Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?trsm_oop
Solves a triangular matrix equation and adds the result to another scaled matrix.
Syntax
call strsm_oop(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
call dtrsm_oop(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
call ctrsm_oop(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
call ztrsm_oop(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb, beta, c, ldc)Include Files
mkl.fi
Description
The ?trsm_oop routines perform a triangular matrix solve followed by a scaled matrix addition.
For a left-side solve, the routine solves
op(A)*X=alpha*Bfor x and then computes
C := X + beta*CFor a right-side solve, the routine solves
X*op(A)=alpha*Bfollowed by the same-scaled addition
C := X + beta*Cwhere:
alpha and beta are scalars.
A is a unit or non-unit upper or lower triangular matrix.
B is an m-by-n matrix.
C is an m-by-n matrix.
op(A) is one of op(A) = A , op(A) = A' , or op(A) = conjg(A') .
Input Parameters
- side
-
CHARACTER*1 . Specifies whether op(A) appears on the left or right of B in the triangular solve. If side = 'L' or side = 'l' , then we solve op(A)*X = alpha*B before performing C := X + beta*C . If side = 'R' or side = 'r' , then we solve X*op(A) = alpha*B before performing C := X + beta*C .
- uplo
-
CHARACTER*1 . Specifies whether the matrix A is upper or lower triangular. If uplo = 'U' or uplo = 'u' , then the matrix is upper triangular. If uplo = 'L' or uplo = 'l' , then the matrix is lower triangular.
- transa
-
CHARACTER*1 . Specifies the form of op(A) used in the triangular solve. If transa='N' or transa = 'n' , then op(A) = A . If transa='T' or transa = 't' , then op(A) = A' . If transa='C' or transa = 'c' , then op(A) = conjg(A') .
- diag
-
CHARACTER*1 . Specifies whether the matrix A is unit triangular. If diag = 'U' or diag = 'u' , then the matrix is unit triangular. If diag = 'N' or diag = 'n' , then the matrix is not unit triangular.
- m
-
INTEGER . Specifies the number of rows of matrix B . The value of m must be at least zero.
- n
-
INTEGER . Specifies the number of columns of matrix B . The value of n must be at least zero.
- alpha
-
REAL for strsm_oop . DOUBLE PRECISION for dtrsm_oop . COMPLEX for ctrsm_oop . DOUBLE COMPLEX for ztrsm_oop . Specifies the scalar alpha .
- a
-
REAL for strsm_oop . DOUBLE PRECISION for dtrsm_oop . COMPLEX for ctrsm_oop . DOUBLE COMPLEX for ztrsm_oop . Array of size lda*k , where k is m when side = CblasLeft and k is n when side = CblasRight . Before entry with uplo = CblasUpper , the leading k by k upper triangular part of the array a must contain the upper triangular matrix and the strictly lower triangular part of a is not referenced. Before entry with uplo = CblasLower the lower triangular part of the array a must contain the lower triangular matrix and the strictly upper triangular part of a is not referenced. When diag = CblasUnit , the diagonal elements of a are not referenced either, but are assumed to be unity.
- lda
-
INTEGER . Specifies the leading dimension of a . When side = CblasLeft , then lda must be at least max(1, m) . When side = CblasRight , then lda must be at least max(1, n) .
- b
-
REAL for strsm_oop . DOUBLE PRECISION for dtrsm_oop . COMPLEX for ctrsm_oop . DOUBLE COMPLEX for ztrsm_oop . For layout = CblasColMajor, array of size ldb*n. Before entry, the leading m-by-n part of the array b must contain the matrix B. For layout = CblasRowMajor, array of size ldb*m. Before entry, the leading n-by-m part of the array b must contain the matrix B.
- ldb
-
INTEGER . Specifies the leading dimension of b . When layout = CblasColMajor , ldb must be at least max(1, m) ; otherwise, ldb must be at least max(1, n) .
- beta
-
REAL for strsm_oop . DOUBLE PRECISION for dtrsm_oop . COMPLEX for ctrsm_oop . DOUBLE COMPLEX for ztrsm_oop . Specifies the scalar beta .
- c
-
REAL for strsm_oop . DOUBLE PRECISION for dtrsm_oop . COMPLEX for ctrsm_oop . DOUBLE COMPLEX for ztrsm_oop . For layout = CblasColMajor , array of size ldc*n . Before entry, the leading m-by-n part of the array c must contain the matrix C . For layout = CblasRowMajor , array of size ldc*m . Before entry, the leading n-by-m part of the array c must contain the matrix C .
- ldc
-
INTEGER . Specifies the leading dimension of c . When layout = CblasColMajor , ldc must be at least max(1, m) ; otherwise, ldc must be at least max(1, n) .
Output Parameters
- c
-
Output matrix overwritten by the operation.