/* Subroutine */ int zpprfs_(char *uplo, integer *n, integer *nrhs, doublecomplex *ap, doublecomplex *afp, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *rwork, integer *info) { /* System generated locals */ integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2, d__3, d__4; doublecomplex z__1; /* Builtin functions */ double d_imag(doublecomplex *); /* Local variables */ integer i__, j, k; doublereal s; integer ik, kk; doublereal xk; integer nz; doublereal eps; integer kase; doublereal safe1, safe2; extern logical lsame_(char *, char *); integer isave[3], count; logical upper; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zhpmv_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_( integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_(integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *); doublereal lstres; extern /* Subroutine */ int zpptrs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZPPRFS improves the computed solution to a system of linear */ /* equations when the coefficient matrix is Hermitian positive definite */ /* and packed, and provides error bounds and backward error estimates */ /* for the solution. */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) */ /* The upper or lower triangle of the Hermitian matrix A, packed */ /* columnwise in a linear array. The j-th column of A is stored */ /* in the array AP as follows: */ /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ /* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */ /* AFP (input) COMPLEX*16 array, dimension (N*(N+1)/2) */ /* The triangular factor U or L from the Cholesky factorization */ /* A = U**H*U or A = L*L**H, as computed by DPPTRF/ZPPTRF, */ /* packed columnwise in a linear array in the same format as A */ /* (see AP). */ /* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */ /* The right hand side matrix B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (input/output) COMPLEX*16 array, dimension (LDX,NRHS) */ /* On entry, the solution matrix X, as computed by ZPPTRS. */ /* On exit, the improved solution matrix X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The estimated forward error bound for each solution vector */ /* X(j) (the j-th column of the solution matrix X). */ /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* is an estimated upper bound for the magnitude of the largest */ /* element in (X(j) - XTRUE) divided by the magnitude of the */ /* largest element in X(j). The estimate is as reliable as */ /* the estimate for RCOND, and is almost always a slight */ /* overestimate of the true error. */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The componentwise relative backward error of each solution */ /* vector X(j) (i.e., the smallest relative change in */ /* any element of A or B that makes X(j) an exact solution). */ /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* Internal Parameters */ /* =================== */ /* ITMAX is the maximum number of steps of iterative refinement. */ /* ==================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Statement Functions .. */ /* .. */ /* .. Statement Function definitions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ --ap; --afp; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --ferr; --berr; --work; --rwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*ldb < max(1,*n)) { *info = -7; } else if (*ldx < max(1,*n)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPPRFS", &i__1); return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] = 0.; berr[j] = 0.; /* L10: */ } return 0; } /* NZ = maximum number of nonzero elements in each row of A, plus 1 */ nz = *n + 1; eps = dlamch_("Epsilon"); safmin = dlamch_("Safe minimum"); safe1 = nz * safmin; safe2 = safe1 / eps; /* Do for each right hand side */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { count = 1; lstres = 3.; L20: /* Loop until stopping criterion is satisfied. */ /* Compute residual R = B - A * X */ zcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1); z__1.r = -1., z__1.i = -0.; zhpmv_(uplo, n, &z__1, &ap[1], &x[j * x_dim1 + 1], &c__1, &c_b1, & work[1], &c__1); /* Compute componentwise relative backward error from formula */ /* max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */ /* where abs(Z) is the componentwise absolute value of the matrix */ /* or vector Z. If the i-th component of the denominator is less */ /* than SAFE2, then SAFE1 is added to the i-th components of the */ /* numerator and denominator before dividing. */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; rwork[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[ i__ + j * b_dim1]), abs(d__2)); /* L30: */ } /* Compute abs(A)*abs(X) + abs(B). */ kk = 1; if (upper) { i__2 = *n; for (k = 1; k <= i__2; ++k) { s = 0.; i__3 = k + j * x_dim1; xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j * x_dim1]), abs(d__2)); ik = kk; i__3 = k - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ik; rwork[i__] += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 = d_imag(&ap[ik]), abs(d__2))) * xk; i__4 = ik; i__5 = i__ + j * x_dim1; s += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 = d_imag(&ap[ ik]), abs(d__2))) * ((d__3 = x[i__5].r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j * x_dim1]), abs(d__4) )); ++ik; /* L40: */ } i__3 = kk + k - 1; rwork[k] = rwork[k] + (d__1 = ap[i__3].r, abs(d__1)) * xk + s; kk += k; /* L50: */ } } else { i__2 = *n; for (k = 1; k <= i__2; ++k) { s = 0.; i__3 = k + j * x_dim1; xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j * x_dim1]), abs(d__2)); i__3 = kk; rwork[k] += (d__1 = ap[i__3].r, abs(d__1)) * xk; ik = kk + 1; i__3 = *n; for (i__ = k + 1; i__ <= i__3; ++i__) { i__4 = ik; rwork[i__] += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 = d_imag(&ap[ik]), abs(d__2))) * xk; i__4 = ik; i__5 = i__ + j * x_dim1; s += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 = d_imag(&ap[ ik]), abs(d__2))) * ((d__3 = x[i__5].r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j * x_dim1]), abs(d__4) )); ++ik; /* L60: */ } rwork[k] += s; kk += *n - k + 1; /* L70: */ } } s = 0.; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { /* Computing MAX */ i__3 = i__; d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2))) / rwork[i__]; s = max(d__3,d__4); } else { /* Computing MAX */ i__3 = i__; d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__] + safe1); s = max(d__3,d__4); } /* L80: */ } berr[j] = s; /* Test stopping criterion. Continue iterating if */ /* 1) The residual BERR(J) is larger than machine epsilon, and */ /* 2) BERR(J) decreased by at least a factor of 2 during the */ /* last iteration, and */ /* 3) At most ITMAX iterations tried. */ if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) { /* Update solution and try again. */ zpptrs_(uplo, n, &c__1, &afp[1], &work[1], n, info); zaxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1); lstres = berr[j]; ++count; goto L20; } /* Bound error from formula */ /* norm(X - XTRUE) / norm(X) .le. FERR = */ /* norm( abs(inv(A))* */ /* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */ /* where */ /* norm(Z) is the magnitude of the largest component of Z */ /* inv(A) is the inverse of A */ /* abs(Z) is the componentwise absolute value of the matrix or */ /* vector Z */ /* NZ is the maximum number of nonzeros in any row of A, plus 1 */ /* EPS is machine epsilon */ /* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */ /* is incremented by SAFE1 if the i-th component of */ /* abs(A)*abs(X) + abs(B) is less than SAFE2. */ /* Use ZLACN2 to estimate the infinity-norm of the matrix */ /* inv(A) * diag(W), */ /* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { i__3 = i__; rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__] ; } else { i__3 = i__; rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 = d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__] + safe1; } /* L90: */ } kase = 0; L100: zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave); if (kase != 0) { if (kase == 1) { /* Multiply by diag(W)*inv(A'). */ zpptrs_(uplo, n, &c__1, &afp[1], &work[1], n, info) ; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__; z__1.r = rwork[i__4] * work[i__5].r, z__1.i = rwork[i__4] * work[i__5].i; work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* L110: */ } } else if (kase == 2) { /* Multiply by inv(A)*diag(W). */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__; z__1.r = rwork[i__4] * work[i__5].r, z__1.i = rwork[i__4] * work[i__5].i; work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* L120: */ } zpptrs_(uplo, n, &c__1, &afp[1], &work[1], n, info) ; } goto L100; } /* Normalize error. */ lstres = 0.; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__3 = i__ + j * x_dim1; d__3 = lstres, d__4 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[i__ + j * x_dim1]), abs(d__2)); lstres = max(d__3,d__4); /* L130: */ } if (lstres != 0.) { ferr[j] /= lstres; } /* L140: */ } return 0; /* End of ZPPRFS */ } /* zpprfs_ */
/* Subroutine */ int zerrpo_(char *path, integer *nunit) { /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ doublecomplex a[16] /* was [4][4] */, b[4]; integer i__, j; doublereal r__[4]; doublecomplex w[8], x[4]; char c2[2]; doublereal r1[4], r2[4]; doublecomplex af[16] /* was [4][4] */; integer info; doublereal anrm, rcond; extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zpotf2_(char *, integer *, doublecomplex *, integer *, integer *), alaesm_(char *, logical *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), zpbcon_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbequ_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zpbrfs_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbtrf_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zppcon_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zpbtrs_( char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zporfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zppequ_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublereal *, integer *), zpprfs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpptrf_(char * , integer *, doublecomplex *, integer *), zpptri_(char *, integer *, doublecomplex *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zpptrs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZERRPO tests the error exits for the