--- rpl/lapack/lapack/ztrsyl.f 2010/08/07 13:22:46 1.5
+++ rpl/lapack/lapack/ztrsyl.f 2023/08/07 08:39:42 1.18
@@ -1,10 +1,163 @@
+*> \brief \b ZTRSYL
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZTRSYL + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
+* LDC, SCALE, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANA, TRANB
+* INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
+* DOUBLE PRECISION SCALE
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZTRSYL solves the complex Sylvester matrix equation:
+*>
+*> op(A)*X + X*op(B) = scale*C or
+*> op(A)*X - X*op(B) = scale*C,
+*>
+*> where op(A) = A or A**H, and A and B are both upper triangular. A is
+*> M-by-M and B is N-by-N; the right hand side C and the solution X are
+*> M-by-N; and scale is an output scale factor, set <= 1 to avoid
+*> overflow in X.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANA
+*> \verbatim
+*> TRANA is CHARACTER*1
+*> Specifies the option op(A):
+*> = 'N': op(A) = A (No transpose)
+*> = 'C': op(A) = A**H (Conjugate transpose)
+*> \endverbatim
+*>
+*> \param[in] TRANB
+*> \verbatim
+*> TRANB is CHARACTER*1
+*> Specifies the option op(B):
+*> = 'N': op(B) = B (No transpose)
+*> = 'C': op(B) = B**H (Conjugate transpose)
+*> \endverbatim
+*>
+*> \param[in] ISGN
+*> \verbatim
+*> ISGN is INTEGER
+*> Specifies the sign in the equation:
+*> = +1: solve op(A)*X + X*op(B) = scale*C
+*> = -1: solve op(A)*X - X*op(B) = scale*C
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The order of the matrix A, and the number of rows in the
+*> matrices X and C. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix B, and the number of columns in the
+*> matrices X and C. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,M)
+*> The upper triangular matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,N)
+*> The upper triangular matrix B.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*> C is COMPLEX*16 array, dimension (LDC,N)
+*> On entry, the M-by-N right hand side matrix C.
+*> On exit, C is overwritten by the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the array C. LDC >= max(1,M)
+*> \endverbatim
+*>
+*> \param[out] SCALE
+*> \verbatim
+*> SCALE is DOUBLE PRECISION
+*> The scale factor, scale, set <= 1 to avoid overflow in X.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> = 1: A and B have common or very close eigenvalues; perturbed
+*> values were used to solve the equation (but the matrices
+*> A and B are unchanged).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16SYcomputational
+*
+* =====================================================================
SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
$ LDC, SCALE, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER TRANA, TRANB
@@ -15,74 +168,6 @@
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
-*
-* ZTRSYL solves the complex Sylvester matrix equation:
-*
-* op(A)*X + X*op(B) = scale*C or
-* op(A)*X - X*op(B) = scale*C,
-*
-* where op(A) = A or A**H, and A and B are both upper triangular. A is
-* M-by-M and B is N-by-N; the right hand side C and the solution X are
-* M-by-N; and scale is an output scale factor, set <= 1 to avoid
-* overflow in X.
-*
-* Arguments
-* =========
-*
-* TRANA (input) CHARACTER*1
-* Specifies the option op(A):
-* = 'N': op(A) = A (No transpose)
-* = 'C': op(A) = A**H (Conjugate transpose)
-*
-* TRANB (input) CHARACTER*1
-* Specifies the option op(B):
-* = 'N': op(B) = B (No transpose)
-* = 'C': op(B) = B**H (Conjugate transpose)
-*
-* ISGN (input) INTEGER
-* Specifies the sign in the equation:
-* = +1: solve op(A)*X + X*op(B) = scale*C
-* = -1: solve op(A)*X - X*op(B) = scale*C
-*
-* M (input) INTEGER
-* The order of the matrix A, and the number of rows in the
-* matrices X and C. M >= 0.
-*
-* N (input) INTEGER
-* The order of the matrix B, and the number of columns in the
-* matrices X and C. N >= 0.
-*
-* A (input) COMPLEX*16 array, dimension (LDA,M)
-* The upper triangular matrix A.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* B (input) COMPLEX*16 array, dimension (LDB,N)
-* The upper triangular matrix B.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* C (input/output) COMPLEX*16 array, dimension (LDC,N)
-* On entry, the M-by-N right hand side matrix C.
-* On exit, C is overwritten by the solution matrix X.
-*
-* LDC (input) INTEGER
-* The leading dimension of the array C. LDC >= max(1,M)
-*
-* SCALE (output) DOUBLE PRECISION
-* The scale factor, scale, set <= 1 to avoid overflow in X.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* = 1: A and B have common or very close eigenvalues; perturbed
-* values were used to solve the equation (but the matrices
-* A and B are unchanged).
-*
* =====================================================================
*
* .. Parameters ..
@@ -209,17 +294,17 @@
*
ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
*
-* Solve A' *X + ISGN*X*B = scale*C.
+* Solve A**H *X + ISGN*X*B = scale*C.
*
* The (K,L)th block of X is determined starting from
* upper-left corner column by column by
*
-* A'(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
+* A**H(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
*
* Where
-* K-1 L-1
-* R(K,L) = SUM [A'(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
-* I=1 J=1
+* K-1 L-1
+* R(K,L) = SUM [A**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
+* I=1 J=1
*
DO 60 L = 1, N
DO 50 K = 1, M
@@ -257,19 +342,19 @@
*
ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
*
-* Solve A'*X + ISGN*X*B' = C.
+* Solve A**H*X + ISGN*X*B**H = C.
*
* The (K,L)th block of X is determined starting from
* upper-right corner column by column by
*
-* A'(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
+* A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
*
* Where
* K-1
-* R(K,L) = SUM [A'(I,K)*X(I,L)] +
+* R(K,L) = SUM [A**H(I,K)*X(I,L)] +
* I=1
* N
-* ISGN*SUM [X(K,J)*B'(L,J)].
+* ISGN*SUM [X(K,J)*B**H(L,J)].
* J=L+1
*
DO 90 L = N, 1, -1
@@ -309,16 +394,16 @@
*
ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
*
-* Solve A*X + ISGN*X*B' = C.
+* Solve A*X + ISGN*X*B**H = C.
*
* The (K,L)th block of X is determined starting from
* bottom-left corner column by column by
*
-* A(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
+* A(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
*
* Where
* M N
-* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B'(L,J)]
+* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B**H(L,J)]
* I=K+1 J=L+1
*
DO 120 L = N, 1, -1