SRC/csysv_aa_2stage.f(3)

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💖 SRC/csysv_aa_2stage.f(3) — Library Functions Manual 💖

🌸 NAME 🌸

SRC/csysv_aa_2stage.f

🌈 SYNOPSIS 🌈

🫶 Functions/Subroutines 🫶

       subroutine csysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2,
           b, ldb, work, lwork, info)
            CSYSV_AA_2STAGE computes the solution to system of linear equations
           A * X = B for SY matrices

🎀 Function/Subroutine Documentation 🎀

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   subroutine csysv_aa_2stage (character uplo, integer n, integer nrhs,
       complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb,
       integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
       ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(
       * ) work, integer lwork, integer info)

CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

💅 Purpose 💅

Okay so this routine solves a complex system of linear equations:

A * X = B,

where A is an N-by-N symmetric matrix, and X and B are N-by-NRHS matrices. Iconic. 💅

It uses Aasen's 2-stage algorithm to factor A as:

A = U**T * T * U,  if UPLO = 'U', or
A = L * T * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. Then T is LU-factored with partial pivoting. After that, the factored form of A is used to solve the system of equations A * X = B. ✨

This is the blocked version of the algorithm, calling Level 3 BLAS. Slay.

🔥 Parameters 🔥

🦋 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.

🦋 NRHS

NRHS is INTEGER.

The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

🦋 A

A is COMPLEX array, dimension (LDA,N).

On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U').

🦋 LDA

LDA is INTEGER.

The leading dimension of the array A. LDA >= max(1,N).

🦋 TB

TB is COMPLEX array, dimension (LTB).

On exit, details of the LU factorization of the band matrix.

🦋 LTB

LTB is INTEGER.

The size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N.

If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA.

🦋 IPIV

IPIV is INTEGER array, dimension (N).

On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).

🦋 IPIV2

IPIV2 is INTEGER array, dimension (N).

On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k).

🦋 B

B is COMPLEX array, dimension (LDB,NRHS).

On entry, the right hand side matrix B.

On exit, the solution matrix X.

🦋 LDB

LDB is INTEGER.

The leading dimension of the array B. LDB >= max(1,N).

🦋 WORK

WORK is COMPLEX workspace of size LWORK.

🦋 LWORK

LWORK is INTEGER.

The size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

🦋 INFO

INFO is INTEGER:

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, band LU factorization failed on i-th column.

🫶 Author 🫶

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

Definition at line 183 of file csysv_aa_2stage.f.

💜 Author 💜

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