COMPLEX*16 routines */ /* for Hermitian positive definite matrices. */ /* Arguments */ /* ========= */ /* PATH (input) CHARACTER*3 */ /* The LAPACK path name for the routines to be tested. */ /* NUNIT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { i__1 = i__ + (j << 2) - 5; d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = i__ + (j << 2) - 5; d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; af[i__1].r = z__1.r, af[i__1].i = z__1.i; /* L10: */ } i__1 = j - 1; b[i__1].r = 0., b[i__1].i = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; i__1 = j - 1; w[i__1].r = 0., w[i__1].i = 0.; i__1 = j - 1; x[i__1].r = 0., x[i__1].i = 0.; /* L20: */ } anrm = 1.; infoc_1.ok = TRUE_; /* Test error exits of the routines that use the Cholesky */ /* decomposition of a Hermitian positive definite matrix. */ if (lsamen_(&c__2, c2, "PO")) { /* ZPOTRF */ s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrf_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrf_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotrf_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTF2 */ s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotf2_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotf2_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotf2_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRI */ s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotri_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotri_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotri_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRS */ s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPORFS */ s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 11; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOCON */ s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; d__1 = -anrm; zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOEQU */ s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky */ /* decomposition of a Hermitian positive definite packed matrix. */ } else if (lsamen_(&c__2, c2, "PP")) { /* ZPPTRF */ s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrf_("/", &c__0, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrf_("U", &c_n1, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRI */ s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptri_("/", &c__0, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptri_("U", &c_n1, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRS */ s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPRFS */ s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPCON */ s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; d__1 = -anrm; zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPEQU */ s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky */ /* decomposition of a Hermitian positive definite band matrix. */ } else if (lsamen_(&c__2, c2, "PB")) { /* ZPBTRF */ s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrf_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtrf_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTF2 */ s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtf2_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtf2_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTRS */ s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBRFS */ s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBCON */ s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; d__1 = -anrm; zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBEQU */ s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of ZERRPO */ } /* zerrpo_ */
/* Subroutine */ int zppsv_(char *uplo, integer *n, integer *nrhs, doublecomplex *ap, doublecomplex *b, integer *ldb, integer *info) { /* -- LAPACK driver routine (version 2.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= ZPPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as A = U**H* U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A. B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. Further Details =============== The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Two-dimensional storage of the Hermitian matrix A: a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = conjg(aji)) a44 Packed storage of the upper triangle of A: AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] ===================================================================== Test the input parameters. Parameter adjustments Function Body */ /* System generated locals */ integer b_dim1, b_offset, i__1; /* Local variables */ extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *), zpptrf_( char *, integer *, doublecomplex *, integer *), zpptrs_( char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); #define AP(I) ap[(I)-1] #define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)] *info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*ldb < max(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPPSV ", &i__1); return 0; } /* Compute the Cholesky factorization A = U'*U or A = L*L'. */ zpptrf_(uplo, n, &AP(1), info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ zpptrs_(uplo, n, nrhs, &AP(1), &B(1,1), ldb, info); } return 0; /* End of ZPPSV */ } /* zppsv_ */
