 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ clarhs()

 subroutine clarhs ( character*3 PATH, character XTYPE, character UPLO, character TRANS, integer M, integer N, integer KL, integer KU, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, integer, dimension( 4 ) ISEED, integer INFO )

CLARHS

Purpose:
``` CLARHS chooses a set of NRHS random solution vectors and sets
up the right hand sides for the linear system
op(A) * X = B,
where op(A) = A, A**T or A**H, depending on TRANS.```
Parameters
 [in] PATH ``` PATH is CHARACTER*3 The type of the complex matrix A. PATH may be given in any combination of upper and lower case. Valid paths include xGE: General m x n matrix xGB: General banded matrix xPO: Hermitian positive definite, 2-D storage xPP: Hermitian positive definite packed xPB: Hermitian positive definite banded xHE: Hermitian indefinite, 2-D storage xHP: Hermitian indefinite packed xHB: Hermitian indefinite banded xSY: Symmetric indefinite, 2-D storage xSP: Symmetric indefinite packed xSB: Symmetric indefinite banded xTR: Triangular xTP: Triangular packed xTB: Triangular banded xQR: General m x n matrix xLQ: General m x n matrix xQL: General m x n matrix xRQ: General m x n matrix where the leading character indicates the precision.``` [in] XTYPE ``` XTYPE is CHARACTER*1 Specifies how the exact solution X will be determined: = 'N': New solution; generate a random X. = 'C': Computed; use value of X on entry.``` [in] UPLO ``` UPLO is CHARACTER*1 Used only if A is symmetric or triangular; specifies whether the upper or lower triangular part of the matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] TRANS ``` TRANS is CHARACTER*1 Used only if A is nonsymmetric; specifies the operation applied to the matrix A. = 'N': B := A * X (No transpose) = 'T': B := A**T * X (Transpose) = 'C': B := A**H * X (Conjugate transpose)``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in] KL ``` KL is INTEGER Used only if A is a band matrix; specifies the number of subdiagonals of A if A is a general band matrix or if A is symmetric or triangular and UPLO = 'L'; specifies the number of superdiagonals of A if A is symmetric or triangular and UPLO = 'U'. 0 <= KL <= M-1.``` [in] KU ``` KU is INTEGER Used only if A is a general band matrix or if A is triangular. If PATH = xGB, specifies the number of superdiagonals of A, and 0 <= KU <= N-1. If PATH = xTR, xTP, or xTB, specifies whether or not the matrix has unit diagonal: = 1: matrix has non-unit diagonal (default) = 2: matrix has unit diagonal``` [in] NRHS ``` NRHS is INTEGER The number of right hand side vectors in the system A*X = B.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The test matrix whose type is given by PATH.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. If PATH = xGB, LDA >= KL+KU+1. If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1. Otherwise, LDA >= max(1,M).``` [in,out] X ``` X is or output) COMPLEX array, dimension (LDX,NRHS) On entry, if XTYPE = 'C' (for 'Computed'), then X contains the exact solution to the system of linear equations. On exit, if XTYPE = 'N' (for 'New'), then X is initialized with random values.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).``` [out] B ``` B is COMPLEX array, dimension (LDB,NRHS) The right hand side vector(s) for the system of equations, computed from B = op(A) * X, where op(A) is determined by TRANS.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. If TRANS = 'N', LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).``` [in,out] ISEED ``` ISEED is INTEGER array, dimension (4) The seed vector for the random number generator (used in CLATMS). Modified on exit.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 206 of file clarhs.f.

208 *
209 * -- LAPACK test routine --
210 * -- LAPACK is a software package provided by Univ. of Tennessee, --
211 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
212 *
213 * .. Scalar Arguments ..
214  CHARACTER TRANS, UPLO, XTYPE
215  CHARACTER*3 PATH
216  INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
217 * ..
218 * .. Array Arguments ..
219  INTEGER ISEED( 4 )
220  COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
221 * ..
222 *
223 * =====================================================================
224 *
225 * .. Parameters ..
226  COMPLEX ONE, ZERO
227  parameter( one = ( 1.0e+0, 0.0e+0 ),
228  \$ zero = ( 0.0e+0, 0.0e+0 ) )
229 * ..
230 * .. Local Scalars ..
231  LOGICAL BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
232  CHARACTER C1, DIAG
233  CHARACTER*2 C2
234  INTEGER J, MB, NX
235 * ..
236 * .. External Functions ..
237  LOGICAL LSAME, LSAMEN
238  EXTERNAL lsame, lsamen
239 * ..
240 * .. External Subroutines ..
