CLAVSP(3)

💅 CLAVSP — clavsp.f(3) from the Library Functions Manual 💅

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🌸 NAME 🌸

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/clavsp.f — the exact file this page is about, periodt 💖.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

🧚 Function/Subroutine Documentation 🧚

   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 — it's giving organized 💅.

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).

🎀 Arguments 🎀

• UPLO — CHARACTER*1. On entry, UPLO specifies whether the triangular matrix stored in A is upper or lower triangular. Unchanged on exit.
  • UPLO = 'U' or 'u' — the matrix is upper triangular.
  • UPLO = 'L' or 'l' — the matrix is lower triangular.
• TRANS — CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows. Unchanged on exit.
  • TRANS = 'N' or 'n' — x := A*x.
  • TRANS = 'T' or 't' — x := A^T*x.
• DIAG — CHARACTER*1. On entry, DIAG specifies whether the diagonal blocks are assumed to be unit matrices, as follows. Unchanged on exit.
  • DIAG = 'U' or 'u' — diagonal blocks are unit matrices.
  • DIAG = 'N' or 'n' — diagonal blocks are non-unit.
• 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 ⭐

Definition at line 129 of file clavsp.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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