int zppsv_(char *uplo, int *n, int *nrhs, doublecomplex *ap, doublecomplex *b, int *ldb, int *info) { /* System generated locals */ int b_dim1, b_offset, i__1; /* Local variables */ extern int lsame_(char *, char *); extern int xerbla_(char *, int *), zpptrf_( char *, int *, doublecomplex *, int *), zpptrs_( char *, int *, int *, doublecomplex *, doublecomplex *, int *, int *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZPPSV computes the solution to a complex system of linear equations */ /* A * X = B, */ /* where A is an N-by-N Hermitian positive definite matrix stored in */ /* packed format and X and B are N-by-NRHS matrices. */ /* The Cholesky decomposition is used to factor A as */ /* A = U**H* U, if UPLO = 'U', or */ /* A = L * L**H, if UPLO = 'L', */ /* where U is an upper triangular matrix and L is a lower triangular */ /* matrix. The factored form of A is then used to solve the system of */ /* equations A * X = B. */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrix B. NRHS >= 0. */ /* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */ /* On entry, the upper or lower triangle of the Hermitian matrix */ /* A, packed columnwise in a linear array. The j-th column of A */ /* is stored in the array AP as follows: */ /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ /* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */ /* See below for further details. */ /* On exit, if INFO = 0, the factor U or L from the Cholesky */ /* factorization A = U**H*U or A = L*L**H, in the same storage */ /* format as A. */ /* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */ /* On entry, the N-by-NRHS right hand side matrix B. */ /* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= MAX(1,N). */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, the leading minor of order i of A is not */ /* positive definite, so the factorization could not be */ /* completed, and the solution has not been computed. */ /* Further Details */ /* =============== */ /* The packed storage scheme is illustrated by the following example */ /* when N = 4, UPLO = 'U': */ /* Two-dimensional storage of the Hermitian matrix A: */ /* a11 a12 a13 a14 */ /* a22 a23 a24 */ /* a33 a34 (aij = conjg(aji)) */ /* a44 */ /* Packed storage of the upper triangle of A: */ /* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */ /* ===================================================================== */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ --ap; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; /* Function Body */ *info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*ldb < MAX(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPPSV ", &i__1); return 0; } /* Compute the Cholesky factorization A = U'*U or A = L*L'. */ zpptrf_(uplo, n, &ap[1], info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ zpptrs_(uplo, n, nrhs, &ap[1], &b[b_offset], ldb, info); } return 0; /* End of ZPPSV */ } /* zppsv_ */
/* Subroutine */ int zerrpo_(char *path, integer *nunit) { /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ static integer info; static doublereal anrm; static doublecomplex a[16] /* was [4][4] */, b[4]; static integer i__, j; static doublereal r__[4]; static doublecomplex w[8], x[4]; static doublereal rcond; static char c2[2]; static doublereal r1[4], r2[4]; static doublecomplex af[16] /* was [4][4] */; extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zpotf2_(char *, integer *, doublecomplex *, integer *, integer *), alaesm_(char *, logical *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), zpbcon_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbequ_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zpbrfs_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbtrf_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zppcon_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zpbtrs_( char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zporfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zppequ_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublereal *, integer *), zpprfs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpptrf_(char * , integer *, doublecomplex *, integer *), zpptri_(char *, integer *, doublecomplex *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zpptrs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; #define a_subscr(a_1,a_2) (a_2)*4 + a_1 - 5 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define af_subscr(a_1,a_2) (a_2)*4 + a_1 - 5 #define af_ref(a_1,a_2) af[af_subscr(a_1,a_2)] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= ZERRPO tests the error exits for the COMPLEX*16 routines for Hermitian positive definite matrices. Arguments ========= PATH (input) CHARACTER*3 The LAPACK path name for the routines to be tested. NUNIT (input) INTEGER The unit number for output. ===================================================================== */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { i__1 = a_subscr(i__, j); d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = af_subscr(i__, j); d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; af[i__1].r = z__1.r, af[i__1].i = z__1.i; /* L10: */ } i__1 = j - 