LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ slarhs()

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

SLARHS

Purpose:
``` SLARHS 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 or A**T, depending on TRANS.```
Parameters
 [in] PATH ``` PATH is CHARACTER*3 The type of the real matrix A. PATH may be given in any combination of upper and lower case. Valid types include xGE: General m x n matrix xGB: General banded matrix xPO: Symmetric positive definite, 2-D storage xPP: Symmetric positive definite packed xPB: Symmetric positive definite 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 Specifies whether the upper or lower triangular part of the matrix A is stored, if A is symmetric. = '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 = Transpose)``` [in] M ``` M is INTEGER The number or 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 REAL 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) REAL 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 REAL 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 SLATMS). 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 203 of file slarhs.f.

205 *
206 * -- LAPACK test routine --
207 * -- LAPACK is a software package provided by Univ. of Tennessee, --
208 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
209 *
210 * .. Scalar Arguments ..
211  CHARACTER TRANS, UPLO, XTYPE
212  CHARACTER*3 PATH
213  INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
214 * ..
215 * .. Array Arguments ..
216  INTEGER ISEED( 4 )
217  REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
218 * ..
219 *
220 * =====================================================================
221 *
222 * .. Parameters ..
223  REAL ONE, ZERO
224  parameter( one = 1.0e+0, zero = 0.0e+0 )
225 * ..
226 * .. Local Scalars ..
227  LOGICAL BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
228  CHARACTER C1, DIAG
229  CHARACTER*2 C2
230  INTEGER J, MB, NX
231 * ..
232 * .. External Functions ..
233  LOGICAL LSAME, LSAMEN
234  EXTERNAL lsame, lsamen
235 * ..
236 * .. External Subroutines ..
237  EXTERNAL sgbmv, sgemm, slacpy, slarnv, ssbmv, sspmv,
239 * ..
240 * .. Intrinsic Functions ..
241  INTRINSIC max
242 * ..
243 * .. Executable Statements ..
244 *
245 * Test the input parameters.
246 *
247  info = 0
248  c1 = path( 1: 1 )
249  c2 = path( 2: 3 )
250  tran = lsame( trans, 'T' ) .OR. lsame( trans, 'C' )
251  notran = .NOT.tran
252  gen = lsame( path( 2: 2 ), 'G' )
253  qrs = lsame( path( 2: 2 ), 'Q' ) .OR. lsame( path( 3: 3 ), 'Q' )
254  sym = lsame( path( 2: 2 ), 'P' ) .OR. lsame( path( 2: 2 ), 'S' )
255  tri = lsame( path( 2: 2 ), 'T' )
256  band = lsame( path( 3: 3 ), 'B' )
257  IF( .NOT.lsame( c1, 'Single precision' ) ) THEN
258  info = -1
259  ELSE IF( .NOT.( lsame( xtype, 'N' ) .OR. lsame( xtype, 'C' ) ) )
260  \$ THEN
261  info = -2
262  ELSE IF( ( sym .OR. tri ) .AND. .NOT.
263  \$ ( lsame( uplo, 'U' ) .OR. lsame( uplo, 'L' ) ) ) THEN
264  info = -3
265  ELSE IF( ( gen .OR. qrs ) .AND. .NOT.
266  \$ ( tran .OR. lsame( trans, 'N' ) ) ) THEN
267  info = -4
268  ELSE IF( m.LT.0 ) THEN
269  info = -5
270  ELSE IF( n.LT.0 ) THEN
271  info = -6
272  ELSE IF( band .AND. kl.LT.0 ) THEN
273  info = -7
274  ELSE IF( band .AND. ku.LT.0 ) THEN
275  info = -8
276  ELSE IF( nrhs.LT.0 ) THEN
277  info = -9
278  ELSE IF( ( .NOT.band .AND. lda.LT.max( 1, m ) ) .OR.
279  \$ ( band .AND. ( sym .OR. tri ) .AND. lda.LT.kl+1 ) .OR.
280  \$ ( band .AND. gen .AND. lda.LT.kl+ku+1 ) ) THEN
281  info = -11
282  ELSE IF( ( notran .AND. ldx.LT.max( 1, n ) ) .OR.
283  \$ ( tran .AND. ldx.LT.max( 1, m ) ) ) THEN
284  info = -13
285  ELSE IF( ( notran .AND. ldb.LT.max( 1, m ) ) .OR.
286  \$ ( tran .AND. ldb.LT.max( 1, n ) ) ) THEN
287  info = -15
288  END IF
