100 lines
2.6 KiB
FortranFixed
100 lines
2.6 KiB
FortranFixed
SUBROUTINE SLAPLL( N, X, INCX, Y, INCY, SSMIN )
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER INCX, INCY, N
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REAL SSMIN
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* ..
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* .. Array Arguments ..
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REAL X( * ), Y( * )
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* ..
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*
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* Purpose
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* =======
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*
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* Given two column vectors X and Y, let
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*
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* A = ( X Y ).
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*
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* The subroutine first computes the QR factorization of A = Q*R,
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* and then computes the SVD of the 2-by-2 upper triangular matrix R.
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* The smaller singular value of R is returned in SSMIN, which is used
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* as the measurement of the linear dependency of the vectors X and Y.
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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 length of the vectors X and Y.
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*
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* X (input/output) REAL array,
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* dimension (1+(N-1)*INCX)
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* On entry, X contains the N-vector X.
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* On exit, X is overwritten.
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*
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* INCX (input) INTEGER
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* The increment between successive elements of X. INCX > 0.
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*
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* Y (input/output) REAL array,
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* dimension (1+(N-1)*INCY)
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* On entry, Y contains the N-vector Y.
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* On exit, Y is overwritten.
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*
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* INCY (input) INTEGER
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* The increment between successive elements of Y. INCY > 0.
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*
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* SSMIN (output) REAL
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* The smallest singular value of the N-by-2 matrix A = ( X Y ).
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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REAL A11, A12, A22, C, SSMAX, TAU
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* ..
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* .. External Functions ..
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REAL SDOT
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EXTERNAL SDOT
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SLARFG, SLAS2
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.LE.1 ) THEN
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SSMIN = ZERO
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RETURN
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END IF
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*
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* Compute the QR factorization of the N-by-2 matrix ( X Y )
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*
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CALL SLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
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A11 = X( 1 )
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X( 1 ) = ONE
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*
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C = -TAU*SDOT( N, X, INCX, Y, INCY )
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CALL SAXPY( N, C, X, INCX, Y, INCY )
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*
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CALL SLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
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*
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A12 = Y( 1 )
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A22 = Y( 1+INCY )
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*
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* Compute the SVD of 2-by-2 Upper triangular matrix.
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*
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CALL SLAS2( A11, A12, A22, SSMIN, SSMAX )
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*
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RETURN
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*
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* End of SLAPLL
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*
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END
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