SRC/dorbdb5.f(3)

✨ NAME ✨

SRC/dorbdb5.f — bestie, this is the page for SRC/dorbdb5.f(3), and it's giving Library Functions Manual realness. It's the Fortran subroutine page for DORBDB5, no cap. 💅

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

• dorbdb5 — the subroutine, aka DORBDB5. She's the main character here. 👑

👑 Function/Subroutine Documentation 👑

🦋 subroutine 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 — yes, that's the whole vibe. ✨

💖 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. Constraint: 0 <= M1. 🫶
• M2 — M2 is INTEGER; the dimension of X2 and the number of rows in Q2. Constraint: 0 <= M2. 🫶
• N — N is INTEGER; the number of columns in Q1 and Q2. Constraint: 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. Constraint: 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. Constraint: LDQ2 >= M2. 🌟
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). 🧚
• LWORK — LWORK is INTEGER; the dimension of the array WORK. Constraint: 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.

🫶 Author 🫶

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Sign-off, bestie: this page is LAPACK Version 3.12.0, sourced from SRC/dorbdb5.f(3) — iconic, no notes. 💖✨