# lapll - Man Page

lapll: linear dependence of 2 vectors

## Synopsis

### Functions

subroutine **clapll** (n, x, incx, y, incy, ssmin)**CLAPLL** measures the linear dependence of two vectors.

subroutine **dlapll** (n, x, incx, y, incy, ssmin)**DLAPLL** measures the linear dependence of two vectors.

subroutine **slapll** (n, x, incx, y, incy, ssmin)**SLAPLL** measures the linear dependence of two vectors.

subroutine **zlapll** (n, x, incx, y, incy, ssmin)**ZLAPLL** measures the linear dependence of two vectors.

## Detailed Description

## Function Documentation

### subroutine clapll (integer n, complex, dimension( * ) x, integer incx, complex, dimension( * ) y, integer incy, real ssmin)

**CLAPLL** 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***N*N is INTEGER The length of the vectors X and Y.

*X*X is COMPLEX array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten.

*INCX*INCX is INTEGER The increment between successive elements of X. INCX > 0.

*Y*Y is COMPLEX array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten.

*INCY*INCY is INTEGER The increment between successive elements of Y. INCY > 0.

*SSMIN*SSMIN is REAL The smallest singular value of the N-by-2 matrix A = ( X Y ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **99** of file **clapll.f**.

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

**DLAPLL** 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***N*N is INTEGER The length of the vectors X and Y.

*X*X is DOUBLE PRECISION array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten.

*INCX*INCX is INTEGER The increment between successive elements of X. INCX > 0.

*Y*Y is DOUBLE PRECISION array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten.

*INCY*INCY is INTEGER The increment between successive elements of Y. INCY > 0.

*SSMIN*SSMIN is DOUBLE PRECISION The smallest singular value of the N-by-2 matrix A = ( X Y ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **101** of file **dlapll.f**.

### subroutine slapll (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real ssmin)

**SLAPLL** 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***N*N is INTEGER The length of the vectors X and Y.

*X*X is REAL array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten.

*INCX*INCX is INTEGER The increment between successive elements of X. INCX > 0.

*Y*Y is REAL array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten.

*INCY*INCY is INTEGER The increment between successive elements of Y. INCY > 0.

*SSMIN*SSMIN is REAL The smallest singular value of the N-by-2 matrix A = ( X Y ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **101** of file **slapll.f**.

### 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:**

**Parameters***N*N is INTEGER The length of the vectors X and Y.

*X*X is COMPLEX*16 array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten.

*INCX*INCX is INTEGER The increment between successive elements of X. INCX > 0.

*Y*Y is COMPLEX*16 array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten.

*INCY*INCY is INTEGER The increment between successive elements of Y. INCY > 0.

*SSMIN*SSMIN is DOUBLE PRECISION The smallest singular value of the N-by-2 matrix A = ( X Y ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **99** of file **zlapll.f**.

## Author

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