# dlasq1.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dlasq1** (**N**, D, E, WORK, INFO)**DLASQ1** computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

## Function/Subroutine Documentation

### subroutine dlasq1 (integer N, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( * ) WORK, integer INFO)

**DLASQ1** computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

**Purpose:**

DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. The algorithm was first presented in "Accurate singular values and differential qd algorithms" by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994, and the present implementation is described in "An implementation of the dqds Algorithm (Positive Case)", LAPACK Working Note.

**Parameters:***N*N is INTEGER The number of rows and columns in the matrix. N >= 0.

*D*D is DOUBLE PRECISION array, dimension (N) On entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in decreasing order.

*E*E is DOUBLE PRECISION array, dimension (N) On entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E is overwritten.

*WORK*WORK is DOUBLE PRECISION array, dimension (4*N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: the algorithm failed = 1, a split was marked by a positive value in E = 2, current block of Z not diagonalized after 100*N iterations (in inner while loop) On exit D and E represent a matrix with the same singular values which the calling subroutine could use to finish the computation, or even feed back into DLASQ1 = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 110 of file dlasq1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlasq1(3) is an alias of dlasq1.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK