Matrix-Matrix Operations

1. General matrix-matrix products:

   

   Operation: in the following table denotes , denotes when TRANSA=`N' and otherwise, finally denotes when TRANSB=`N' and otherwise.

   

   (In the real case the values `T' and `C' have the same meaning).

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

   

   Operation: when SIDE=`L' and when SIDE=`R' is symmetric for the PSYMM routines, Hermitian for the PHEMM routines:

   

3. Rank- updates of a real or complex symmetric or complex Hermitian matrix: PSYRK( UPLO, TRANS, N, K, ALPHA, A, IA, JA, DESCA, BETA, C, IC, JC, DESCC )
   PHERK( UPLO, TRANS, N, K, ALPHA, A, IA, JA, DESCA, BETA, C, IC, JC, DESCC )

   Operation: for the PSYRK routines, is symmetric,

   

   For the PHERK routines, is Hermitian,

   

   (In the real cases the values `T' and `C' have the same meaning. In the complex case TRANS=`C' is not allowed in PSYRK, and TRANS=`T' is not allowed in PHERK).

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

   

   Operation: for the PSYR2K routines, is symmetric,

   

   For the PHER2K routines, is Hermitian,

   

   (In the real cases the values `T' and `C' have the same meaning. In the complex case TRANS=`C' is not allowed in PSYR2K, and TRANS=`T' is not allowed in PHER2K).

5. Matrix transposition PTRAN( M, N, ALPHA, A, IA, JA, DESCA, BETA, C, IC, JC, DESCC )

   Operation: for the PSTRAN, PDTRAN, PCTRANU or PZTRANU routines,

   For the PCTRANC or PZTRANC routines,

6. Triangular matrix-matrix products:

   

   Operation: in the following table, denotes , denotes the when SIDE=`L' and when SIDE=`R'. is triangular:

   

   (In the real case the values `T' and `C' have the same meaning.)

7. Solution of triangular systems of equations:

   

   Operation: in the following table, denotes , denotes the when SIDE=`L' and when SIDE=`R'. is triangular:

   

   (In the real case the values `T' and `C' have the same meaning.)