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SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
* .. Scalar Arguments ..
COMPLEX ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
COMPLEX A(LDA,*),B(LDB,*)
* ..
*
* Purpose
* =======
*
* CTRSM solves one of the matrix equations
*
* op( A )*X = alpha*B, or X*op( A ) = alpha*B,
*
* 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 ) = A' or op( A ) = conjg( A' ).
*
* 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 = 'L' or 'l' op( A )*X = alpha*B.
*
* SIDE = 'R' or 'r' 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 = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' 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 = 'N' or 'n' op( A ) = A.
*
* TRANSA = 'T' or 't' op( A ) = A'.
*
* TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit triangular
* as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' 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 = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
* Before entry with UPLO = 'U' or 'u', 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 = 'L' or 'l', 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 = 'U' or 'u', 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 = 'L' or 'l' then
* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
* 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.
*
*
* 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.
*
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,MAX
* ..
* .. Local Scalars ..
COMPLEX TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
* ..
* .. Parameters ..
COMPLEX ONE
PARAMETER (ONE= (1.0E+0,0.0E+0))
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
*
* Test the input parameters.
*
LSIDE = LSAME(SIDE,'L')
IF (LSIDE) THEN
NROWA = M
ELSE
NROWA = N
END IF
NOCONJ = LSAME(TRANSA,'T')
NOUNIT = LSAME(DIAG,'N')
UPPER = LSAME(UPLO,'U')
*
INFO = 0
IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
INFO = 1
ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
INFO = 2
ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
+ (.NOT.LSAME(TRANSA,'T')) .AND.
+ (.NOT.LSAME(TRANSA,'C'))) THEN
INFO = 3
ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
INFO = 4
ELSE IF (M.LT.0) THEN
INFO = 5
ELSE IF (N.LT.0) THEN
INFO = 6
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
INFO = 9
ELSE IF (LDB.LT.MAX(1,M)) THEN
INFO = 11
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CTRSM ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (M.EQ.0 .OR. N.EQ.0) RETURN
*
* And when alpha.eq.zero.
*
IF (ALPHA.EQ.ZERO) THEN
DO 20 J = 1,N
DO 10 I = 1,M
B(I,J) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
*
* Start the operations.
*
IF (LSIDE) THEN
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*inv( A )*B.
*
IF (UPPER) THEN
DO 60 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 30 I = 1,M
B(I,J) = ALPHA*B(I,J)
30 CONTINUE
END IF
DO 50 K = M,1,-1
IF (B(K,J).NE.ZERO) THEN
IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
DO 40 I = 1,K - 1
B(I,J) = B(I,J) - B(K,J)*A(I,K)
40 CONTINUE
END IF
50 CONTINUE
60 CONTINUE
ELSE
DO 100 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 70 I = 1,M
B(I,J) = ALPHA*B(I,J)
70 CONTINUE
END IF
DO 90 K = 1,M
IF (B(K,J).NE.ZERO) THEN
IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
DO 80 I = K + 1,M
B(I,J) = B(I,J) - B(K,J)*A(I,K)
80 CONTINUE
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
*
* Form B := alpha*inv( A' )*B
* or B := alpha*inv( conjg( A' ) )*B.
*
IF (UPPER) THEN
DO 140 J = 1,N
DO 130 I = 1,M
TEMP = ALPHA*B(I,J)
IF (NOCONJ) THEN
DO 110 K = 1,I - 1
TEMP = TEMP - A(K,I)*B(K,J)
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
ELSE
DO 120 K = 1,I - 1
TEMP = TEMP - CONJG(A(K,I))*B(K,J)
120 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(A(I,I))
END IF
B(I,J) = TEMP
130 CONTINUE
140 CONTINUE
ELSE
DO 180 J = 1,N
DO 170 I = M,1,-1
TEMP = ALPHA*B(I,J)
IF (NOCONJ) THEN
DO 150 K = I + 1,M
TEMP = TEMP - A(K,I)*B(K,J)
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
ELSE
DO 160 K = I + 1,M
TEMP = TEMP - CONJG(A(K,I))*B(K,J)
160 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(A(I,I))
END IF
B(I,J) = TEMP
170 CONTINUE
180 CONTINUE
END IF
END IF
ELSE
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*B*inv( A ).
*
IF (UPPER) THEN
DO 230 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 190 I = 1,M
B(I,J) = ALPHA*B(I,J)
190 CONTINUE
END IF
DO 210 K = 1,J - 1
IF (A(K,J).NE.ZERO) THEN
DO 200 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
200 CONTINUE
END IF
210 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 220 I = 1,M
B(I,J) = TEMP*B(I,J)
220 CONTINUE
END IF
230 CONTINUE
ELSE
DO 280 J = N,1,-1
IF (ALPHA.NE.ONE) THEN
DO 240 I = 1,M
B(I,J) = ALPHA*B(I,J)
240 CONTINUE
END IF
DO 260 K = J + 1,N
IF (A(K,J).NE.ZERO) THEN
DO 250 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
250 CONTINUE
END IF
260 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 270 I = 1,M
B(I,J) = TEMP*B(I,J)
270 CONTINUE
END IF
280 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*inv( A' )
* or B := alpha*B*inv( conjg( A' ) ).
*
IF (UPPER) THEN
DO 330 K = N,1,-1
IF (NOUNIT) THEN
IF (NOCONJ) THEN
TEMP = ONE/A(K,K)
ELSE
TEMP = ONE/CONJG(A(K,K))
END IF
DO 290 I = 1,M
B(I,K) = TEMP*B(I,K)
290 CONTINUE
END IF
DO 310 J = 1,K - 1
IF (A(J,K).NE.ZERO) THEN
IF (NOCONJ) THEN
TEMP = A(J,K)
ELSE
TEMP = CONJG(A(J,K))
END IF
DO 300 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
300 CONTINUE
END IF
310 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 320 I = 1,M
B(I,K) = ALPHA*B(I,K)
320 CONTINUE
END IF
330 CONTINUE
ELSE
DO 380 K = 1,N
IF (NOUNIT) THEN
IF (NOCONJ) THEN
TEMP = ONE/A(K,K)
ELSE
TEMP = ONE/CONJG(A(K,K))
END IF
DO 340 I = 1,M
B(I,K) = TEMP*B(I,K)
340 CONTINUE
END IF
DO 360 J = K + 1,N
IF (A(J,K).NE.ZERO) THEN
IF (NOCONJ) THEN
TEMP = A(J,K)
ELSE
TEMP = CONJG(A(J,K))
END IF
DO 350 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
350 CONTINUE
END IF
360 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 370 I = 1,M
B(I,K) = ALPHA*B(I,K)
370 CONTINUE
END IF
380 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of CTRSM .
*
END
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