LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zpttrs()

 subroutine zpttrs ( character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info )

ZPTTRS

Purpose:
``` ZPTTRS solves a tridiagonal system of the form
A * X = B
using the factorization A = U**H *D* U or A = L*D*L**H computed by ZPTTRF.
D is a diagonal matrix specified in the vector D, U (or L) is a unit
bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
the vector E, and X and B are N by NRHS matrices.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = 'U': A = U**H *D*U, E is the superdiagonal of U = 'L': A = L*D*L**H, E is the subdiagonal of L``` [in] N ``` N is INTEGER The order of the tridiagonal matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in] D ``` D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H.``` [in] E ``` E is COMPLEX*16 array, dimension (N-1) If UPLO = 'U', the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If UPLO = 'L', the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H.``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value```

Definition at line 120 of file zpttrs.f.

121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER UPLO
128 INTEGER INFO, LDB, N, NRHS
129* ..
130* .. Array Arguments ..
131 DOUBLE PRECISION D( * )
132 COMPLEX*16 B( LDB, * ), E( * )
133* ..
134*
135* =====================================================================
136*
137* .. Local Scalars ..
138 LOGICAL UPPER
139 INTEGER IUPLO, J, JB, NB
140* ..
141* .. External Functions ..
142 INTEGER ILAENV
143 EXTERNAL ilaenv
144* ..
145* .. External Subroutines ..
146 EXTERNAL xerbla, zptts2
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min
150* ..
151* .. Executable Statements ..
152*
153* Test the input arguments.
154*
155 info = 0
156 upper = ( uplo.EQ.'U' .OR. uplo.EQ.'u' )
157 IF( .NOT.upper .AND. .NOT.( uplo.EQ.'L' .OR. uplo.EQ.'l' ) ) THEN
158 info = -1
159 ELSE IF( n.LT.0 ) THEN
160 info = -2
161 ELSE IF( nrhs.LT.0 ) THEN
162 info = -3
163 ELSE IF( ldb.LT.max( 1, n ) ) THEN
164 info = -7
165 END IF
166 IF( info.NE.0 ) THEN
167 CALL xerbla( 'ZPTTRS', -info )
168 RETURN
169 END IF
170*
171* Quick return if possible
172*
173 IF( n.EQ.0 .OR. nrhs.EQ.0 )
174 \$ RETURN
175*
176* Determine the number of right-hand sides to solve at a time.
177*
178 IF( nrhs.EQ.1 ) THEN
179 nb = 1
180 ELSE
181 nb = max( 1, ilaenv( 1, 'ZPTTRS', uplo, n, nrhs, -1, -1 ) )
182 END IF
183*
184* Decode UPLO
185*
186 IF( upper ) THEN
187 iuplo = 1
188 ELSE
189 iuplo = 0
190 END IF
191*
192 IF( nb.GE.nrhs ) THEN
193 CALL zptts2( iuplo, n, nrhs, d, e, b, ldb )
194 ELSE
195 DO 10 j = 1, nrhs, nb
196 jb = min( nrhs-j+1, nb )
197 CALL zptts2( iuplo, n, jb, d, e, b( 1, j ), ldb )
198 10 CONTINUE
199 END IF
200*
201 RETURN
202*
203* End of ZPTTRS
204*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
subroutine zptts2(iuplo, n, nrhs, d, e, b, ldb)
ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf...
Definition zptts2.f:113
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