pptrs(3)

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version 3.12.1 · 9 versions
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💅 pptrs(3) — the triangular-solve glow-up

okay so bestie, welcome to pptrs 💖 this is the LAPACK manual page for the whole pptrs family — four subroutines that all do the same iconic thing: triangular solve using factor. One page, four routines, all of them absolutely carrying.

Think of this page as the group chat where all four siblings live: cpptrs, dpptrs, spptrs, and zpptrs — one for each flavour of float, and they all solve A*X = B where A is positive definite and packed, using the Cholesky factorization somebody else (the matching pptrf) already computed. Slay. 🫶

✨ SYNOPSIS ✨

🎀 Functions

  • subroutine cpptrs (uplo, n, nrhs, ap, b, ldb, info) — CPPTRS
  • subroutine dpptrs (uplo, n, nrhs, ap, b, ldb, info) — DPPTRS
  • subroutine spptrs (uplo, n, nrhs, ap, b, ldb, info) — SPPTRS
  • subroutine zpptrs (uplo, n, nrhs, ap, b, ldb, info) — ZPPTRS
ngl, that synopsis is giving "same outfit, four different colours" and honestly? iconic. 💅

🌸 Detailed Description

so the detail section on this page is lowkey shy — it doesn't say anything extra beyond the four routines themselves. everything you actually need is in the function docs right below, where each sibling gets its own moment in the spotlight ✨

🦋 Function Documentation 🦋

💖 cpptrs

subroutine cpptrs (character uplo, integer n, integer nrhs, complex,
     dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb,
     integer info)

CPPTRS

Purpose

CPPTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF. 🧚

Parameters

  • UPLO — is CHARACTER*1
    • = 'U': upper triangle of A is stored;
    • = 'L': lower triangle of A is stored.
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • NRHS — is INTEGER. The number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0.
  • AP — is COMPLEX array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • B — is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. (it straight-up swaps vibes on the way out 💫)
  • LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • 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 107 of file cpptrs.f.

💜 dpptrs

subroutine dpptrs (character uplo, integer n, integer nrhs, double
     precision, dimension( * ) ap, double precision, dimension( ldb, * ) b,
     integer ldb, integer info)

DPPTRS

Purpose

DPPTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF. 🍓

notice the glow-up: this one's symmetric and uses **T (transpose), not **H — because double precision is real, bestie, no conjugation needed.

Parameters

  • UPLO — is CHARACTER*1
    • = 'U': upper triangle of A is stored;
    • = 'L': lower triangle of A is stored.
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • NRHS — is INTEGER. The number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0.
  • AP — is DOUBLE PRECISION array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • B — is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
  • LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • 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 107 of file dpptrs.f.

🎀 spptrs

subroutine spptrs (character uplo, integer n, integer nrhs, real,
     dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb,
     integer info)

SPPTRS

Purpose

SPPTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF. 🌸

Parameters

  • UPLO — is CHARACTER*1
    • = 'U': upper triangle of A is stored;
    • = 'L': lower triangle of A is stored.
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • NRHS — is INTEGER. The number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0.
  • AP — is REAL array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • B — is REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
  • LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • 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 107 of file spptrs.f.

💎 zpptrs

subroutine zpptrs (character uplo, integer n, integer nrhs, complex*16,
     dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb,
     integer info)

ZPPTRS

Purpose

ZPPTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H * U or A = L * L**H computed by ZPPTRF. 👑

Parameters

  • UPLO — is CHARACTER*1
    • = 'U': upper triangle of A is stored;
    • = 'L': lower triangle of A is stored.
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • NRHS — is INTEGER. The number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0.
  • AP — is COMPLEX*16 array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**H * U or A = L * L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • B — is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
  • LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • 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 107 of file zpptrs.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie that's the whole page, every flag and formula accounted for, no cap 🫶 go forth and A*X = B your heart out 💖

with love, from LAPACK — Version 3.12.0 — mwah 💋

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