1; b[i__1].r = 0., b[i__1].i = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; i__1 = j - 1; w[i__1].r = 0., w[i__1].i = 0.; i__1 = j - 1; x[i__1].r = 0., x[i__1].i = 0.; /* L20: */ } anrm = 1.; infoc_1.ok = TRUE_; /* Test error exits of the routines that use the Cholesky decomposition of a Hermitian positive definite matrix. */ if (lsamen_(&c__2, c2, "PO")) { /* ZPOTRF */ s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrf_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrf_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotrf_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTF2 */ s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotf2_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotf2_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotf2_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRI */ s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotri_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotri_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotri_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRS */ s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPORFS */ s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 11; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOCON */ s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; d__1 = -anrm; zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOEQU */ s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky decomposition of a Hermitian positive definite packed matrix. */ } else if (lsamen_(&c__2, c2, "PP")) { /* ZPPTRF */ s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrf_("/", &c__0, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrf_("U", &c_n1, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRI */ s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptri_("/", &c__0, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptri_("U", &c_n1, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRS */ s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPRFS */ s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPCON */ s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; d__1 = -anrm; zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPEQU */ s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky decomposition of a Hermitian positive definite band matrix. */ } else if (lsamen_(&c__2, c2, "PB")) { /* ZPBTRF */ s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrf_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtrf_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTF2 */ s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtf2_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtf2_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTRS */ s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBRFS */ s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBCON */ s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; d__1 = -anrm; zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBEQU */ s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of ZERRPO */ } /* zerrpo_ */
/* Subroutine */ int zchkpp_(logical *dotype, integer *nn, integer *nval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a, doublecomplex *afac, doublecomplex * ainv, doublecomplex *b, doublecomplex *x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; static char packs[1*2] = "C" "R"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "type \002,i2,\002, test \002,i2,\002, ratio =\002,g12.5)"; static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g" "12.5)"; /* System generated locals */ integer i__1, i__2, i__3, i__4; /* Local variables */ integer i__, k, n, in, kl, ku, lda, npp, ioff, mode, imat, info; char path[3], dist[1]; integer irhs, nrhs; char uplo[1], type__[1]; integer nrun; integer nfail, iseed[4]; doublereal rcond; integer nimat; doublereal anorm; integer iuplo, izero, nerrs; logical zerot; char xtype[1]; doublereal rcondc; char packit[1]; doublereal cndnum; doublereal result[8]; /* Fortran I/O blocks */ static cilist io___34 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___37 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___39 = { 0, 0, 0, fmt_9999, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZCHKPP tests ZPPTRF, -TRI, -TRS, -RFS, and -CON */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix dimension N. */ /* NNS (input) INTEGER */ /* The number of values of NRHS contained in the vector NSVAL. */ /* NSVAL (input) INTEGER array, dimension (NNS) */ /* The values of the number of right hand sides NRHS. */ /* THRESH (input) DOUBLE PRECISION */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) COMPLEX*16 array, dimension */ /* (NMAX*(NMAX+1)/2) */ /* AFAC (workspace) COMPLEX*16 array, dimension */ /* (NMAX*(NMAX+1)/2) */ /* AINV (workspace) COMPLEX*16 array, dimension */ /* (NMAX*(NMAX+1)/2) */ /* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* where NSMAX is the largest entry in NSVAL. */ /* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* WORK (workspace) COMPLEX*16 array, dimension */ /* (NMAX*max(3,NSMAX)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "PP", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Test