241  EXTERNAL cgbmv, cgemm, chbmv, chemm, chpmv, clacpy,
243  \$ ctrmm, xerbla
244 * ..
245 * .. Intrinsic Functions ..
246  INTRINSIC max
247 * ..
248 * .. Executable Statements ..
249 *
250 * Test the input parameters.
251 *
252  info = 0
253  c1 = path( 1: 1 )
254  c2 = path( 2: 3 )
255  tran = lsame( trans, 'T' ) .OR. lsame( trans, 'C' )
256  notran = .NOT.tran
257  gen = lsame( path( 2: 2 ), 'G' )
258  qrs = lsame( path( 2: 2 ), 'Q' ) .OR. lsame( path( 3: 3 ), 'Q' )
259  sym = lsame( path( 2: 2 ), 'P' ) .OR.
260  \$ lsame( path( 2: 2 ), 'S' ) .OR. lsame( path( 2: 2 ), 'H' )
261  tri = lsame( path( 2: 2 ), 'T' )
262  band = lsame( path( 3: 3 ), 'B' )
263  IF( .NOT.lsame( c1, 'Complex precision' ) ) THEN
264  info = -1
265  ELSE IF( .NOT.( lsame( xtype, 'N' ) .OR. lsame( xtype, 'C' ) ) )
266  \$ THEN
267  info = -2
268  ELSE IF( ( sym .OR. tri ) .AND. .NOT.
269  \$ ( lsame( uplo, 'U' ) .OR. lsame( uplo, 'L' ) ) ) THEN
270  info = -3
271  ELSE IF( ( gen.OR.qrs ) .AND.
272  \$ .NOT.( tran .OR. lsame( trans, 'N' ) ) ) THEN
273  info = -4
274  ELSE IF( m.LT.0 ) THEN
275  info = -5
276  ELSE IF( n.LT.0 ) THEN
277  info = -6
278  ELSE IF( band .AND. kl.LT.0 ) THEN
279  info = -7
280  ELSE IF( band .AND. ku.LT.0 ) THEN
281  info = -8
282  ELSE IF( nrhs.LT.0 ) THEN
283  info = -9
284  ELSE IF( ( .NOT.band .AND. lda.LT.max( 1, m ) ) .OR.
285  \$ ( band .AND. ( sym .OR. tri ) .AND. lda.LT.kl+1 ) .OR.
286  \$ ( band .AND. gen .AND. lda.LT.kl+ku+1 ) ) THEN
287  info = -11
288  ELSE IF( ( notran .AND. ldx.LT.max( 1, n ) ) .OR.
289  \$ ( tran .AND. ldx.LT.max( 1, m ) ) ) THEN
290  info = -13
291  ELSE IF( ( notran .AND. ldb.LT.max( 1, m ) ) .OR.
292  \$ ( tran .AND. ldb.LT.max( 1, n ) ) ) THEN
293  info = -15
294  END IF
295  IF( info.NE.0 ) THEN
296  CALL xerbla( 'CLARHS', -info )
297  RETURN
298  END IF
299 *
300 * Initialize X to NRHS random vectors unless XTYPE = 'C'.
301 *
302  IF( tran ) THEN
303  nx = m
304  mb = n
305  ELSE
306  nx = n
307  mb = m
308  END IF
309  IF( .NOT.lsame( xtype, 'C' ) ) THEN
310  DO 10 j = 1, nrhs
311  CALL clarnv( 2, iseed, n, x( 1, j ) )
312  10 CONTINUE
313  END IF
314 *
315 * Multiply X by op(A) using an appropriate
316 * matrix multiply routine.
317 *
318  IF( lsamen( 2, c2, 'GE' ) .OR. lsamen( 2, c2, 'QR' ) .OR.
319  \$ lsamen( 2, c2, 'LQ' ) .OR. lsamen( 2, c2, 'QL' ) .OR.
