lasd8 - lasd8: D&C step: secular equation

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subroutinedlasd8(integericompq,integerk,doubleprecision,dimension(*)d,doubleprecision,dimension(*)z,doubleprecision,dimension(*)vf,doubleprecision,dimension(*)vl,doubleprecision,dimension(*)difl,doubleprecision,dimension(lddifr,*)difr,integerlddifr,doubleprecision,dimension(*)dsigma,doubleprecision,dimension(*)work,integerinfo)DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. Purpose: DLASD8 finds the square roots of the roots of the secular equation, as defined by the values in DSIGMA and Z. It makes the appropriate calls to DLASD4, and stores, for each element in D, the distance to its two nearest poles (elements in DSIGMA). It also updates the arrays VF and VL, the first and last components of all the right singular vectors of the original bidiagonal matrix. DLASD8 is called from DLASD6. ParametersICOMPQ ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form in the calling routine: = 0: Compute singular values only. = 1: Compute singular vectors in factored form as well. K K is INTEGER The number of terms in the rational function to be solved by DLASD4. K >= 1. D D is DOUBLE PRECISION array, dimension ( K ) On output, D contains the updated singular values. Z Z is DOUBLE PRECISION array, dimension ( K ) On entry, the first K elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated. VF VF is DOUBLE PRECISION array, dimension ( K ) On entry, VF contains information passed through DBEDE8. On exit, VF contains the first K components of the first components of all right singular vectors of the bidiagonal matrix. VL VL is DOUBLE PRECISION array, dimension ( K ) On entry, VL contains information passed through DBEDE8. On exit, VL contains the first K components of the last components of all right singular vectors of the bidiagonal matrix. DIFL DIFL is DOUBLE PRECISION array, dimension ( K ) On exit, DIFL(I) = D(I) - DSIGMA(I). DIFR DIFR is DOUBLE PRECISION array, dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and dimension ( K ) if ICOMPQ = 0. On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not defined and will not be referenced. If ICOMPQ = 1, DIFR(1:K,2) is an array containing the normalizing factors for the right singular vector matrix. LDDIFR LDDIFR is INTEGER The leading dimension of DIFR, must be at least K. DSIGMA DSIGMA is DOUBLE PRECISION array, dimension ( K ) On entry, the first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation. WORK WORK is DOUBLE PRECISION array, dimension (3*K) 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 subroutineslasd8(integericompq,integerk,real,dimension(*)d,real,dimension(*)z,real,dimension(*)vf,real,dimension(*)vl,real,dimension(*)difl,real,dimension(lddifr,*)difr,integerlddifr,real,dimension(*)dsigma,real,dimension(*)work,integerinfo)SLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. Purpose: SLASD8 finds the square roots of the roots of the secular equation, as defined by the values in DSIGMA and Z. It makes the appropriate calls to SLASD4, and stores, for each element in D, the distance to its two nearest poles (elements in DSIGMA). It also updates the arrays VF and VL, the first and last components of all the right singular vectors of the original bidiagonal matrix. SLASD8 is called from SLASD6. ParametersICOMPQ ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form in the calling routine: = 0: Compute singular values only. = 1: Compute singular vectors in factored form as well. K K is INTEGER The number of terms in the rational function to be solved by SLASD4. K >= 1. D D is REAL array, dimension ( K ) On output, D contains the updated singular values. Z Z is REAL array, dimension ( K ) On entry, the first K elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated. VF VF is REAL array, dimension ( K ) On entry, VF contains information passed through DBEDE8. On exit, VF contains the first K components of the first components of all right singular vectors of the bidiagonal matrix. VL VL is REAL array, dimension ( K ) On entry, VL contains information passed through DBEDE8. On exit, VL contains the first K components of the last components of all right singular vectors of the bidiagonal matrix. DIFL DIFL is REAL array, dimension ( K ) On exit, DIFL(I) = D(I) - DSIGMA(I). DIFR DIFR is REAL array, dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and dimension ( K ) if ICOMPQ = 0. On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not defined and will not be referenced. If ICOMPQ = 1, DIFR(1:K,2) is an array containing the normalizing factors for the right singular vector matrix. LDDIFR LDDIFR is INTEGER The leading dimension of DIFR, must be at least K. DSIGMA DSIGMA is REAL array, dimension ( K ) On entry, the first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation. WORK WORK is REAL array, dimension (3*K) 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

lasd8 - lasd8: D&C step: secular equation

Functions subroutine dlasd8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info) DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. subroutine slasd8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info) SLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.