unbdb5(3)

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version 3.12.1 · 9 versions
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🎀 unbdb5(3) — {un,or}bdb5: step in uncsd2by1 🎀

✨ NAME ✨

Okay bestie, this manual page is for unbdb5 — aka {un,or}bdb5: a step in uncsd2by1. That’s the name, no cap. 💅

🌸 SYNOPSIS 🌸

💖 Functions 💖

subroutine cunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
    work, lwork, info)

CUNBDB5

subroutine dorbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
    work, lwork, info)

DORBDB5

subroutine sorbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
    work, lwork, info)

SORBDB5

subroutine zunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
    work, lwork, info)

ZUNBDB5

🦋 Detailed Description 🦋

This is the detailed receipts section, bestie. It’s giving “four routines, one very specific job.” Scroll for each one. 🫶

📚 Function Documentation 📚

💜 cunbdb5 💜

subroutine cunbdb5 (integer m1, integer m2, integer n, complex, dimension(*)
    x1, integer incx1, complex, dimension(*) x2, integer incx2, complex,
    dimension(ldq1,*) q1, integer ldq1, complex, dimension(ldq2,*) q2,
    integer ldq2, complex, dimension(*) work, integer lwork, integer info)

CUNBDB5

Purpose:

CUNBDB5 orthogonalizes the column vector

X = [ X1 ]
    [ X2 ]

with respect to the columns of

Q = [ Q1 ] .
    [ Q2 ]

The columns of Q must be orthonormal.

If the projection is zero according to Kahan's criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way.

Parameters

  • M1 — M1 is INTEGER. The dimension of X1 and the number of rows in Q1. 0 <= M1.
  • M2 — M2 is INTEGER. The dimension of X2 and the number of rows in Q2. 0 <= M2.
  • N — N is INTEGER. The number of columns in Q1 and Q2. 0 <= N.
  • X1 — X1 is COMPLEX array, dimension (M1). On entry, the top part of the vector to be orthogonalized. On exit, the top part of the projected vector.
  • INCX1 — INCX1 is INTEGER. Increment for entries of X1.
  • X2 — X2 is COMPLEX array, dimension (M2). On entry, the bottom part of the vector to be orthogonalized. On exit, the bottom part of the projected vector.
  • INCX2 — INCX2 is INTEGER. Increment for entries of X2.
  • Q1 — Q1 is COMPLEX array, dimension (LDQ1, N). The top part of the orthonormal basis matrix.
  • LDQ1 — LDQ1 is INTEGER. The leading dimension of Q1. LDQ1 >= M1.
  • Q2 — Q2 is COMPLEX array, dimension (LDQ2, N). The bottom part of the orthonormal basis matrix.
  • LDQ2 — LDQ2 is INTEGER. The leading dimension of Q2. LDQ2 >= M2.
  • WORK — WORK is COMPLEX array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 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.

Definition at line 154 of file cunbdb5.f.

💙 dorbdb5 💙

subroutine dorbdb5 (integer m1, integer m2, integer n, double precision,
    dimension(*) x1, integer incx1, double precision, dimension(*) x2,
    integer incx2, double precision, dimension(ldq1,*) q1, integer ldq1,
    double precision, dimension(ldq2,*) q2, integer ldq2, double precision,
    dimension(*) work, integer lwork, integer info)

DORBDB5

Purpose:

DORBDB5 orthogonalizes the column vector

X = [ X1 ]
    [ X2 ]

with respect to the columns of

Q = [ Q1 ] .
    [ Q2 ]

The columns of Q must be orthonormal.

If the projection is zero according to Kahan's criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way.

Parameters

  • M1 — M1 is INTEGER. The dimension of X1 and the number of rows in Q1. 0 <= M1.
  • M2 — M2 is INTEGER. The dimension of X2 and the number of rows in Q2. 0 <= M2.
  • N — N is INTEGER. The number of columns in Q1 and Q2. 0 <= N.
  • X1 — X1 is DOUBLE PRECISION array, dimension (M1). On entry, the top part of the vector to be orthogonalized. On exit, the top part of the projected vector.
  • INCX1 — INCX1 is INTEGER. Increment for entries of X1.
  • X2 — X2 is DOUBLE PRECISION array, dimension (M2). On entry, the bottom part of the vector to be orthogonalized. On exit, the bottom part of the projected vector.
  • INCX2 — INCX2 is INTEGER. Increment for entries of X2.
  • Q1 — Q1 is DOUBLE PRECISION array, dimension (LDQ1, N). The top part of the orthonormal basis matrix.
  • LDQ1 — LDQ1 is INTEGER. The leading dimension of Q1. LDQ1 >= M1.
  • Q2 — Q2 is DOUBLE PRECISION array, dimension (LDQ2, N). The bottom part of the orthonormal basis matrix.
  • LDQ2 — LDQ2 is INTEGER. The leading dimension of Q2. LDQ2 >= M2.
  • WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 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.

Definition at line 154 of file dorbdb5.f.

