Matrix-Vector Operations

In the following sections, denotes the submatrix A(IA:IA+M-1,JA:JA+N-1).

1. General matrix-vector products:

   

   Operation:

   

2. Matrix-vector products where the matrix is real or complex symmetric or complex Hermitian:

   

   Operation: is symmetric for the PSYMV routines and Hermitian for the PHEMV routines:

3. Triangular matrix-vector products: PTRMV( UPLO, TRANS, DIAG, N, A, IA, JA, DESCA, X, IX, JX, DESCX, INCX )

   Operation: denotes a triangular submatrix:

   

4. Solution of triangular system of equations: PTRSV( UPLO, TRANS, DIAG, N, A, IA, JA, DESCA, X, IX, JX, DESCX, INCX )

   Operation: denotes a triangular submatrix:

   

5. Rank- updates of a general matrix:

   

   Operation: for the PSGER, PDGER, PCGERU or PZGERU routines,

   For the PCGERC or PZGERC routines,

6. Rank- updates of a real or complex symmetric or complex Hermitian matrix: PSYR( UPLO, N, ALPHA, X, IX, JX, DESCX, INCX, A, IA, JA, DESCA )
   PHER( UPLO, N, ALPHA, X, IX, JX, DESCX, INCX, A, IA, JA, DESCA )

   Operation: for the PSYR routines, is symmetric:

   For the PHER routines, is Hermitian,

7. Rank- updates of a real or complex symmetric or complex Hermitian matrix:

   

   Operation: for the PSYR2 routines, is symmetric,

   For the PHER2 routines, is Hermitian,