ctrsm (l) - Linux Manuals
ctrsm: solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
Command to display ctrsm
manual in Linux: $ man l ctrsm
NAME
CTRSM - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
SYNOPSIS
- SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
-
-
COMPLEX
ALPHA
-
INTEGER
LDA,LDB,M,N
-
CHARACTER
DIAG,SIDE,TRANSA,UPLO
-
COMPLEX
A(LDA,*),B(LDB,*)
PURPOSE
CTRSM solves one of the matrix equations
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = Aaq or op( A ) = conjg( Aaq ).
The matrix X is overwritten on B.
ARGUMENTS
- SIDE - CHARACTER*1.
-
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = aqLaq or aqlaq op( A )*X = alpha*B.
SIDE = aqRaq or aqraq X*op( A ) = alpha*B.
Unchanged on exit.
- UPLO - CHARACTER*1.
-
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = aqUaq or aquaq A is an upper triangular matrix.
UPLO = aqLaq or aqlaq A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = aqNaq or aqnaq op( A ) = A.
TRANSA = aqTaq or aqtaq op( A ) = Aaq.
TRANSA = aqCaq or aqcaq op( A ) = conjg( Aaq ).
Unchanged on exit.
- DIAG - CHARACTER*1.
-
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = aqUaq or aquaq A is assumed to be unit triangular.
DIAG = aqNaq or aqnaq A is not assumed to be unit
triangular.
Unchanged on exit.
- M - INTEGER.
-
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
- N - INTEGER.
-
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
- ALPHA - COMPLEX .
-
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
- A - COMPLEX array of DIMENSION ( LDA, k ), where k is m
-
when SIDE = aqLaq or aqlaq and is n when SIDE = aqRaq or aqraq.
Before entry with UPLO = aqUaq or aquaq, 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 = aqLaq or aqlaq, the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = aqUaq or aquaq, the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
- LDA - INTEGER.
-
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = aqLaq or aqlaq then
LDA must be at least max( 1, m ), when SIDE = aqRaq or aqraq
then LDA must be at least max( 1, n ).
Unchanged on exit.
- B - COMPLEX array of DIMENSION ( LDB, n ).
-
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
- LDB - INTEGER.
-
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
FURTHER DETAILS
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Pages related to ctrsm
- ctrsm (3)
- ctrsen (l) - reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
- ctrsna (l) - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)
- ctrsv (l) - solves one of the systems of equations A*x = b, or Aaq*x = b, or conjg( Aaq )*x = b,
- ctrsyl (l) - solves the complex Sylvester matrix equation
- ctrcon (l) - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
- ctrevc (l) - computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
- ctrexc (l) - reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
- ctrmm (l) - performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = Aaq or op( A ) = conjg( Aaq )