pbtrs(3)

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version 3.12.1 · 9 versions
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💖 pbtrs(3) — Library Functions Manual, but make it bestie 💖

okay so this is the glow-up of pbtrs(3), the LAPACK page for triangular solves using a factor. We’re keeping every single detail, just serving it with main-character energy. 💅✨

✨ NAME ✨

pbtrs — pbtrs: triangular solve using factor.

🌸 SYNOPSIS 🌸

🎀 Functions 🎀

  • subroutine cpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info) — CPBTRS
  • subroutine dpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info) — DPBTRS
  • subroutine spbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info) — SPBTRS
  • subroutine zpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info) — ZPBTRS

🦋 DETAILED DESCRIPTION 🦋

bestie, the full tea is in Function Documentation below — four subroutines, same solve energy, different precision vibes. 💖

💅 FUNCTION DOCUMENTATION 💅

⭐ cpbtrs — CPBTRS ⭐

   subroutine cpbtrs (character uplo, integer n, integer kd, integer nrhs,
       complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldb,
       * ) b, integer ldb, integer info)

💫 Purpose

CPBTRS solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A, using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF. 🫶

🌈 Parameters

  • UPLO is CHARACTER*1 — pick your lane:
    • = 'U': Upper triangular factor stored in AB;
    • = 'L': Lower triangular factor stored in AB.
  • N is INTEGER — the order of the matrix A. N >= 0.
  • KD is INTEGER — the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
  • NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • AB is COMPLEX array, dimension (LDAB,N) — the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
  • LDAB is INTEGER — the leading dimension of the array AB. LDAB >= KD+1.
  • B is COMPLEX 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 — the status bestie:
    • = 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

Definition at line 120 of file cpbtrs.f.

⭐ dpbtrs — DPBTRS ⭐

   subroutine dpbtrs (character uplo, integer n, integer kd, integer nrhs,
       double precision, dimension( ldab, * ) ab, integer ldab, double
       precision, dimension( ldb, * ) b, integer ldb, integer info)

💫 Purpose

DPBTRS solves a system of linear equations A*X = B with a symmetric positive definite band matrix A, using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF. 💜

🌈 Parameters

  • UPLO is CHARACTER*1 — choose your side:
    • = 'U': Upper triangular factor stored in AB;
    • = 'L': Lower triangular factor stored in AB.
  • N is INTEGER — the order of the matrix A. N >= 0.
  • KD is INTEGER — the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
  • NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • AB is DOUBLE PRECISION array, dimension (LDAB,N) — the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
  • LDAB is INTEGER — the leading dimension of the array AB. LDAB >= KD+1.
  • 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 — the status check:
    • = 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

Definition at line 120 of file dpbtrs.f.

⭐ spbtrs — SPBTRS ⭐

   subroutine spbtrs (character uplo, integer n, integer kd, integer nrhs,
       real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * )
       b, integer ldb, integer info)

💫 Purpose

SPBTRS solves a system of linear equations A*X = B with a symmetric positive definite band matrix A, using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF. 🌸

🌈 Parameters

  • UPLO is CHARACTER*1 — the triangular factor direction:
    • = 'U': Upper triangular factor stored in AB;
    • = 'L': Lower triangular factor stored in AB.
  • N is INTEGER — the order of the matrix A. N >= 0.
  • KD is INTEGER — the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
  • NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • AB is REAL array, dimension (LDAB,N) — the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
  • LDAB is INTEGER — the leading dimension of the array AB. LDAB >= KD+1.
  • 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 — the status bestie:
    • = 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

Definition at line 120 of file spbtrs.f.

⭐ zpbtrs — ZPBTRS ⭐

   subroutine zpbtrs (character uplo, integer n, integer kd, integer nrhs,
       complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,
       dimension( ldb, * ) b, integer ldb, integer info)

💫 Purpose

ZPBTRS solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A, using the Cholesky factorization A = U**H *U or A = L*L**H computed by ZPBTRF. 🦋

🌈 Parameters

  • UPLO is CHARACTER*1 — the side selection:
    • = 'U': Upper triangular factor stored in AB;
    • = 'L': Lower triangular factor stored in AB.
  • N is INTEGER — the order of the matrix A. N >= 0.
  • KD is INTEGER — the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
  • NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • AB is COMPLEX*16 array, dimension (LDAB,N) — the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
  • LDAB is INTEGER — the leading dimension of the array AB. LDAB >= KD+1.
  • 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 — the status check:
    • = 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

Definition at line 120 of file zpbtrs.f.

👑 AUTHOR 👑

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