# dlasq1.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlasq1.f

## 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