289  IF( info.NE.0 ) THEN
290  CALL xerbla( 'SLARHS', -info )
291  RETURN
292  END IF
293 *
294 * Initialize X to NRHS random vectors unless XTYPE = 'C'.
295 *
296  IF( tran ) THEN
297  nx = m
298  mb = n
299  ELSE
300  nx = n
301  mb = m
302  END IF
303  IF( .NOT.lsame( xtype, 'C' ) ) THEN
304  DO 10 j = 1, nrhs
305  CALL slarnv( 2, iseed, n, x( 1, j ) )
306  10 CONTINUE
307  END IF
308 *
309 * Multiply X by op(A) using an appropriate
310 * matrix multiply routine.
311 *
312  IF( lsamen( 2, c2, 'GE' ) .OR. lsamen( 2, c2, 'QR' ) .OR.
313  \$ lsamen( 2, c2, 'LQ' ) .OR. lsamen( 2, c2, 'QL' ) .OR.
314  \$ lsamen( 2, c2, 'RQ' ) ) THEN
315 *
316 * General matrix
317 *
318  CALL sgemm( trans, 'N', mb, nrhs, nx, one, a, lda, x, ldx,
319  \$ zero, b, ldb )
320 *
321  ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'SY' ) ) THEN
322 *
323 * Symmetric matrix, 2-D storage
324 *
325  CALL ssymm( 'Left', uplo, n, nrhs, one, a, lda, x, ldx, zero,
326  \$ b, ldb )
327 *
328  ELSE IF( lsamen( 2, c2, 'GB' ) ) THEN
329 *
330 * General matrix, band storage
331 *
332  DO 20 j = 1, nrhs
333  CALL sgbmv( trans, mb, nx, kl, ku, one, a, lda, x( 1, j ),
334  \$ 1, zero, b( 1, j ), 1 )
335  20 CONTINUE
336 *
337  ELSE IF( lsamen( 2, c2, 'PB' ) ) THEN
338 *
339 * Symmetric matrix, band storage
340 *
341  DO 30 j = 1, nrhs
342  CALL ssbmv( uplo, n, kl, one, a, lda, x( 1, j ), 1, zero,
343  \$ b( 1, j ), 1 )
344  30 CONTINUE
345 *
346  ELSE IF( lsamen( 2, c2, 'PP' ) .OR. lsamen( 2, c2, 'SP' ) ) THEN
347 *
348 * Symmetric matrix, packed storage
349 *
350  DO 40 j = 1, nrhs
351  CALL sspmv( uplo, n, one, a, x( 1, j ), 1, zero, b( 1, j ),
352  \$ 1 )
353  40 CONTINUE
354 *
355  ELSE IF( lsamen( 2, c2, 'TR' ) ) THEN
356 *
357 * Triangular matrix. Note that for triangular matrices,
358 * KU = 1 => non-unit triangular
359 * KU = 2 => unit triangular
360 *
361  CALL slacpy( 'Full', n, nrhs, x, ldx, b, ldb )
362  IF( ku.EQ.2 ) THEN
363  diag = 'U'
364  ELSE
365  diag = 'N'
366  END IF
367  CALL strmm( 'Left', uplo, trans, diag, n, nrhs, one, a, lda, b,
368  \$ ldb )
369 *
370  ELSE IF( lsamen( 2, c2, 'TP' ) ) THEN
371 *
372 * Triangular matrix, packed storage
373 *
374  CALL slacpy( 'Full', n, nrhs, x, ldx, b, ldb )
375  IF( ku.EQ.2 ) THEN
376  diag = 'U'
377  ELSE
378  diag = 'N'
379  END IF
380  DO 50 j = 1, nrhs
381  CALL stpmv( uplo, trans, diag, n, a, b( 1, j ), 1 )
382  50 CONTINUE
383 *
384  ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
385 *
386 * Triangular matrix, banded storage
387 *
388  CALL slacpy( 'Full', n, nrhs, x, ldx, b, ldb )
389  IF( ku.EQ.2 ) THEN
390  diag = 'U'
391  ELSE
392  diag = 'N'
393  END IF
394  DO 60 j = 1, nrhs
395  CALL stbmv( uplo, trans, diag, n, kl, a, lda, b( 1, j ), 1 )
396  60 CONTINUE
397 *
398  ELSE
399 *
400 * If PATH is none of the above, return with an error code.
401 *
402  info = -1
403  CALL xerbla( 'SLARHS', -info )
404  END IF
405 *
406  RETURN
407 *
408 * End of SLARHS
409 *
logical function lsamen(N, CA, CB)
LSAMEN
Definition: lsamen.f:74
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:97
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGBMV
Definition: sgbmv.f:185
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:142
subroutine stbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBMV
Definition: stbmv.f:186
subroutine sspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
Definition: sspmv.f:147
subroutine ssbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSBMV
Definition: ssbmv.f:184
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
Definition: strmm.f:177
subroutine ssymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SSYMM
Definition: ssymm.f:189
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
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