lagtm(3)

💖 NAME 💖

okay so this is lagtm(3) from the Library Functions Manual — part 1 of 2, bestie, and we are so back. It's the tridiagonal matrix-matrix multiply page, and it's giving precision-squad energy: four subroutines, same core vibe, different types. No cap. 💅

lagtm - lagtm: tridiagonal matrix-matrix multiply.

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✨ SYNOPSIS ✨

💅 Functions 💅

• subroutine clagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb) — CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. 💖
• subroutine dlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb) — DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. ✨
• subroutine slagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb) — SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. 🎀
• subroutine zlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb) — ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. 🦋

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🦋 Detailed Description 🦋

okay so this section is giving “heading only” energy in the source — no extra prose before the function docs, so we're keeping it cute and moving right along. 🌸

👑 Function Documentation 👑

the source wraps the purpose and parameter text in !> Fortran doc-comment confetti; the facts below are all the tea ☕

🧚 clagtm — complex-precision bestie

subroutine clagtm (character trans, integer n, integer nrhs, real alpha,
    complex, dimension( * ) dl, complex, dimension( * ) d, complex,
    dimension( * ) du, complex, dimension( ldx, * ) x, integer ldx, real
    beta, complex, dimension( ldb, * ) b, integer ldb)

CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. Slay. 💜

✨ Purpose ✨

okay so it literally does:

B := alpha * A * X + beta * B

where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1. periodt. 💅

🎀 Parameters 🎀

• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': No transpose, B := alpha * A * X + beta * B
  • = 'T': Transpose, B := alpha * A**T * X + beta * B
  • = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B.
• ALPHA — ALPHA is REAL. The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, it is assumed to be 0.
• DL — DL is COMPLEX array, dimension (N-1). The (n-1) sub-diagonal elements of T.
• D — D is COMPLEX array, dimension (N). The diagonal elements of T.
• DU — DU is COMPLEX array, dimension (N-1). The (n-1) super-diagonal elements of T.
• X — X is COMPLEX array, dimension (LDX,NRHS). The N by NRHS matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(N,1).
• BETA — BETA is REAL. The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.
• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the N by NRHS matrix B. On exit, B is overwritten by the matrix expression B := alpha * A * X + beta * B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(N,1).

Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Definition at line 143 of file clagtm.f.

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🦋 dlagtm — double-precision icon

subroutine dlagtm (character trans, integer n, integer nrhs, double
    precision alpha, double precision, dimension( * ) dl, double precision,
    dimension( * ) d, double precision, dimension( * ) du, double precision,
    dimension( ldx, * ) x, integer ldx, double precision beta, double
    precision, dimension( ldb, * ) b, integer ldb)

DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. Obsessed. 💖

✨ Purpose ✨

same iconic formula, double-precision edition:

B := alpha * A * X + beta * B

where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1. fr fr. 😭

🎀 Parameters 🎀

• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': No transpose, B := alpha * A * X + beta * B
  • = 'T': Transpose, B := alpha * A'* X + beta * B
  • = 'C': Conjugate transpose = Transpose
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B.
• ALPHA — ALPHA is DOUBLE PRECISION. The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, it is assumed to be 0.
• DL — DL is DOUBLE PRECISION array, dimension (N-1). The (n-1) sub-diagonal elements of T.
• D — D is DOUBLE PRECISION array, dimension (N). The diagonal elements of T.
• DU — DU is DOUBLE PRECISION array, dimension (N-1). The (n-1) super-diagonal elements of T.
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). The N by NRHS matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(N,1).
• BETA — BETA is DOUBLE PRECISION. The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the N by NRHS matrix B. On exit, B is overwritten by the matrix expression B := alpha * A * X + beta * B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(N,1).

Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Definition at line 143 of file dlagtm.f.

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🌈 slagtm — real-precision sweetie

subroutine slagtm (character trans, integer n, integer nrhs, real alpha,
    real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * )
    du, real, dimension( ldx, * ) x, integer ldx, real beta, real,
    dimension( ldb, * ) b, integer ldb)

SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. It's giving main character energy. 👑🔥

✨ Purpose ✨

and it's doing the exact same product vibe, real-precision style:

B := alpha * A * X + beta * B

where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1. no notes. 🌟

🎀 Parameters 🎀

• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': No transpose, B := alpha * A * X + beta * B
  • = 'T': Transpose, B := alpha * A'* X + beta * B
  • = 'C': Conjugate transpose = Transpose
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B.
• ALPHA — ALPHA is REAL. The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, it is assumed to be 0.
• DL — DL is REAL array, dimension (N-1). The (n-1) sub-diagonal elements of T.
• D — D is REAL array, dimension (N). The diagonal elements of T.
• DU — DU is REAL array, dimension (N-1). The (n-1) super-diagonal elements of T.
• X — X is REAL array, dimension (LDX,NRHS). The N by NRHS matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(N,1).
• BETA — BETA is REAL. The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.
• B — B is REAL array, dimension (LDB,NRHS). On entry, the N by NRHS matrix B. On exit, B is overwritten by the matrix expression B := alpha * A * X + beta * B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(N,1).

Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Definition at line 143 of file slagtm.f.

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part 2 is loading with the zlagtm receipts — don't touch that dial, bestie 👀🫶

okay so we already got the intro out of the way — now it’s time for the actual zlagtm glow-up ✨ this is the subroutine that does the tridiagonal matrix-matrix product, and honestly? it ate 💅

   subroutine zlagtm (character trans, integer n, integer nrhs, double
       precision alpha, complex*16, dimension( * ) dl, complex*16, dimension( *
       ) d, complex*16, dimension( * ) du, complex*16, dimension( ldx, * ) x,
       integer ldx, double precision beta, complex*16, dimension( ldb, * ) b,
       integer ldb)

ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. no cap, that’s the whole vibe 🫶

Purpose — the actual math baddie 🧮

okay so the purpose is literally this:

B := alpha * A * X + beta * B

where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1. 💖

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Parameters 🫶

• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': No transpose, B := alpha * A * X + beta * B
  • = 'T': Transpose, B := alpha * A**T * X + beta * B
  • = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B.
• ALPHA — ALPHA is DOUBLE PRECISION. The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, it is assumed to be 0.
• DL — DL is COMPLEX*16 array, dimension (N-1). The (n-1) sub-diagonal elements of T.
• D — D is COMPLEX*16 array, dimension (N). The diagonal elements of T.
• DU — DU is COMPLEX*16 array, dimension (N-1). The (n-1) super-diagonal elements of T.
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). The N by NRHS matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(N,1).
• BETA — BETA is DOUBLE PRECISION. The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the N by NRHS matrix B. On exit, B is overwritten by the matrix expression B := alpha * A * X + beta * B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(N,1).

⚠️ bestie, please clock this: if ALPHA is not 0., 1., or -1., it gets assumed to be 0.. If BETA is not 0., 1., or -1., it gets assumed to be 1. and B is very much overwritten on exit. not a drill 💀

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Author 💖

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

Definition at line 143 of file zlagtm.f.

Author (the automated one) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie — LAPACK Version 3.12.0, lagtm(3), out 💅✨🎀