.TH "lapll" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lapll \- lapll: linear dependence of 2 vectors
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclapll\fP (n, x, incx, y, incy, ssmin)"
.br
.RI "\fBCLAPLL\fP measures the linear dependence of two vectors\&. "
.ti -1c
.RI "subroutine \fBdlapll\fP (n, x, incx, y, incy, ssmin)"
.br
.RI "\fBDLAPLL\fP measures the linear dependence of two vectors\&. "
.ti -1c
.RI "subroutine \fBslapll\fP (n, x, incx, y, incy, ssmin)"
.br
.RI "\fBSLAPLL\fP measures the linear dependence of two vectors\&. "
.ti -1c
.RI "subroutine \fBzlapll\fP (n, x, incx, y, incy, ssmin)"
.br
.RI "\fBZLAPLL\fP measures the linear dependence of two vectors\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clapll (integer n, complex, dimension( * ) x, integer incx, complex, dimension( * ) y, integer incy, real ssmin)"

.PP
\fBCLAPLL\fP measures the linear dependence of two vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The length of the vectors X and Y\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX array, dimension (1+(N-1)*INCX)
          On entry, X contains the N-vector X\&.
          On exit, X is overwritten\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between successive elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is COMPLEX array, dimension (1+(N-1)*INCY)
          On entry, Y contains the N-vector Y\&.
          On exit, Y is overwritten\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between successive elements of Y\&. INCY > 0\&.
.fi
.PP
.br
\fISSMIN\fP 
.PP
.nf
          SSMIN is REAL
          The smallest singular value of the N-by-2 matrix A = ( X Y )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine dlapll (integer n, double precision, dimension( * ) x, integer incx, double precision, dimension( * ) y, integer incy, double precision ssmin)"

.PP
\fBDLAPLL\fP measures the linear dependence of two vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The length of the vectors X and Y\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCX)
          On entry, X contains the N-vector X\&.
          On exit, X is overwritten\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between successive elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCY)
          On entry, Y contains the N-vector Y\&.
          On exit, Y is overwritten\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between successive elements of Y\&. INCY > 0\&.
.fi
.PP
.br
\fISSMIN\fP 
.PP
.nf
          SSMIN is DOUBLE PRECISION
          The smallest singular value of the N-by-2 matrix A = ( X Y )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine slapll (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real ssmin)"

.PP
\fBSLAPLL\fP measures the linear dependence of two vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The length of the vectors X and Y\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is REAL array,
                         dimension (1+(N-1)*INCX)
          On entry, X contains the N-vector X\&.
          On exit, X is overwritten\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between successive elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is REAL array,
                         dimension (1+(N-1)*INCY)
          On entry, Y contains the N-vector Y\&.
          On exit, Y is overwritten\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between successive elements of Y\&. INCY > 0\&.
.fi
.PP
.br
\fISSMIN\fP 
.PP
.nf
          SSMIN is REAL
          The smallest singular value of the N-by-2 matrix A = ( X Y )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine zlapll (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision ssmin)"

.PP
\fBZLAPLL\fP measures the linear dependence of two vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The length of the vectors X and Y\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
          On entry, X contains the N-vector X\&.
          On exit, X is overwritten\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between successive elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
          On entry, Y contains the N-vector Y\&.
          On exit, Y is overwritten\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between successive elements of Y\&. INCY > 0\&.
.fi
.PP
.br
\fISSMIN\fP 
.PP
.nf
          SSMIN is DOUBLE PRECISION
          The smallest singular value of the N-by-2 matrix A = ( X Y )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.