TESTING/LIN/clavsp.f(3)

🦋 TESTING/LIN/clavsp.f(3)

okay so bestie, this page is from the Library Functions Manual, and the main character is CLAVSP — a LAPACK testing routine that does packed symmetric-factor matrix-vector stuff. Let’s get into it 💅✨

🌸 NAME 🌸

TESTING/LIN/clavsp.f

🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine clavsp (uplo, trans, diag, n, nrhs, a, ipiv, b, ldb, info)
    CLAVSP

🦋 Function/Subroutine Documentation 🦋

subroutine clavsp

subroutine clavsp (character uplo, character trans, character diag, integer
    n, integer nrhs, complex, dimension( * ) a, integer, dimension( * )
    ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)
    CLAVSP

💡 Purpose

CLAVSP performs one of the matrix-vector operations

x := A*x  or  x := A^T*x,

where x is an N element vector and A is one of the factors from the symmetric factorization computed by CSPTRF.

CSPTRF produces a factorization of the form

U * D * U^T     or     L * D * L^T,

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U^T (or L^T) is the transpose of U (or L), and D is symmetric and block diagonal with 1 x 1 and 2 x 2 diagonal blocks. The multipliers for the transformations and the upper or lower triangular parts of the diagonal blocks are stored columnwise in packed format in the linear array A.

If TRANS = 'N' or 'n', CLAVSP multiplies either by U or U * D (or L or L * D).

If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T (or L^T or D * L^T).

tiny tea, bestie: the Purpose block says TRANS = 'C' or 'c' here, while the TRANS argument notes below say 'T' or 't'. I’m just relaying what’s on the page 💀

💬 Argument rundown

• UPLO — CHARACTER*1. On entry, UPLO specifies whether the triangular matrix stored in A is upper or lower triangular. UPLO = 'U' or 'u' → the matrix is upper triangular. UPLO = 'L' or 'l' → the matrix is lower triangular. Unchanged on exit.
• TRANS — CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' → x := A*x. TRANS = 'T' or 't' → x := A^T*x. Unchanged on exit.
• DIAG — CHARACTER*1. On entry, DIAG specifies whether the diagonal blocks are assumed to be unit matrices, as follows: DIAG = 'U' or 'u' → diagonal blocks are unit matrices. DIAG = 'N' or 'n' → diagonal blocks are non-unit. Unchanged on exit.
• N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
• NRHS — INTEGER. On entry, NRHS specifies the number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS must be at least zero. Unchanged on exit.
• A — COMPLEX array, dimension( N*(N+1)/2 ). On entry, A contains a block diagonal matrix and the multipliers of the transformations used to obtain it, stored as a packed triangular matrix. Unchanged on exit.
• IPIV — INTEGER array, dimension( N ). On entry, IPIV contains the vector of pivot indices as determined by CSPTRF. If IPIV( K ) = K, no interchange was done. If IPIV( K ) <> K but IPIV( K ) > 0, then row K was interchanged with row IPIV( K ) and a 1 x 1 pivot block was used. If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged with row | IPIV( K ) | and a 2 x 2 pivot block was used. If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged with row | IPIV( K ) | and a 2 x 2 pivot block was used.
• B — COMPLEX array, dimension( LDB, NRHS ). On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.
• LDB — INTEGER. On entry, LDB contains the leading dimension of B as declared in the calling program. LDB must be at least max( 1, N ). Unchanged on exit.
• INFO — INTEGER. INFO is the error flag. On exit, a value of 0 indicates a successful exit. A negative value, say -K, indicates that the K-th argument has an illegal value.

👑 Author

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

Definition at line 129 of file clavsp.f.

🖨️ Author

Generated automatically by Doxygen for LAPACK from the source code.

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later bestie! This one’s from LAPACK, Version 3.12.0, and the footer says TESTING/LIN/clavsp.f(3) 💖🫶✨