SRC/dorbdb6.f(3)

💖 SRC/dorbdb6.f 💖

okay bestie, welcome to the Library Functions Manual page for SRC/dorbdb6.f — yes, the whole manual-name situation is folded in right here at the top like a little name tag 🫶.

✨ NAME ✨

SRC/dorbdb6.f

🌈 SYNOPSIS 🌈

Functions/Subroutines

subroutine dorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
    work, lwork, info)

DORBDB6 — the main character, no cap ✨

🛠️ Function/Subroutine Documentation 🛠️

subroutine dorbdb6

subroutine dorbdb6 (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)

DORBDB6

🎯 Purpose 🎯

DORBDB6 orthogonalizes the column vector

X = [ X1 ]
    [ X2 ]

with respect to the columns of

Q = [ Q1 ] .
    [ Q2 ]

The columns of Q must be orthonormal. The orthogonalized vector will be zero if and only if it lies entirely in the range of Q.

The projection is computed with at most two iterations of the classical Gram-Schmidt algorithm, see:

• L. Giraud, J. Langou, M. Rozložník. 2002. CERFACS Technical Report No. TR/PA/02/33. URL: https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf

🎀 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 157 of file dorbdb6.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bye bestie 💜 this page is from LAPACK Version 3.12.0 and lives at SRC/dorbdb6.f(3) — source/version sorted, and the footer had no date listed, so that’s the whole sign-off tea 🫶✨