320  \$ lsamen( 2, c2, 'RQ' ) ) THEN
321 *
322 * General matrix
323 *
324  CALL cgemm( trans, 'N', mb, nrhs, nx, one, a, lda, x, ldx,
325  \$ zero, b, ldb )
326 *
327  ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'HE' ) ) THEN
328 *
329 * Hermitian matrix, 2-D storage
330 *
331  CALL chemm( 'Left', uplo, n, nrhs, one, a, lda, x, ldx, zero,
332  \$ b, ldb )
333 *
334  ELSE IF( lsamen( 2, c2, 'SY' ) ) THEN
335 *
336 * Symmetric matrix, 2-D storage
337 *
338  CALL csymm( 'Left', uplo, n, nrhs, one, a, lda, x, ldx, zero,
339  \$ b, ldb )
340 *
341  ELSE IF( lsamen( 2, c2, 'GB' ) ) THEN
342 *
343 * General matrix, band storage
344 *
345  DO 20 j = 1, nrhs
346  CALL cgbmv( trans, m, n, kl, ku, one, a, lda, x( 1, j ), 1,
347  \$ zero, b( 1, j ), 1 )
348  20 CONTINUE
349 *
350  ELSE IF( lsamen( 2, c2, 'PB' ) .OR. lsamen( 2, c2, 'HB' ) ) THEN
351 *
352 * Hermitian matrix, band storage
353 *
354  DO 30 j = 1, nrhs
355  CALL chbmv( uplo, n, kl, one, a, lda, x( 1, j ), 1, zero,
356  \$ b( 1, j ), 1 )
357  30 CONTINUE
358 *
359  ELSE IF( lsamen( 2, c2, 'SB' ) ) THEN
360 *
361 * Symmetric matrix, band storage
362 *
363  DO 40 j = 1, nrhs
364  CALL csbmv( uplo, n, kl, one, a, lda, x( 1, j ), 1, zero,
365  \$ b( 1, j ), 1 )
366  40 CONTINUE
367 *
368  ELSE IF( lsamen( 2, c2, 'PP' ) .OR. lsamen( 2, c2, 'HP' ) ) THEN
369 *
370 * Hermitian matrix, packed storage
371 *
372  DO 50 j = 1, nrhs
373  CALL chpmv( uplo, n, one, a, x( 1, j ), 1, zero, b( 1, j ),
374  \$ 1 )
375  50 CONTINUE
376 *
377  ELSE IF( lsamen( 2, c2, 'SP' ) ) THEN
378 *
379 * Symmetric matrix, packed storage
380 *
381  DO 60 j = 1, nrhs
382  CALL cspmv( uplo, n, one, a, x( 1, j ), 1, zero, b( 1, j ),
383  \$ 1 )
384  60 CONTINUE
385 *
386  ELSE IF( lsamen( 2, c2, 'TR' ) ) THEN
387 *
388 * Triangular matrix. Note that for triangular matrices,
389 * KU = 1 => non-unit triangular
390 * KU = 2 => unit triangular
391 *
392  CALL clacpy( 'Full', n, nrhs, x, ldx, b, ldb )
393  IF( ku.EQ.2 ) THEN
394  diag = 'U'
395  ELSE
396  diag = 'N'
397  END IF
398  CALL ctrmm( 'Left', uplo, trans, diag, n, nrhs, one, a, lda, b,
399  \$ ldb )
400 *
401  ELSE IF( lsamen( 2, c2, 'TP' ) ) THEN
402 *
403 * Triangular matrix, packed storage
404 *
405  CALL clacpy( 'Full', n, nrhs, x, ldx, b, ldb )
406  IF( ku.EQ.2 ) THEN
407  diag = 'U'
408  ELSE
409  diag = 'N'
410  END IF
411  DO 70 j = 1, nrhs
412  CALL ctpmv( uplo, trans, diag, n, a, b( 1, j ), 1 )
413  70 CONTINUE
414 *
415  ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
416 *
417 * Triangular matrix, banded storage
418 *
419  CALL clacpy( 'Full', n, nrhs, x, ldx, b, ldb )
420  IF( ku.EQ.2 ) THEN
421  diag = 'U'
422  ELSE
423  diag = 'N'
424  END IF
425  DO 80 j = 1, nrhs
426  CALL ctbmv( uplo, trans, diag, n, kl, a, lda, b( 1, j ), 1 )
427  80 CONTINUE
428 *
429  ELSE
430 *
431 * If none of the above, set INFO = -1 and return
432 *
433  info = -1
434  CALL xerbla( 'CLARHS', -info )
435  END IF
436 *
437  RETURN
438 *
439 * End of CLARHS
440 *
logical function lsamen(N, CA, CB)
LSAMEN
Definition: lsamen.f:74
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ctbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBMV
Definition: ctbmv.f:186
subroutine chbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CHBMV
Definition: chbmv.f:187
subroutine cgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGBMV
Definition: cgbmv.f:187
subroutine chpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV
Definition: chpmv.f:149
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
subroutine csymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CSYMM
Definition: csymm.f:189
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine chemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CHEMM
Definition: chemm.f:191
subroutine ctrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRMM
Definition: ctrmm.f:177
subroutine csbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CSBMV
Definition: csbmv.f:152
subroutine clarnv(IDIST, ISEED, N, X)
CLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: clarnv.f:99
subroutine cspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
Definition: cspmv.f:151
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
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