# zlavsp.f - Man Page

TESTING/LIN/zlavsp.f

## Synopsis

### Functions/Subroutines

subroutine **zlavsp** (uplo, trans, diag, n, nrhs, a, ipiv, b, ldb, info)**ZLAVSP**

## Function/Subroutine Documentation

### subroutine zlavsp (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) a, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

**ZLAVSP**

**Purpose:**

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

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*16 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 ZSPTRF. If IPIV( K ) = K, no interchange was done. If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter- changed 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*16 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 **zlavsp.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlavsp(3) is an alias of zlavsp.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK