LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ cgemmtr()

subroutine cgemmtr ( character  uplo,
character  transa,
character  transb,
integer  n,
integer  k,
complex  alpha,
complex, dimension(lda,*)  a,
integer  lda,
complex, dimension(ldb,*)  b,
integer  ldb,
complex  beta,
complex, dimension(ldc,*)  c,
integer  ldc 
)

CGEMMTR

Purpose:
 CGEMMTR  performs one of the matrix-matrix operations

    C := alpha*op( A )*op( B ) + beta*C,

 where  op( X ) is one of

    op( X ) = X   or   op( X ) = X**T,

 alpha and beta are scalars, and A, B and C are matrices, with op( A )
 an n by k matrix,  op( B )  a  k by n matrix and  C an n by n matrix.
 Thereby, the routine only accesses and updates the upper or lower
 triangular part of the result matrix C. This behaviour can be used if
 the resulting matrix C is known to be Hermitian or symmetric.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the lower or the upper
           triangular part of C is access and updated.

              UPLO = 'L' or 'l', the lower triangular part of C is used.

              UPLO = 'U' or 'u', the upper triangular part of C is used.
[in]TRANSA
          TRANSA is CHARACTER*1
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n',  op( A ) = A.

              TRANSA = 'T' or 't',  op( A ) = A**T.

              TRANSA = 'C' or 'c',  op( A ) = A**H.
[in]TRANSB
          TRANSB is CHARACTER*1
           On entry, TRANSB specifies the form of op( B ) to be used in
           the matrix multiplication as follows:

              TRANSB = 'N' or 'n',  op( B ) = B.

              TRANSB = 'T' or 't',  op( B ) = B**T.

              TRANSB = 'C' or 'c',  op( B ) = B**H.
[in]N
          N is INTEGER
           On entry,  N specifies the number of rows and columns of
           the matrix C, the number of columns of op(B) and the number
           of rows of op(A).  N must be at least zero.
[in]K
          K is INTEGER
           On entry,  K  specifies  the number of columns of the matrix
           op( A ) and the number of rows of the matrix op( B ). K must
           be at least  zero.
[in]ALPHA
          ALPHA is COMPLEX.
           On entry, ALPHA specifies the scalar alpha.
[in]A
          A is COMPLEX array, dimension ( LDA, ka ), where ka is
           k  when  TRANSA = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANSA = 'N' or 'n',  the leading  n by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by m  part of the array  A  must contain  the
           matrix A.
[in]LDA
          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
           LDA must be at least  max( 1, n ), otherwise  LDA must be at
           least  max( 1, k ).
[in]B
          B is COMPLEX array, dimension ( LDB, kb ), where kb is
           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
           part of the array  B  must contain the matrix  B,  otherwise
           the leading  n by k  part of the array  B  must contain  the
           matrix B.
[in]LDB
          LDB is INTEGER
           On entry, LDB specifies the first dimension of B as declared
           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
           LDB must be at least  max( 1, k ), otherwise  LDB must be at
           least  max( 1, n ).
[in]BETA
          BETA is COMPLEX.
           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
           supplied as zero then C need not be set on input.
[in,out]C
          C is COMPLEX array, dimension ( LDC, N )
           Before entry, the leading  n by n  part of the array  C must
           contain the matrix  C,  except when  beta  is zero, in which
           case C need not be set on entry.
           On exit, the upper or lower triangular part of the matrix
           C  is overwritten by the n by n matrix
           ( alpha*op( A )*op( B ) + beta*C ).
[in]LDC
          LDC is INTEGER
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, n ).
Author
Martin Koehler
Further Details:
  Level 3 Blas routine.

  -- Written on 19-July-2023.
     Martin Koehler, MPI Magdeburg