the error exits */ if (*tsterr) { zerrpo_(path, nout); } infoc_1.infot = 0; /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; nimat = 9; if (n <= 0) { nimat = 1; } i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L100; } /* Skip types 3, 4, or 5 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 5; if (zerot && n < imat - 2) { goto L100; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; *(unsigned char *)packit = *(unsigned char *)&packs[iuplo - 1] ; /* Set up parameters with ZLATB4 and generate a test matrix */ /* with ZLATMS. */ zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)32, (ftnlen)6); zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, packit, &a[1], &lda, &work[ 1], &info); /* Check error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L90; } /* For types 3-5, zero one row and column of the matrix to */ /* test that INFO is returned correctly. */ if (zerot) { if (imat == 3) { izero = 1; } else if (imat == 4) { izero = n; } else { izero = n / 2 + 1; } /* Set row and column IZERO of A to 0. */ if (iuplo == 1) { ioff = (izero - 1) * izero / 2; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += i__; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff = ioff + n - i__; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L50: */ } } } else { izero = 0; } /* Set the imaginary part of the diagonals. */ if (iuplo == 1) { zlaipd_(&n, &a[1], &c__2, &c__1); } else { zlaipd_(&n, &a[1], &n, &c_n1); } /* Compute the L*L' or U'*U factorization of the matrix. */ npp = n * (n + 1) / 2; zcopy_(&npp, &a[1], &c__1, &afac[1], &c__1); s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)32, (ftnlen)6); zpptrf_(uplo, &n, &afac[1], &info); /* Check error code from ZPPTRF. */ if (info != izero) { alaerh_(path, "ZPPTRF", &info, &izero, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L90; } /* Skip the tests if INFO is not 0. */ if (info != 0) { goto L90; } /* + TEST 1 */ /* Reconstruct matrix from factors and compute residual. */ zcopy_(&npp, &afac[1], &c__1, &ainv[1], &c__1); zppt01_(uplo, &n, &a[1], &ainv[1], &rwork[1], result); /* + TEST 2 */ /* Form the inverse and compute the residual. */ zcopy_(&npp, &afac[1], &c__1, &ainv[1], &c__1); s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)32, (ftnlen)6); zpptri_(uplo, &n, &ainv[1], &info); /* Check error code from ZPPTRI. */ if (info != 0) { alaerh_(path, "ZPPTRI", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } zppt03_(uplo, &n, &a[1], &ainv[1], &work[1], &lda, &rwork[1], &rcondc, &result[1]); /* Print information about the tests that did not pass */ /* the threshold. */ for (k = 1; k <= 2; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___34.ciunit = *nout; s_wsfe(&io___34); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } /* L60: */ } nrun += 2; i__3 = *nns; for (irhs = 1; irhs <= i__3; ++irhs) { nrhs = nsval[irhs]; /* + TEST 3 */ /* Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)32, (ftnlen)6); zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &nrhs, & a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, & info); zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)32, (ftnlen)6); zpptrs_(uplo, &n, &nrhs, &afac[1], &x[1], &lda, &info); /* Check error code from ZPPTRS. */ if (info != 0) { alaerh_(path, "ZPPTRS", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda); zppt02_(uplo, &n, &nrhs, &a[1], &x[1], &lda, &work[1], & lda, &rwork[1], &result[2]); /* + TEST 4 */ /* Check solution from generated exact solution. */ zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, & result[3]); /* + TESTS 5, 6, and 7 */ /* Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)32, (ftnlen)6); zpprfs_(uplo, &n, &nrhs, &a[1], &afac[1], &b[1], &lda, &x[ 1], &lda, &rwork[1], &rwork[nrhs + 1], &work[1], & rwork[(nrhs << 1) + 1], &info); /* Check error code from ZPPRFS. */ if (info != 0) { alaerh_(path, "ZPPRFS", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs, nout); } zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, & result[4]); zppt05_(uplo, &n, &nrhs, &a[1], &b[1], &lda, &x[1], &lda, &xact[1], &lda, &rwork[1], &rwork[nrhs + 1], & result[5]); /* Print information about the tests that did not pass */ /* the threshold. */ for (k = 3; k <= 7; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___37.ciunit = *nout; s_wsfe(&io___37); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(doublereal)); e_wsfe(); ++nfail; } /* L70: */ } nrun += 5; /* L80: */ } /* + TEST 8 */ /* Get an estimate of RCOND = 1/CNDNUM. */ anorm = zlanhp_("1", uplo, &n, &a[1], &rwork[1]); s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)32, (ftnlen)6); zppcon_(uplo, &n, &afac[1], &anorm, &rcond, &work[1], &rwork[ 1], &info); /* Check error code from ZPPCON. */ if (info != 0) { alaerh_(path, "ZPPCON", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[7] = dget06_(&rcond, &rcondc); /* Print the test ratio if greater than or equal to THRESH. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___39.ciunit = *nout; s_wsfe(&io___39); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; L90: ; } L100: ; } /* L110: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKPP */ } /* zchkpp_ */