LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zlapll()

 subroutine zlapll ( integer N, complex*16, dimension( * ) X, integer INCX, complex*16, dimension( * ) Y, integer INCY, double precision SSMIN )

ZLAPLL measures the linear dependence of two vectors.

Purpose:
``` Given two column vectors X and Y, let

A = ( X Y ).

The subroutine first computes the QR factorization of A = Q*R,
and then computes the SVD of the 2-by-2 upper triangular matrix R.
The smaller singular value of R is returned in SSMIN, which is used
as the measurement of the linear dependency of the vectors X and Y.```
Parameters
 [in] N ``` N is INTEGER The length of the vectors X and Y.``` [in,out] X ``` X is COMPLEX*16 array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten.``` [in] INCX ``` INCX is INTEGER The increment between successive elements of X. INCX > 0.``` [in,out] Y ``` Y is COMPLEX*16 array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten.``` [in] INCY ``` INCY is INTEGER The increment between successive elements of Y. INCY > 0.``` [out] SSMIN ``` SSMIN is DOUBLE PRECISION The smallest singular value of the N-by-2 matrix A = ( X Y ).```

Definition at line 99 of file zlapll.f.

100 *
101 * -- LAPACK auxiliary routine --
102 * -- LAPACK is a software package provided by Univ. of Tennessee, --
103 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104 *
105 * .. Scalar Arguments ..
106  INTEGER INCX, INCY, N
107  DOUBLE PRECISION SSMIN
108 * ..
109 * .. Array Arguments ..
110  COMPLEX*16 X( * ), Y( * )
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Parameters ..
116  DOUBLE PRECISION ZERO
117  parameter( zero = 0.0d+0 )
118  COMPLEX*16 CONE
119  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
120 * ..
121 * .. Local Scalars ..
122  DOUBLE PRECISION SSMAX
123  COMPLEX*16 A11, A12, A22, C, TAU
124 * ..
125 * .. Intrinsic Functions ..
126  INTRINSIC abs, dconjg
127 * ..
128 * .. External Functions ..
129  COMPLEX*16 ZDOTC
130  EXTERNAL zdotc
131 * ..
132 * .. External Subroutines ..
133  EXTERNAL dlas2, zaxpy, zlarfg
134 * ..
135 * .. Executable Statements ..
136 *
137 * Quick return if possible
138 *
139  IF( n.LE.1 ) THEN
140  ssmin = zero
141  RETURN
142  END IF
143 *
144 * Compute the QR factorization of the N-by-2 matrix ( X Y )
145 *
146  CALL zlarfg( n, x( 1 ), x( 1+incx ), incx, tau )
147  a11 = x( 1 )
148  x( 1 ) = cone
149 *
150  c = -dconjg( tau )*zdotc( n, x, incx, y, incy )
151  CALL zaxpy( n, c, x, incx, y, incy )
152 *
153  CALL zlarfg( n-1, y( 1+incy ), y( 1+2*incy ), incy, tau )
154 *
155  a12 = y( 1 )
156  a22 = y( 1+incy )
157 *
158 * Compute the SVD of 2-by-2 Upper triangular matrix.
159 *
160  CALL dlas2( abs( a11 ), abs( a12 ), abs( a22 ), ssmin, ssmax )
161 *
162  RETURN
163 *
164 * End of ZLAPLL
165 *
subroutine dlas2(F, G, H, SSMIN, SSMAX)
DLAS2 computes singular values of a 2-by-2 triangular matrix.
Definition: dlas2.f:107
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:83
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zlarfg(N, ALPHA, X, INCX, TAU)
ZLARFG generates an elementary reflector (Householder matrix).
Definition: zlarfg.f:106
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