Provided by: liblapack-doc_3.12.0-3build1_all 
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
NL is INTEGER
The row dimension of the upper block. NL >= 1.
NR
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
K is INTEGER
The size of the secular equation, 1 =< K = < N.
D
D is DOUBLE PRECISION array, dimension(K)
On exit the square roots of the roots of the secular equation,
in ascending order.
Q
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
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
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
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
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
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.
Purpose:
SLASD3 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 SLASD4 and then updates the singular
vectors by matrix multiplication.
SLASD3 is called from SLASD1.
Parameters
NL
NL is INTEGER
The row dimension of the upper block. NL >= 1.
NR
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
K is INTEGER
The size of the secular equation, 1 =< K = < N.
D
D is REAL array, dimension(K)
On exit the square roots of the roots of the secular equation,
in ascending order.
Q
Q is REAL array, dimension (LDQ,K)
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= K.
DSIGMA
DSIGMA is REAL 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
U is REAL 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
U2 is REAL 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
VT is REAL 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 REAL 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 SLASD4
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
Z is REAL 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
Author
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