# slasd3.f - Man Page

## Synopsis

### Functions/Subroutines

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.

## Function/Subroutine Documentation

### 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. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. 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.

**Date:**June 2017

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

Definition at line 226 of file slasd3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasd3(3) is an alias of slasd3.f(3).