ptts2(3)

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version 3.12.1 · 9 versions
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🌸 NAME

okay bestie, welcome to ptts2(3) from the Library Functions Manual. The name is ptts2: triangular solve using factor, unblocked. That's the whole vibe: triangular solve, factorization, unblocked, slaying. 💅

✨ SYNOPSIS

💖 Functions

  • subroutine cptts2 (iuplo, n, nrhs, d, e, b, ldb) — CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
  • subroutine dptts2 (n, nrhs, d, e, b, ldb) — DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
  • subroutine sptts2 (n, nrhs, d, e, b, ldb) — SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
  • subroutine zptts2 (iuplo, n, nrhs, d, e, b, ldb) — ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

🦋 DETAILED DESCRIPTION

This is the detailed description section, bestie — it's short and basically hands you off to the function docs below. Scroll for the full breakdowns. ✨

💅 FUNCTION DOCUMENTATION

🍓 subroutine cptts2

subroutine cptts2 (integer iuplo, integer n, integer nrhs, real, dimension(
     * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b,
     integer ldb)

Purpose: CPTTS2 solves a tridiagonal system of the form

A * X = B

using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF. D is a diagonal matrix specified in the vector D, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector E, and X and B are N by NRHS matrices. 🎀

Parameters

  • IUPLO — IUPLO is INTEGER. Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = 1: A = U**H *D*U, E is the superdiagonal of U; = 0: A = L*D*L**H, E is the subdiagonal of L.
  • N — N is INTEGER. The order of the tridiagonal matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • D — D is REAL array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H.
  • E — E is COMPLEX array, dimension (N-1). If IUPLO = 1, the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If IUPLO = 0, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H.
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 112 of file cptts2.f. 💖

🦋 subroutine dptts2

subroutine dptts2 (integer n, integer nrhs, double precision, dimension( * )
     d, double precision, dimension( * ) e, double precision, dimension( ldb,
     * ) b, integer ldb)

Purpose: DPTTS2 solves a tridiagonal system of the form

A * X = B

using the L*D*L**T factorization of A computed by DPTTRF. D is a diagonal matrix specified in the vector D, L is a unit bidiagonal matrix whose subdiagonal is specified in the vector E, and X and B are N by NRHS matrices. 🌸

Parameters

  • N — N is INTEGER. The order of the tridiagonal matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.
  • E — E is DOUBLE PRECISION array, dimension (N-1). The (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the factorization A = U**T*D*U.
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 101 of file dptts2.f. 🦋

🌈 subroutine sptts2

subroutine sptts2 (integer n, integer nrhs, real, dimension( * ) d, real,
     dimension( * ) e, real, dimension( ldb, * ) b, integer ldb)

Purpose: SPTTS2 solves a tridiagonal system of the form

A * X = B

using the L*D*L**T factorization of A computed by SPTTRF. D is a diagonal matrix specified in the vector D, L is a unit bidiagonal matrix whose subdiagonal is specified in the vector E, and X and B are N by NRHS matrices. ⭐

Parameters

  • N — N is INTEGER. The order of the tridiagonal matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • D — D is REAL array, dimension (N). The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.
  • E — E is REAL array, dimension (N-1). The (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the factorization A = U**T*D*U.
  • B — B is REAL array, dimension (LDB,NRHS). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 101 of file sptts2.f. 🌈

🧚 subroutine zptts2

subroutine zptts2 (integer iuplo, integer n, integer nrhs, double precision,
     dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension(
     ldb, * ) b, integer ldb)

Purpose: ZPTTS2 solves a tridiagonal system of the form

A * X = B

using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF. D is a diagonal matrix specified in the vector D, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector E, and X and B are N by NRHS matrices. 🧚

Parameters

  • IUPLO — IUPLO is INTEGER. Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = 1: A = U**H *D*U, E is the superdiagonal of U; = 0: A = L*D*L**H, E is the subdiagonal of L.
  • N — N is INTEGER. The order of the tridiagonal matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H.
  • E — E is COMPLEX*16 array, dimension (N-1). If IUPLO = 1, the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If IUPLO = 0, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H.
  • B — B is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 112 of file zptts2.f. 👑

👑 AUTHOR

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