SRC/slasd7.f(3)

💅 SRC/slasd7.f(3) 💅

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🌸 NAME 🌸

SRC/slasd7.f — that’s the file, periodt.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine slasd7 (icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw,
    alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol,
    givnum, ldgnum, c, s, info)

SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc. 🎀

🦋 Function/Subroutine Documentation 🦋

💖 subroutine slasd7 💖

subroutine slasd7 (integer icompq, integer nl, integer nr, integer sqre,
    integer k, real, dimension( * ) d, real, dimension( * ) z, real,
    dimension( * ) zw, real, dimension( * ) vf, real, dimension( * ) vfw,
    real, dimension( * ) vl, real, dimension( * ) vlw, real alpha, real
    beta, real, dimension( * ) dsigma, integer, dimension( * ) idx, integer,
    dimension( * ) idxp, integer, dimension( * ) idxq, integer, dimension( *
    ) perm, integer givptr, integer, dimension( ldgcol, * ) givcol, integer
    ldgcol, real, dimension( ldgnum, * ) givnum, integer ldgnum, real c,
    real s, integer info)

SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

🎀 Purpose 🎀

okay so, the purpose is giving: SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur:

• when two or more singular values are close together
• if there is a tiny entry in the Z vector

For each such occurrence the order of the related secular equation problem is reduced by one. 💫

And yes: SLASD7 is called from SLASD6. iykyk.

💅 Parameters 💅

• ICOMPQ — ICOMPQ is INTEGER. Specifies whether singular vectors are to be computed in compact form, as follows:
  • = 0: Compute singular values only.
  • = 1: Compute singular vectors of upper bidiagonal matrix in compact form.
• 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. Contains the dimension of the non-deflated matrix, this is the order of the related secular equation. 1 <= K <=N.
• D — D is REAL array, dimension ( N ). On entry D contains the singular values of the two submatrices to be combined. On exit D contains the trailing (N-K) updated singular values (those which were deflated) sorted into increasing order.
• Z — Z is REAL array, dimension ( M ). On exit Z contains the updating row vector in the secular equation.
• ZW — ZW is REAL array, dimension ( M ). Workspace for Z.
• VF — VF is REAL array, dimension ( M ). On entry, VF(1:NL+1) contains the first components of all right singular vectors of the upper block; and VF(NL+2:M) contains the first components of all right singular vectors of the lower block. On exit, VF contains the first components of all right singular vectors of the bidiagonal matrix.
• VFW — VFW is REAL array, dimension ( M ). Workspace for VF.
• VL — VL is REAL array, dimension ( M ). On entry, VL(1:NL+1) contains the last components of all right singular vectors of the upper block; and VL(NL+2:M) contains the last components of all right singular vectors of the lower block. On exit, VL contains the last components of all right singular vectors of the bidiagonal matrix.
• VLW — VLW is REAL array, dimension ( M ). Workspace for VL.
• ALPHA — ALPHA is REAL. Contains the diagonal element associated with the added row.
• BETA — BETA is REAL. Contains the off-diagonal element associated with the added row.
• DSIGMA — DSIGMA is REAL array, dimension ( N ). Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation.
• IDX — IDX is INTEGER array, dimension ( N ). This will contain the permutation used to sort the contents of D into ascending order.
• IDXP — IDXP is INTEGER array, dimension ( N ). This will contain the permutation used to place deflated values of D at the end of the array. On output IDXP(2:K) points to the nondeflated D-values and IDXP(K+1:N) points to the deflated singular values.
• IDXQ — IDXQ is INTEGER array, dimension ( N ). This contains the permutation which separately sorts the two sub-problems in D into ascending order. Note that entries in the first half of this permutation must first be moved one position backward; and entries in the second half must first have NL+1 added to their values.
• PERM — PERM is INTEGER array, dimension ( N ). The permutations (from deflation and sorting) to be applied to each singular block. Not referenced if ICOMPQ = 0.
• GIVPTR — GIVPTR is INTEGER. The number of Givens rotations which took place in this subproblem. Not referenced if ICOMPQ = 0.
• GIVCOL — GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of columns to take place in a Givens rotation. Not referenced if ICOMPQ = 0.
• LDGCOL — LDGCOL is INTEGER. The leading dimension of GIVCOL, must be at least N.
• GIVNUM — GIVNUM is REAL array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value to be used in the corresponding Givens rotation. Not referenced if ICOMPQ = 0.
• LDGNUM — LDGNUM is INTEGER. The leading dimension of GIVNUM, must be at least N.
• C — C is REAL. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1.
• S — S is REAL. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1.
• INFO — INFO is INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.

👑 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 📌

Definition at line 276 of file slasd7.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay bestie, that’s the whole page. This is LAPACK Version 3.12.0, source page SRC/slasd7.f(3) — no date is printed in this footer, so we’re not inventing one. Mwah! 💖