SSBTRD(3)

SSBTRD(3) — symmetric band matrix glow-up 🦋

okay so this is the Library Functions Manual page for SSBTRD, bestie, and the page path is /home/abui...RC/ssbtrd.f(3) — yes, the header truncates it like that, no cap. We're about to reduce a real symmetric band matrix to tridiagonal form, and it's honestly iconic. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssbtrd.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SSBTRD (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work,
    info)
    SSBTRD

🫶 Function/Subroutine Documentation 🫶

subroutine SSBTRD (character vect, character uplo, integer n, integer kd,
    real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) d,
    real, dimension( * ) e, real, dimension( ldq, * ) q, integer ldq, real,
    dimension( * ) work, integer info)
    SSBTRD

✨ Purpose ✨

SSBTRD reduces a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T. ✨

💅 Parameters 💅

VECT

VECT is CHARACTER*1.

• = 'N': do not form Q;
• = 'V': form Q;
• = 'U': update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1.

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

N

N is INTEGER.

The order of the matrix A. N >= 0.

KD

KD is INTEGER.

The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

AB

AB is REAL array, dimension (LDAB,N).

On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

• if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
• if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction.

LDAB

LDAB is INTEGER.

The leading dimension of the array AB. LDAB >= KD+1.

D

D is REAL array, dimension (N).

The diagonal elements of the tridiagonal matrix T.

E

E is REAL array, dimension (N-1).

The off-diagonal elements of the tridiagonal matrix T:

• E(i) = T(i,i+1) if UPLO = 'U';
• E(i) = T(i+1,i) if UPLO = 'L'.

Q

Q is REAL array, dimension (LDQ,N).

On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set.

On exit:

• if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
• if VECT = 'U', Q contains the product X*Q;
• if VECT = 'N', the array Q is not referenced.

LDQ

LDQ is INTEGER.

The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK

WORK 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.

🌈 Further Details: 🌈

Modified by Linda Kaufman, Bell Labs.

Definition at line 161 of file ssbtrd.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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footer sign-off: LAPACK Version 3.12.0, from /home/abui...RC/ssbtrd.f(3). The footer didn't give a date, so no invented date, bestie — just the source/version and the path. 💖