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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| 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.
Download SLASD3 + dependencies [TGZ] [ZIP] [TXT]
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.
| [in] | NL | NL is INTEGER
The row dimension of the upper block. NL >= 1. |
| [in] | NR | NR is INTEGER
The row dimension of the lower block. NR >= 1. |
| [in] | 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. |
| [in] | K | K is INTEGER
The size of the secular equation, 1 =< K = < N. |
| [out] | D | D is REAL array, dimension(K)
On exit the square roots of the roots of the secular equation,
in ascending order. |
| [out] | Q | Q is REAL array, dimension (LDQ,K) |
| [in] | LDQ | LDQ is INTEGER
The leading dimension of the array Q. LDQ >= K. |
| [in] | 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. |
| [out] | U | U is REAL array, dimension (LDU, N)
The last N - K columns of this matrix contain the deflated
left singular vectors. |
| [in] | LDU | LDU is INTEGER
The leading dimension of the array U. LDU >= N. |
| [in] | 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. |
| [in] | LDU2 | LDU2 is INTEGER
The leading dimension of the array U2. LDU2 >= N. |
| [out] | VT | VT is REAL array, dimension (LDVT, M)
The last M - K columns of VT**T contain the deflated
right singular vectors. |
| [in] | LDVT | LDVT is INTEGER
The leading dimension of the array VT. LDVT >= N. |
| [in,out] | 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. |
| [in] | LDVT2 | LDVT2 is INTEGER
The leading dimension of the array VT2. LDVT2 >= N. |
| [in] | 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. |
| [in] | 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. |
| [in,out] | Z | Z is REAL array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating row vector. |
| [out] | 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 |
1.9.8