[j];
|
||||
stemp = s[j];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
temp = a[i__ + j * a_dim1];
|
||||
a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1]
|
||||
+ ctemp * temp;
|
||||
a[i__ + *n * a_dim1] = ctemp * a[i__ + *n *
|
||||
a_dim1] - stemp * temp;
|
||||
/* L210: */
|
||||
}
|
||||
}
|
||||
/* L220: */
|
||||
}
|
||||
} else if (igraphlsame_(direct, "B")) {
|
||||
for (j = *n - 1; j >= 1; --j) {
|
||||
ctemp = c__[j];
|
||||
stemp = s[j];
|
||||
if (ctemp != 1. || stemp != 0.) {
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
temp = a[i__ + j * a_dim1];
|
||||
a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1]
|
||||
+ ctemp * temp;
|
||||
a[i__ + *n * a_dim1] = ctemp * a[i__ + *n *
|
||||
a_dim1] - stemp * temp;
|
||||
/* L230: */
|
||||
}
|
||||
}
|
||||
/* L240: */
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of DLASR */
|
||||
|
||||
} /* igraphdlasr_ */
|
||||
|
||||
Reference in New Issue
Block a user