laeda(3)

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version 3.12.1 · 9 versions
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💅 laeda(3) — Library Functions Manual ✨

okay so bestie, this is laeda(3) from the Library Functions Manual, and it's giving two LAPACK subroutines: one DOUBLE PRECISION girlie and one REAL girlie. Both are here to compute the Z vector for the rank-one modification of the diagonal matrix when the original matrix is dense. No cap.

🌸 NAME

laeda — laeda: D&C step: z vector 💖

✨ SYNOPSIS

🛠️ Functions

  • subroutine dlaeda (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info) — DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.
  • subroutine slaeda (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info) — SLAEDA used by SSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.

💖 DETAILED DESCRIPTION

This part is lowkey just the doorway into the function docs. The page has a Detailed Description section, then it goes straight into Function Documentation. No extra lore, bestie.

🦋 FUNCTION DOCUMENTATION

🌈 dlaeda

subroutine dlaeda (integer n, integer tlvls, integer curlvl, integer curpbm, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum, double precision, dimension( * ) q, integer, dimension( * ) qptr, double precision, dimension( * ) z, double precision, dimension( * ) ztemp, integer info)

DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.

🎯 Purpose

DLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem.

🧸 Parameters

  • N — N is INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
  • TLVLS — TLVLS is INTEGER. The total number of merging levels in the overall divide and conquer tree.
  • CURLVL — CURLVL is INTEGER. The current level in the overall merge routine, 0 <= curlvl <= tlvls.
  • CURPBM — CURPBM is INTEGER. The current problem in the current level in the overall merge routine (counting from upper left to lower right).
  • PRMPTR — PRMPTR is INTEGER array, dimension (N lg N). Contains a list of pointers which indicate where in PERM a level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation and incidentally the size of the full, non-deflated problem.
  • PERM — PERM is INTEGER array, dimension (N lg N). Contains the permutations (from deflation and sorting) to be applied to each eigenblock.
  • GIVPTR — GIVPTR is INTEGER array, dimension (N lg N). Contains a list of pointers which indicate where in GIVCOL a level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rotations.
  • GIVCOL — GIVCOL is INTEGER array, dimension (2, N lg N). Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
  • GIVNUM — GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N). Each number indicates the S value to be used in the corresponding Givens rotation.
  • Q — Q is DOUBLE PRECISION array, dimension (N**2). Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR.
  • QPTR — QPTR is INTEGER array, dimension (N+2). Contains a list of pointers which indicate where in Q an eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block.
  • Z — Z is DOUBLE PRECISION array, dimension (N). On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix).
  • ZTEMP — ZTEMP is DOUBLE PRECISION array, dimension (N).
  • 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

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

📌 Definition at line 164 of file dlaeda.f.

🍓 slaeda

subroutine slaeda (integer n, integer tlvls, integer curlvl, integer curpbm, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, real, dimension( * ) q, integer, dimension( * ) qptr, real, dimension( * ) z, real, dimension( * ) ztemp, integer info)

SLAEDA used by SSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.

🎯 Purpose

SLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem.

🧸 Parameters

  • N — N is INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
  • TLVLS — TLVLS is INTEGER. The total number of merging levels in the overall divide and conquer tree.
  • CURLVL — CURLVL is INTEGER. The current level in the overall merge routine, 0 <= curlvl <= tlvls.
  • CURPBM — CURPBM is INTEGER. The current problem in the current level in the overall merge routine (counting from upper left to lower right).
  • PRMPTR — PRMPTR is INTEGER array, dimension (N lg N). Contains a list of pointers which indicate where in PERM a level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation and incidentally the size of the full, non-deflated problem.
  • PERM — PERM is INTEGER array, dimension (N lg N). Contains the permutations (from deflation and sorting) to be applied to each eigenblock.
  • GIVPTR — GIVPTR is INTEGER array, dimension (N lg N). Contains a list of pointers which indicate where in GIVCOL a level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rotations.
  • GIVCOL — GIVCOL is INTEGER array, dimension (2, N lg N). Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
  • GIVNUM — GIVNUM is REAL array, dimension (2, N lg N). Each number indicates the S value to be used in the corresponding Givens rotation.
  • Q — Q is REAL array, dimension (N**2). Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR.
  • QPTR — QPTR is INTEGER array, dimension (N+2). Contains a list of pointers which indicate where in Q an eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block.
  • Z — Z is REAL array, dimension (N). On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix).
  • ZTEMP — ZTEMP is REAL array, dimension (N).
  • 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

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

📌 Definition at line 164 of file slaeda.f.

👑 AUTHOR

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okay that's the whole page, bestie. Signing off with LAPACK Version 3.12.0 and laeda(3) — the footer doesn't list a date, so I'm not inventing one. Periodt. 💅✨

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