💚 sorbdb5 💚

subroutine sorbdb5 (integer m1, integer m2, integer n, real, dimension(*)
    x1, integer incx1, real, dimension(*) x2, integer incx2, real,
    dimension(ldq1,*) q1, integer ldq1, real, dimension(ldq2,*) q2, integer
    ldq2, real, dimension(*) work, integer lwork, integer info)

SORBDB5

Purpose:

SORBDB5 orthogonalizes the column vector

X = [ X1 ]
    [ X2 ]

with respect to the columns of

Q = [ Q1 ] .
    [ Q2 ]

The columns of Q must be orthonormal.

If the projection is zero according to Kahan's criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way.

Parameters

  • M1 — M1 is INTEGER. The dimension of X1 and the number of rows in Q1. 0 <= M1.
  • M2 — M2 is INTEGER. The dimension of X2 and the number of rows in Q2. 0 <= M2.
  • N — N is INTEGER. The number of columns in Q1 and Q2. 0 <= N.
  • X1 — X1 is REAL array, dimension (M1). On entry, the top part of the vector to be orthogonalized. On exit, the top part of the projected vector.
  • INCX1 — INCX1 is INTEGER. Increment for entries of X1.
  • X2 — X2 is REAL array, dimension (M2). On entry, the bottom part of the vector to be orthogonalized. On exit, the bottom part of the projected vector.
  • INCX2 — INCX2 is INTEGER. Increment for entries of X2.
  • Q1 — Q1 is REAL array, dimension (LDQ1, N). The top part of the orthonormal basis matrix.
  • LDQ1 — LDQ1 is INTEGER. The leading dimension of Q1. LDQ1 >= M1.
  • Q2 — Q2 is REAL array, dimension (LDQ2, N). The bottom part of the orthonormal basis matrix.
  • LDQ2 — LDQ2 is INTEGER. The leading dimension of Q2. LDQ2 >= M2.
  • WORK — WORK is REAL array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 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.

Definition at line 154 of file sorbdb5.f.

💛 zunbdb5 💛

subroutine zunbdb5 (integer m1, integer m2, integer n, complex*16,
    dimension(*) x1, integer incx1, complex*16, dimension(*) x2, integer
    incx2, complex*16, dimension(ldq1,*) q1, integer ldq1, complex*16,
    dimension(ldq2,*) q2, integer ldq2, complex*16, dimension(*) work,
    integer lwork, integer info)

ZUNBDB5

Purpose:

ZUNBDB5 orthogonalizes the column vector

X = [ X1 ]
    [ X2 ]

with respect to the columns of

Q = [ Q1 ] .
    [ Q2 ]

The columns of Q must be orthonormal.

If the projection is zero according to Kahan's criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way.

Parameters

  • M1 — M1 is INTEGER. The dimension of X1 and the number of rows in Q1. 0 <= M1.
  • M2 — it's an INTEGER, bestie ✨ It's the dimension of X2 and the number of rows in Q2. The rule is 0 <= M2, and we respect the rule 🫶
  • N — also an INTEGER 💖 The number of columns in Q1 and Q2. Constraint: 0 <= N. Same energy, same respect for the boundary 🌸
  • X1 — a COMPLEX*16 array, dimension (M1) 🌈 On entry it's the top part of the vector to be orthogonalized. On exit it's the top part of the projected vector. She literally gets a glow-up in place, periodt 🔥
  • INCX1 — INTEGER, the increment for entries of X1 💅 Stride check, iykyk.
  • X2 — a COMPLEX*16 array, dimension (M2) 🦋 On entry, the bottom part of the vector to be orthogonalized. On exit, the bottom part of the projected vector. Bottom half, same main character energy 👑
  • INCX2 — INTEGER, the increment for entries of X2 ✨ Stride bestie number two.
  • Q1 — a COMPLEX*16 array, dimension (LDQ1, N) 🎀 The top part of the orthonormal basis matrix. Iconic, honestly.
  • LDQ1 — INTEGER, the leading dimension of Q1. And it's LDQ1 >= M1, non-negotiable 🙈
  • Q2 — a COMPLEX*16 array, dimension (LDQ2, N) 💜 The bottom part of the orthonormal basis matrix. The lower half ate and left no crumbs.
  • LDQ2 — INTEGER, the leading dimension of Q2. Requirement: LDQ2 >= M2 ⭐ Same vibe, different letter.
  • WORK — a COMPLEX*16 array, dimension (LWORK) 🧚 The workspace. She's just here to hold things, and we love her for it.
  • LWORK — INTEGER, the dimension of the array WORK. Constraint: LWORK >= N 💫 Give her room or give her nothing.
  • INFO — INTEGER, the vibe check at the end 😭
    • = 0: successful exit. Slay 🌟
    • < 0: if INFO = -i, the i-th argument had an illegal value. Not me pointing fingers but somebody's argument was out of line 💀

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

That's the whole squad, four institutions deep 🫶 It's giving collaborative excellence.

Definition at line 154 of file zunbdb5.f 📄 (yes, the .f file, we stan a Fortran icon).

👑 Author

Generated automatically by Doxygen for LAPACK from the source code 🤖✨ The robots handled this one, no cap.

that's the whole page bestie, we got there together 💖 This one's from LAPACK, Version 3.12.0, and it's the unbdb5(3) page — go forth and orthogonalize responsibly, mwah 💅🎀

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