Mercurial > octave-nkf
diff libcruft/lapack/dlasr.f @ 7034:68db500cb558
[project @ 2007-10-16 18:54:19 by jwe]
author | jwe |
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date | Tue, 16 Oct 2007 18:54:23 +0000 |
parents | 15cddaacbc2d |
children |
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--- a/libcruft/lapack/dlasr.f Tue Oct 16 17:46:44 2007 +0000 +++ b/libcruft/lapack/dlasr.f Tue Oct 16 18:54:23 2007 +0000 @@ -1,9 +1,8 @@ SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * -* -- LAPACK auxiliary routine (version 3.0) -- -* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -* Courant Institute, Argonne National Lab, and Rice University -* October 31, 1992 +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 * * .. Scalar Arguments .. CHARACTER DIRECT, PIVOT, SIDE @@ -16,44 +15,77 @@ * Purpose * ======= * -* DLASR performs the transformation -* -* A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) -* -* A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) -* -* where A is an m by n real matrix and P is an orthogonal matrix, -* consisting of a sequence of plane rotations determined by the -* parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l' -* and z = n when SIDE = 'R' or 'r' ): -* -* When DIRECT = 'F' or 'f' ( Forward sequence ) then -* -* P = P( z - 1 )*...*P( 2 )*P( 1 ), -* -* and when DIRECT = 'B' or 'b' ( Backward sequence ) then -* -* P = P( 1 )*P( 2 )*...*P( z - 1 ), -* -* where P( k ) is a plane rotation matrix for the following planes: -* -* when PIVOT = 'V' or 'v' ( Variable pivot ), -* the plane ( k, k + 1 ) -* -* when PIVOT = 'T' or 't' ( Top pivot ), -* the plane ( 1, k + 1 ) -* -* when PIVOT = 'B' or 'b' ( Bottom pivot ), -* the plane ( k, z ) -* -* c( k ) and s( k ) must contain the cosine and sine that define the -* matrix P( k ). The two by two plane rotation part of the matrix -* P( k ), R( k ), is assumed to be of the form -* -* R( k ) = ( c( k ) s( k ) ). -* ( -s( k ) c( k ) ) -* -* This version vectorises across rows of the array A when SIDE = 'L'. +* DLASR applies a sequence of plane rotations to a real matrix A, +* from either the left or the right. +* +* When SIDE = 'L', the transformation takes the form +* +* A := P*A +* +* and when SIDE = 'R', the transformation takes the form +* +* A := A*P**T +* +* where P is an orthogonal matrix consisting of a sequence of z plane +* rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', +* and P**T is the transpose of P. +* +* When DIRECT = 'F' (Forward sequence), then +* +* P = P(z-1) * ... * P(2) * P(1) +* +* and when DIRECT = 'B' (Backward sequence), then +* +* P = P(1) * P(2) * ... * P(z-1) +* +* where P(k) is a plane rotation matrix defined by the 2-by-2 rotation +* +* R(k) = ( c(k) s(k) ) +* = ( -s(k) c(k) ). +* +* When PIVOT = 'V' (Variable pivot), the rotation is performed +* for the plane (k,k+1), i.e., P(k) has the form +* +* P(k) = ( 1 ) +* ( ... ) +* ( 1 ) +* ( c(k) s(k) ) +* ( -s(k) c(k) ) +* ( 1 ) +* ( ... ) +* ( 1 ) +* +* where R(k) appears as a rank-2 modification to the identity matrix in +* rows and columns k and k+1. +* +* When PIVOT = 'T' (Top pivot), the rotation is performed for the +* plane (1,k+1), so P(k) has the form +* +* P(k) = ( c(k) s(k) ) +* ( 1 ) +* ( ... ) +* ( 1 ) +* ( -s(k) c(k) ) +* ( 1 ) +* ( ... ) +* ( 1 ) +* +* where R(k) appears in rows and columns 1 and k+1. +* +* Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is +* performed for the plane (k,z), giving P(k) the form +* +* P(k) = ( 1 ) +* ( ... ) +* ( 1 ) +* ( c(k) s(k) ) +* ( 1 ) +* ( ... ) +* ( 1 ) +* ( -s(k) c(k) ) +* +* where R(k) appears in rows and columns k and z. The rotations are +* performed without ever forming P(k) explicitly. * * Arguments * ========= @@ -62,13 +94,7 @@ * Specifies whether the plane rotation matrix P is applied to * A on the left or the right. * = 'L': Left, compute A := P*A -* = 'R': Right, compute A:= A*P' -* -* DIRECT (input) CHARACTER*1 -* Specifies whether P is a forward or backward sequence of -* plane rotations. -* = 'F': Forward, P = P( z - 1 )*...*P( 2 )*P( 1 ) -* = 'B': Backward, P = P( 1 )*P( 2 )*...*P( z - 1 ) +* = 'R': Right, compute A:= A*P**T * * PIVOT (input) CHARACTER*1 * Specifies the plane for which P(k) is a plane rotation @@ -77,6 +103,12 @@ * = 'T': Top pivot, the plane (1,k+1) * = 'B': Bottom pivot, the plane (k,z) * +* DIRECT (input) CHARACTER*1 +* Specifies whether P is a forward or backward sequence of +* plane rotations. +* = 'F': Forward, P = P(z-1)*...*P(2)*P(1) +* = 'B': Backward, P = P(1)*P(2)*...*P(z-1) +* * M (input) INTEGER * The number of rows of the matrix A. If m <= 1, an immediate * return is effected. @@ -85,18 +117,22 @@ * The number of columns of the matrix A. If n <= 1, an * immediate return is effected. * -* C, S (input) DOUBLE PRECISION arrays, dimension +* C (input) DOUBLE PRECISION array, dimension +* (M-1) if SIDE = 'L' +* (N-1) if SIDE = 'R' +* The cosines c(k) of the plane rotations. +* +* S (input) DOUBLE PRECISION array, dimension * (M-1) if SIDE = 'L' * (N-1) if SIDE = 'R' -* c(k) and s(k) contain the cosine and sine that define the -* matrix P(k). The two by two plane rotation part of the -* matrix P(k), R(k), is assumed to be of the form -* R( k ) = ( c( k ) s( k ) ). -* ( -s( k ) c( k ) ) +* The sines s(k) of the plane rotations. The 2-by-2 plane +* rotation part of the matrix P(k), R(k), has the form +* R(k) = ( c(k) s(k) ) +* ( -s(k) c(k) ). * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -* The m by n matrix A. On exit, A is overwritten by P*A if -* SIDE = 'R' or by A*P' if SIDE = 'L'. +* The M-by-N matrix A. On exit, A is overwritten by P*A if +* SIDE = 'R' or by A*P**T if SIDE = 'L'. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M).