NAME

lasd3 - lasd3: D&C step: secular equation

SYNOPSIS

Functions

subroutine dlasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, info)
DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc. subroutine slasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, info)
SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Detailed Description

Function Documentation

subroutine dlasd3 (integer nl, integer nr, integer sqre, integer k, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) dsigma, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldu2, * ) u2, integer ldu2, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( ldvt2, * ) vt2, integer ldvt2, integer, dimension( * ) idxc, integer, dimension( * ) ctot, double precision, dimension( * ) z, integer info)

DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Purpose:



 DLASD3 finds all the square roots of the roots of the secular


 equation, as defined by the values in D and Z.  It makes the


 appropriate calls to DLASD4 and then updates the singular


 vectors by matrix multiplication.


 DLASD3 is called from DLASD1.

Parameters



          NL is INTEGER


         The row dimension of the upper block.  NL >= 1.



          NR is INTEGER


         The row dimension of the lower block.  NR >= 1.

SQRE



          SQRE is INTEGER


         = 0: the lower block is an NR-by-NR square matrix.


         = 1: the lower block is an NR-by-(NR+1) rectangular matrix.


         The bidiagonal matrix has N = NL + NR + 1 rows and


         M = N + SQRE >= N columns.



          K is INTEGER


         The size of the secular equation, 1 =< K = < N.



          D is DOUBLE PRECISION array, dimension(K)


         On exit the square roots of the roots of the secular equation,


         in ascending order.



          Q is DOUBLE PRECISION array, dimension (LDQ,K)

LDQ



          LDQ is INTEGER


         The leading dimension of the array Q.  LDQ >= K.

DSIGMA



          DSIGMA is DOUBLE PRECISION array, dimension(K)


         The first K elements of this array contain the old roots


         of the deflated updating problem.  These are the poles


         of the secular equation.



          U is DOUBLE PRECISION array, dimension (LDU, N)


         The last N - K columns of this matrix contain the deflated


         left singular vectors.

LDU



          LDU is INTEGER


         The leading dimension of the array U.  LDU >= N.



          U2 is DOUBLE PRECISION array, dimension (LDU2, N)


         The first K columns of this matrix contain the non-deflated


         left singular vectors for the split problem.

LDU2



          LDU2 is INTEGER


         The leading dimension of the array U2.  LDU2 >= N.



          VT is DOUBLE PRECISION array, dimension (LDVT, M)


         The last M - K columns of VT**T contain the deflated


         right singular vectors.

LDVT



          LDVT is INTEGER


         The leading dimension of the array VT.  LDVT >= N.

VT2



          VT2 is DOUBLE PRECISION array, dimension (LDVT2, N)


         The first K columns of VT2**T contain the non-deflated


         right singular vectors for the split problem.

LDVT2



          LDVT2 is INTEGER


         The leading dimension of the array VT2.  LDVT2 >= N.

IDXC



          IDXC is INTEGER array, dimension ( N )


         The permutation used to arrange the columns of U (and rows of


         VT) into three groups:  the first group contains non-zero


         entries only at and above (or before) NL +1; the second


         contains non-zero entries only at and below (or after) NL+2;


         and the third is dense. The first column of U and the row of


         VT are treated separately, however.


         The rows of the singular vectors found by DLASD4


         must be likewise permuted before the matrix multiplies can


         take place.

CTOT



          CTOT is INTEGER array, dimension ( 4 )


         A count of the total number of the various types of columns


         in U (or rows in VT), as described in IDXC. The fourth column


         type is any column which has been deflated.



          Z is DOUBLE PRECISION array, dimension (K)


         The first K elements of this array contain the components


         of the deflation-adjusted updating row vector.

INFO



          INFO is INTEGER


         = 0:  successful exit.


         < 0:  if INFO = -i, the i-th argument had an illegal value.


         > 0:  if INFO = 1, a singular value did not converge

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 214 of file dlasd3.f.

subroutine slasd3 (integer nl, integer nr, integer sqre, integer k, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) dsigma, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldu2, * ) u2, integer ldu2, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( ldvt2, * ) vt2, integer ldvt2, integer, dimension( * ) idxc, integer, dimension( * ) ctot, real, dimension( * ) z, integer info)

SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.